%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT061+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 06:24:25 AM UTC 2026 % Result : Theorem 31.13s 31.48s % Output : Proof 31.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT061+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.11/0.37 % Computer : n011.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Mon Sep 7 13:35:15 UTC 2026 % 0.11/0.38 % CPUTime : % 31.13/31.48 (* PROOF-FOUND *) % 31.13/31.48 % SZS status Theorem % 31.13/31.48 (* BEGIN-PROOF *) % 31.13/31.48 % SZS output start Proof % 31.13/31.48 Theorem theorem_7 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((fragile_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age X T1) (sigma))/\(greater (age X T2) (sigma))))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))). % 31.13/31.48 Proof. % 31.13/31.48 assert (zenon_L1_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (greater (sigma) (age zenon_TX_v zenon_TT1_u)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H12 zenon_H13. % 31.13/31.48 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16. % 31.13/31.48 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 31.13/31.48 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 31.13/31.48 generalize (definition_smaller (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H1d. % 31.13/31.48 generalize (zenon_H1d (sigma)). zenon_intro zenon_H1e. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H1c; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H12 ]. % 31.13/31.48 exact (zenon_H20 zenon_H12). % 31.13/31.48 exact (zenon_H1c zenon_H1f). % 31.13/31.48 exact (zenon_H13 zenon_H19). % 31.13/31.48 (* end of lemma zenon_L1_ *) % 31.13/31.48 assert (zenon_L2_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT1_u))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False). % 31.13/31.48 do 2 intro. intros zenon_H21 zenon_H22 zenon_H23. % 31.13/31.48 apply zenon_H21. zenon_intro zenon_H24. % 31.13/31.48 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25. % 31.13/31.48 generalize (zenon_H25 zenon_TT1_u). zenon_intro zenon_H26. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H29 zenon_H23). % 31.13/31.48 exact (zenon_H27 zenon_H24). % 31.13/31.48 (* end of lemma zenon_L2_ *) % 31.13/31.48 assert (zenon_L3_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(is_aligned zenon_TX_v zenon_TT1_u)) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> False). % 31.13/31.48 do 3 intro. intros zenon_H2b zenon_H2c zenon_H2d zenon_H2e zenon_H2f zenon_H22. % 31.13/31.48 generalize (zenon_H2b zenon_TT0_bw). zenon_intro zenon_H31. % 31.13/31.48 generalize (zenon_H31 zenon_TT1_u). zenon_intro zenon_H32. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H2e; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 31.13/31.48 generalize (definition_2 zenon_TX_v). zenon_intro zenon_H39. % 31.13/31.48 generalize (zenon_H39 zenon_TT0_bw). zenon_intro zenon_H3a. % 31.13/31.48 generalize (zenon_H3a zenon_TT1_u). zenon_intro zenon_H3b. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H38; zenon_intro zenon_H3d | zenon_intro zenon_H36; zenon_intro zenon_H3c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H2a | zenon_intro zenon_H3e ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply zenon_H3e. zenon_intro zenon_H3f. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H41; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H40 ]. % 31.13/31.48 exact (zenon_H41 zenon_H2c). % 31.13/31.48 exact (zenon_H2d zenon_H40). % 31.13/31.48 exact (zenon_H38 zenon_H36). % 31.13/31.48 exact (zenon_H2e zenon_H37). % 31.13/31.48 (* end of lemma zenon_L3_ *) % 31.13/31.48 assert (zenon_L4_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT2_cp))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False). % 31.13/31.48 do 2 intro. intros zenon_H42 zenon_H22 zenon_H23. % 31.13/31.48 apply zenon_H42. zenon_intro zenon_H44. % 31.13/31.48 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25. % 31.13/31.48 generalize (zenon_H25 zenon_TT2_cp). zenon_intro zenon_H45. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H28 | zenon_intro zenon_H46 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H29 zenon_H23). % 31.13/31.48 exact (zenon_H46 zenon_H44). % 31.13/31.48 (* end of lemma zenon_L4_ *) % 31.13/31.48 assert (zenon_L5_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), ((greater (age zenon_TX_v zenon_TT2_cp) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT2_cp))) -> (positional_advantage zenon_TX_v zenon_TT2_cp) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> False). % 31.13/31.48 do 2 intro. intros zenon_H47 zenon_H48 zenon_H49. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 31.13/31.48 exact (zenon_H4b zenon_H49). % 31.13/31.48 exact (zenon_H4a zenon_H48). % 31.13/31.48 (* end of lemma zenon_L5_ *) % 31.13/31.48 assert (zenon_L6_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (((smaller_or_equal (age zenon_TX_v zenon_TT2_cp) (sigma))->(positional_advantage zenon_TX_v zenon_TT2_cp))/\((greater (age zenon_TX_v zenon_TT2_cp) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT2_cp)))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (positional_advantage zenon_TX_v zenon_TT2_cp) -> False). % 31.13/31.48 do 2 intro. intros zenon_H4c zenon_H49 zenon_H48. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4d. zenon_intro zenon_H47. % 31.13/31.48 apply (zenon_L5_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L6_ *) % 31.13/31.48 assert (zenon_L7_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (((is_aligned zenon_TX_v zenon_TT2_cp)/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> (~(positional_advantage zenon_TX_v zenon_TT2_cp)) -> (((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H4e zenon_H4a zenon_H4f zenon_H50 zenon_H51. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H54 ]. % 31.13/31.48 exact (zenon_H58 zenon_H55). % 31.13/31.48 exact (zenon_H54 zenon_H4a). % 31.13/31.48 exact (zenon_H50 zenon_H56). % 31.13/31.48 exact (zenon_H54 zenon_H4a). % 31.13/31.48 exact (zenon_H51 zenon_H52). % 31.13/31.48 (* end of lemma zenon_L7_ *) % 31.13/31.48 assert (zenon_L8_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT2_cp)/\(positional_advantage zenon_TX_v zenon_TT2_cp))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(positional_advantage zenon_TX_v zenon_TT2_cp))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT2_cp)/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high)))))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H59 zenon_H51 zenon_H50 zenon_H49 zenon_H5a zenon_H5b. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H4e. zenon_intro zenon_H4f. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H58 | zenon_intro zenon_H4a ]. % 31.13/31.48 apply zenon_H58. zenon_intro zenon_H62. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 31.13/31.48 exact (zenon_H55 zenon_H62). % 31.13/31.48 apply zenon_H54. zenon_intro zenon_H48. % 31.13/31.48 generalize (zenon_H5a zenon_TT2_cp). zenon_intro zenon_H4c. % 31.13/31.48 apply (zenon_L6_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H51 zenon_H52). % 31.13/31.48 apply (zenon_L7_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 apply zenon_H5b. apply sym_equal. exact zenon_H60. % 31.13/31.48 (* end of lemma zenon_L8_ *) % 31.13/31.48 assert (zenon_L9_ : (~((mod2) = (mod2))) -> False). % 31.13/31.48 do 0 intro. intros zenon_H63. % 31.13/31.48 apply zenon_H63. apply refl_equal. % 31.13/31.48 (* end of lemma zenon_L9_ *) % 31.13/31.48 assert (zenon_L10_ : (~((low) = (low))) -> False). % 31.13/31.48 do 0 intro. intros zenon_H64. % 31.13/31.48 apply zenon_H64. apply refl_equal. % 31.13/31.48 (* end of lemma zenon_L10_ *) % 31.13/31.48 assert (zenon_L11_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H49 zenon_H5a zenon_H5b zenon_H66 zenon_H67. % 31.13/31.48 elim (classic ((~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (mod2))))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H51. zenon_intro zenon_H6a. % 31.13/31.48 elim (classic ((~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (high))))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H50. zenon_intro zenon_H6d. % 31.13/31.48 generalize (zenon_H65 zenon_TT2_cp). zenon_intro zenon_H6e. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H2a | zenon_intro zenon_H6f ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H71. zenon_intro zenon_H70. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H42 | zenon_intro zenon_H59 ]. % 31.13/31.48 apply (zenon_L4_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L8_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (mod2))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H6a. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact assumption_18d. % 31.13/31.48 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 31.13/31.48 cut (((high) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 31.13/31.48 congruence. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ]. % 31.13/31.48 apply zenon_H74. zenon_intro zenon_H56. % 31.13/31.48 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp)) = ((high) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H72. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H75. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 31.13/31.48 congruence. % 31.13/31.48 exact (zenon_H50 zenon_H56). % 31.13/31.48 apply zenon_H76. apply refl_equal. % 31.13/31.48 apply zenon_H76. apply refl_equal. % 31.13/31.48 apply zenon_H73. zenon_intro zenon_H77. % 31.13/31.48 generalize (zenon_H66 (hazard_of_mortality zenon_TX_v zenon_TT2_cp)). zenon_intro zenon_H78. % 31.13/31.48 generalize (zenon_H78 (high)). zenon_intro zenon_H79. % 31.13/31.48 generalize (zenon_H79 (mod2)). zenon_intro zenon_H7a. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H6d | zenon_intro zenon_H7b ]. % 31.13/31.48 exact (zenon_H6d zenon_H77). % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 31.13/31.48 exact (zenon_H7d assumption_18d). % 31.13/31.48 exact (zenon_H6a zenon_H7c). % 31.13/31.48 apply zenon_H63. apply refl_equal. % 31.13/31.48 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H67. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact assumption_18e. % 31.13/31.48 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 31.13/31.48 cut (((mod2) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 31.13/31.48 congruence. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ]. % 31.13/31.48 apply zenon_H80. zenon_intro zenon_H52. % 31.13/31.48 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp)) = ((mod2) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H7e. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H75. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 31.13/31.48 congruence. % 31.13/31.48 exact (zenon_H51 zenon_H52). % 31.13/31.48 apply zenon_H76. apply refl_equal. % 31.13/31.48 apply zenon_H76. apply refl_equal. % 31.13/31.48 apply zenon_H7f. zenon_intro zenon_H7c. % 31.13/31.48 generalize (zenon_H66 (hazard_of_mortality zenon_TX_v zenon_TT2_cp)). zenon_intro zenon_H78. % 31.13/31.48 generalize (zenon_H78 (mod2)). zenon_intro zenon_H81. % 31.13/31.48 generalize (zenon_H81 (low)). zenon_intro zenon_H82. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H6a | zenon_intro zenon_H83 ]. % 31.13/31.48 exact (zenon_H6a zenon_H7c). % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 31.13/31.48 exact (zenon_H85 assumption_18e). % 31.13/31.48 exact (zenon_H67 zenon_H84). % 31.13/31.48 apply zenon_H64. apply refl_equal. % 31.13/31.48 (* end of lemma zenon_L11_ *) % 31.13/31.48 assert (zenon_L12_ : forall (zenon_TT1_u : zenon_U) (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (~(has_endowment zenon_TX_v)) -> (organization zenon_TX_v) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False). % 31.13/31.48 do 3 intro. intros zenon_H5b zenon_H5a zenon_H49 zenon_H23 zenon_H22 zenon_H65 zenon_H86 zenon_H66 zenon_H87. % 31.13/31.48 elim (classic ((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 31.13/31.48 elim (classic (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low))); [ zenon_intro zenon_H84 | zenon_intro zenon_H67 ]. % 31.13/31.48 cut ((greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H86. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H84. % 31.13/31.48 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 31.13/31.48 congruence. % 31.13/31.48 apply zenon_H76. apply refl_equal. % 31.13/31.48 exact (zenon_H89 zenon_H88). % 31.13/31.48 apply (zenon_L11_ zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u)) = ((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H89. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H8a. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 31.13/31.48 congruence. % 31.13/31.48 exact (zenon_H8c zenon_H87). % 31.13/31.48 apply zenon_H8b. apply refl_equal. % 31.13/31.48 apply zenon_H8b. apply refl_equal. % 31.13/31.48 (* end of lemma zenon_L12_ *) % 31.13/31.48 assert (zenon_L13_ : forall (zenon_TT2_cp : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (~(has_endowment zenon_TX_v)) -> (organization zenon_TX_v) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 31.13/31.48 do 4 intro. intros zenon_H8d zenon_H8e zenon_H2b zenon_H2c zenon_H2e zenon_H2f zenon_H5b zenon_H5a zenon_H49 zenon_H23 zenon_H22 zenon_H65 zenon_H86 zenon_H66. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ]. % 31.13/31.48 apply (zenon_L3_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H92 zenon_H8e). % 31.13/31.48 apply (zenon_L12_ zenon_TT1_u zenon_TT2_cp zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L13_ *) % 31.13/31.48 assert (zenon_L14_ : forall (zenon_TT2_cp : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> False). % 31.13/31.48 do 4 intro. intros zenon_H66 zenon_H22 zenon_H23 zenon_H2b zenon_H2c zenon_H2e zenon_H2f zenon_H8e zenon_H86 zenon_H5b zenon_H5a zenon_H49 zenon_H65. % 31.13/31.48 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ]. % 31.13/31.48 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L13_ zenon_TT2_cp zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L14_ *) % 31.13/31.48 assert (zenon_L15_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (is_aligned zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H8d zenon_H8e zenon_H40 zenon_H89. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ]. % 31.13/31.48 exact (zenon_H2d zenon_H40). % 31.13/31.48 exact (zenon_H92 zenon_H8e). % 31.13/31.48 apply zenon_H89. apply sym_equal. exact zenon_H87. % 31.13/31.48 (* end of lemma zenon_L15_ *) % 31.13/31.48 assert (zenon_L16_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT1_u) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H40 zenon_H8e zenon_H89. % 31.13/31.48 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ]. % 31.13/31.48 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L15_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L16_ *) % 31.13/31.48 assert (zenon_L17_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(has_endowment zenon_TX_v)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> False). % 31.13/31.48 do 3 intro. intros zenon_H2b zenon_H2c zenon_H65 zenon_H23 zenon_H8e zenon_H89 zenon_H2e zenon_H2f zenon_H22. % 31.13/31.48 generalize (zenon_H2b zenon_TT0_bw). zenon_intro zenon_H31. % 31.13/31.48 generalize (zenon_H31 zenon_TT1_u). zenon_intro zenon_H32. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H2e; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 31.13/31.48 generalize (definition_2 zenon_TX_v). zenon_intro zenon_H39. % 31.13/31.48 generalize (zenon_H39 zenon_TT0_bw). zenon_intro zenon_H3a. % 31.13/31.48 generalize (zenon_H3a zenon_TT1_u). zenon_intro zenon_H3b. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H38; zenon_intro zenon_H3d | zenon_intro zenon_H36; zenon_intro zenon_H3c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H2a | zenon_intro zenon_H3e ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply zenon_H3e. zenon_intro zenon_H3f. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H41; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H40 ]. % 31.13/31.48 exact (zenon_H41 zenon_H2c). % 31.13/31.48 apply (zenon_L16_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H38 zenon_H36). % 31.13/31.48 exact (zenon_H2e zenon_H37). % 31.13/31.48 (* end of lemma zenon_L17_ *) % 31.13/31.48 assert (zenon_L18_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (~(has_endowment zenon_TX_v)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> False). % 31.13/31.48 do 3 intro. intros zenon_H23 zenon_H8e zenon_H89 zenon_H2e zenon_H2f zenon_H22 zenon_H97. % 31.13/31.48 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b. % 31.13/31.48 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65. % 31.13/31.48 apply (zenon_L17_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L18_ *) % 31.13/31.48 assert (zenon_L19_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((greater (age zenon_TX_v zenon_TT1_u) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT1_u))) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> (organization zenon_TX_v) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(has_endowment zenon_TX_v)) -> False). % 31.13/31.48 do 3 intro. intros zenon_H99 zenon_H97 zenon_H22 zenon_H2f zenon_H89 zenon_H8e zenon_H23. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ]. % 31.13/31.48 apply (zenon_L18_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H92 zenon_H8e). % 31.13/31.48 (* end of lemma zenon_L19_ *) % 31.13/31.48 assert (zenon_L20_ : (~((sigma) = (sigma))) -> False). % 31.13/31.48 do 0 intro. intros zenon_H9a. % 31.13/31.48 apply zenon_H9a. apply refl_equal. % 31.13/31.48 (* end of lemma zenon_L20_ *) % 31.13/31.48 assert (zenon_L21_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (~(greater (sigma) (age zenon_TX_v zenon_TT0_bw))) -> (greater (sigma) (zero)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> False). % 31.13/31.48 do 2 intro. intros zenon_H9b zenon_H9c zenon_H2f. % 31.13/31.48 elim (classic ((zero) = (age zenon_TX_v zenon_TT0_bw))); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ]. % 31.13/31.48 cut ((greater (sigma) (zero)) = (greater (sigma) (age zenon_TX_v zenon_TT0_bw))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H9b. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H9c. % 31.13/31.48 cut (((zero) = (age zenon_TX_v zenon_TT0_bw))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 31.13/31.48 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 31.13/31.48 congruence. % 31.13/31.48 apply zenon_H9a. apply refl_equal. % 31.13/31.48 exact (zenon_H9e zenon_H9d). % 31.13/31.48 apply zenon_H9e. apply sym_equal. exact zenon_H2f. % 31.13/31.48 (* end of lemma zenon_L21_ *) % 31.13/31.48 assert (zenon_L22_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (greater (sigma) (zero)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT0_bw) (sigma))) -> False). % 31.13/31.48 do 2 intro. intros zenon_H2f zenon_H9c zenon_H9f. % 31.13/31.48 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT0_bw)). zenon_intro zenon_Ha0. % 31.13/31.48 generalize (zenon_Ha0 (sigma)). zenon_intro zenon_Ha1. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_Ha1); [ zenon_intro zenon_H9f; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3; zenon_intro zenon_Ha2 ]. % 31.13/31.48 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 31.13/31.48 generalize (definition_smaller (age zenon_TX_v zenon_TT0_bw)). zenon_intro zenon_Ha7. % 31.13/31.48 generalize (zenon_Ha7 (sigma)). zenon_intro zenon_Ha8. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_Ha8); [ zenon_intro zenon_Ha6; zenon_intro zenon_H9b | zenon_intro zenon_Haa; zenon_intro zenon_Ha9 ]. % 31.13/31.48 apply (zenon_L21_ zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_Ha6 zenon_Haa). % 31.13/31.48 exact (zenon_H9f zenon_Ha3). % 31.13/31.48 (* end of lemma zenon_L22_ *) % 31.13/31.48 assert (zenon_L23_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT0_bw))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False). % 31.13/31.48 do 2 intro. intros zenon_Hab zenon_H22 zenon_H23. % 31.13/31.48 apply zenon_Hab. zenon_intro zenon_Hac. % 31.13/31.48 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25. % 31.13/31.48 generalize (zenon_H25 zenon_TT0_bw). zenon_intro zenon_Had. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_H28 | zenon_intro zenon_Hae ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H29 zenon_H23). % 31.13/31.48 exact (zenon_Hae zenon_Hac). % 31.13/31.48 (* end of lemma zenon_L23_ *) % 31.13/31.48 assert (zenon_L24_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT0_bw)/\(positional_advantage zenon_TX_v zenon_TT0_bw))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT0_bw))/\(positional_advantage zenon_TX_v zenon_TT0_bw))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT0_bw)/\(~(positional_advantage zenon_TX_v zenon_TT0_bw)))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT0_bw))/\(~(positional_advantage zenon_TX_v zenon_TT0_bw)))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False). % 31.13/31.48 do 3 intro. intros zenon_Haf zenon_Hb0 zenon_H2c zenon_Hb1 zenon_H87. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Haf). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hb4 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H41 | zenon_intro zenon_Hb6 ]. % 31.13/31.48 exact (zenon_H41 zenon_H2c). % 31.13/31.48 exact (zenon_Hb6 zenon_Hb0). % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) = ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_Hb1. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact zenon_H87. % 31.13/31.48 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 31.13/31.48 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 31.13/31.48 congruence. % 31.13/31.48 apply zenon_H8b. apply refl_equal. % 31.13/31.48 apply zenon_Hb7. apply sym_equal. exact zenon_Hb4. % 31.13/31.48 (* end of lemma zenon_L24_ *) % 31.13/31.48 assert (zenon_L25_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False). % 31.13/31.48 do 3 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H2c zenon_Hb0 zenon_Hb1 zenon_H87. % 31.13/31.48 generalize (zenon_H65 zenon_TT0_bw). zenon_intro zenon_Hb8. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb9 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_Hbb. zenon_intro zenon_Hba. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hab | zenon_intro zenon_Haf ]. % 31.13/31.48 apply (zenon_L23_ zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L24_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L25_ *) % 31.13/31.48 assert (zenon_L26_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> False). % 31.13/31.48 do 3 intro. intros zenon_H8d zenon_H8e zenon_H2b zenon_H2e zenon_H2f zenon_H65 zenon_H22 zenon_H23 zenon_H2c zenon_Hb0 zenon_Hb1. % 31.13/31.48 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ]. % 31.13/31.48 apply (zenon_L3_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H92 zenon_H8e). % 31.13/31.48 apply (zenon_L25_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L26_ *) % 31.13/31.48 assert (zenon_L27_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> False). % 31.13/31.48 do 3 intro. intros zenon_H22 zenon_H23 zenon_H2c zenon_H2e zenon_H2f zenon_H8e zenon_Hb0 zenon_Hb1. % 31.13/31.48 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b. % 31.13/31.48 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65. % 31.13/31.48 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ]. % 31.13/31.48 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L26_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L27_ *) % 31.13/31.48 assert (zenon_L28_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))) -> False). % 31.13/31.48 do 2 intro. intros zenon_Hbc zenon_H13. % 31.13/31.48 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16. % 31.13/31.48 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 31.13/31.48 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 31.13/31.48 exact (zenon_H1b zenon_Hbc). % 31.13/31.48 exact (zenon_H13 zenon_H19). % 31.13/31.48 (* end of lemma zenon_L28_ *) % 31.13/31.48 assert (zenon_L29_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> (organization zenon_TX_v) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(has_endowment zenon_TX_v)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> False). % 31.13/31.48 do 3 intro. intros zenon_Hbc zenon_H22 zenon_H2f zenon_H89 zenon_H23 zenon_H5a. % 31.13/31.48 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97. % 31.13/31.48 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.48 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L19_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L29_ *) % 31.13/31.48 assert (zenon_L30_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT2_cp : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> (~(has_endowment zenon_TX_v)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> False). % 31.13/31.48 do 4 intro. intros zenon_H66 zenon_Hbc zenon_H49 zenon_H5a zenon_H86 zenon_H8e zenon_H2e zenon_H23 zenon_H2f zenon_H22 zenon_H97. % 31.13/31.48 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65. % 31.13/31.48 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b. % 31.13/31.48 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H86. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact assumption_18b. % 31.13/31.48 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 31.13/31.48 cut (((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 31.13/31.48 congruence. % 31.13/31.48 apply (zenon_L14_ zenon_TT2_cp zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L29_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L30_ *) % 31.13/31.48 assert (zenon_L31_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))->(positional_advantage zenon_TX_v zenon_TT1_u)) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> (~(has_endowment zenon_TX_v)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> False). % 31.13/31.48 do 3 intro. intros zenon_Hbe zenon_Hb1 zenon_Hb0 zenon_H2e zenon_H23 zenon_H2f zenon_H22 zenon_H97 zenon_Hbc. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.48 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 apply (zenon_L27_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 (* end of lemma zenon_L31_ *) % 31.13/31.48 apply NNPP. intro zenon_G. % 31.13/31.48 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_H66 | zenon_intro zenon_Hbf ]. % 31.13/31.48 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((fragile_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age X T1) (sigma))/\(greater (age X T2) (sigma))))))))->((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_Hc0; idtac ]. % 31.13/31.48 elim zenon_Hc0. zenon_intro zenon_TX_v. zenon_intro zenon_Hc1. % 31.13/31.48 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v T1) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v T1))/\((hazard_of_mortality zenon_TX_v T1) = (hazard_of_mortality zenon_TX_v T0))))))) zenon_Hc1); [ zenon_intro zenon_Hc2; idtac ]. % 31.13/31.48 elim zenon_Hc2. zenon_intro zenon_TT0_bw. zenon_intro zenon_Hc3. % 31.13/31.48 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v zenon_TT0_bw) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v T1) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v T1))/\((hazard_of_mortality zenon_TX_v T1) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw)))))) zenon_Hc3); [ zenon_intro zenon_Hc4; idtac ]. % 31.13/31.48 elim zenon_Hc4. zenon_intro zenon_TT1_u. zenon_intro zenon_Hc5. % 31.13/31.48 apply (zenon_notallex_s (fun T2 : zenon_U => (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v zenon_TT0_bw) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v zenon_TT1_u))/\((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))))) zenon_Hc5); [ zenon_intro zenon_Hc6; idtac ]. % 31.13/31.48 elim zenon_Hc6. zenon_intro zenon_TT2_cp. zenon_intro zenon_Hc7. % 31.13/31.48 apply (zenon_notimply_s _ _ zenon_Hc7). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H22. zenon_intro zenon_Hca. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcc. zenon_intro zenon_Hcb. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H23. zenon_intro zenon_Hcd. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H2f. zenon_intro zenon_Hce. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H9c. zenon_intro zenon_Hcf. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H19. zenon_intro zenon_H49. % 31.13/31.48 generalize (definition_3 zenon_TX_v). zenon_intro zenon_Hd0. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd2; zenon_intro zenon_Hd1 | zenon_intro zenon_Hcc; zenon_intro zenon_H5a ]. % 31.13/31.48 exact (zenon_Hd2 zenon_Hcc). % 31.13/31.48 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16. % 31.13/31.48 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 31.13/31.48 exact (zenon_H13 zenon_H19). % 31.13/31.48 apply (zenon_or_s _ _ zenon_H18); [ zenon_intro zenon_H1f | zenon_intro zenon_Hbc ]. % 31.13/31.48 generalize (definition_smaller (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H1d. % 31.13/31.48 generalize (zenon_H1d (sigma)). zenon_intro zenon_H1e. % 31.13/31.48 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H1c; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H12 ]. % 31.13/31.48 exact (zenon_H1c zenon_H1f). % 31.13/31.48 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H86 | zenon_intro zenon_Hb1 ]. % 31.13/31.48 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97. % 31.13/31.48 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.48 apply (zenon_L1_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ]. % 31.13/31.48 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b. % 31.13/31.48 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65. % 31.13/31.48 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))). % 31.13/31.48 intro zenon_D_pnotp. % 31.13/31.48 apply zenon_H86. % 31.13/31.48 rewrite <- zenon_D_pnotp. % 31.13/31.48 exact assumption_18b. % 31.13/31.48 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 31.13/31.48 cut (((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 31.13/31.48 congruence. % 31.13/31.48 apply (zenon_L14_ zenon_TT2_cp zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 apply (zenon_L19_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.48 exact (zenon_H92 zenon_H8e). % 31.13/31.48 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97. % 31.13/31.48 generalize (zenon_H5a zenon_TT0_bw). zenon_intro zenon_Hd3. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hd5); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb0 ]. % 31.13/31.48 apply (zenon_L22_ zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.48 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ]. % 31.13/31.48 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ]. % 31.13/31.48 exact (zenon_H2a zenon_H22). % 31.13/31.48 exact (zenon_H35 zenon_H2f). % 31.13/31.48 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd. % 31.13/31.48 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99. % 31.13/31.48 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.48 apply (zenon_L1_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ]. % 31.13/31.49 apply (zenon_L27_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.49 exact (zenon_H92 zenon_H8e). % 31.13/31.49 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H86 | zenon_intro zenon_Hb1 ]. % 31.13/31.49 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97. % 31.13/31.49 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd. % 31.13/31.49 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.49 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ]. % 31.13/31.49 apply (zenon_L30_ zenon_TT0_bw zenon_TT2_cp zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.49 exact (zenon_H92 zenon_H8e). % 31.13/31.49 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97. % 31.13/31.49 generalize (zenon_H5a zenon_TT0_bw). zenon_intro zenon_Hd3. % 31.13/31.49 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_Hd5); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb0 ]. % 31.13/31.49 apply (zenon_L22_ zenon_TT0_bw zenon_TX_v); trivial. % 31.13/31.49 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd. % 31.13/31.49 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ]. % 31.13/31.49 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ]. % 31.13/31.49 apply (zenon_L31_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial. % 31.13/31.49 exact (zenon_H92 zenon_H8e). % 31.13/31.49 apply zenon_Hbf. zenon_intro zenon_Tx_ig. apply NNPP. zenon_intro zenon_Hd7. % 31.13/31.49 apply zenon_Hd7. zenon_intro zenon_Ty_ii. apply NNPP. zenon_intro zenon_Hd9. % 31.13/31.49 apply zenon_Hd9. zenon_intro zenon_Tz_ik. apply NNPP. zenon_intro zenon_Hdb. % 31.13/31.49 apply (zenon_notimply_s _ _ zenon_Hdb). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 31.13/31.49 apply (zenon_notimply_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde. % 31.13/31.49 generalize (meaning_postulate_greater_transitive zenon_Tx_ig). zenon_intro zenon_He0. % 31.13/31.49 generalize (zenon_He0 zenon_Ty_ii). zenon_intro zenon_He1. % 31.13/31.49 generalize (zenon_He1 zenon_Tz_ik). zenon_intro zenon_He2. % 31.13/31.49 apply (zenon_imply_s _ _ zenon_He2); [ zenon_intro zenon_He4 | zenon_intro zenon_He3 ]. % 31.13/31.49 apply (zenon_notand_s _ _ zenon_He4); [ zenon_intro zenon_He6 | zenon_intro zenon_He5 ]. % 31.13/31.49 exact (zenon_He6 zenon_Hdd). % 31.13/31.49 exact (zenon_He5 zenon_Hdf). % 31.13/31.49 exact (zenon_Hde zenon_He3). % 31.13/31.49 Qed. % 31.13/31.49 % SZS output end Proof % 31.13/31.49 (* END-PROOF *) % 31.13/31.49 nodes searched: 714138 % 31.13/31.49 max branch formulas: 1260 % 31.13/31.49 proof nodes created: 12573 % 31.13/31.49 formulas created: 337529 % 31.13/31.49 %------------------------------------------------------------------------------