%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT047+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n002.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 06:24:23 AM UTC 2026 % Result : Theorem 65.33s 65.64s % Output : Proof 65.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT047+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n002.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 13:14:07 UTC 2026 % 0.09/0.35 % CPUTime : % 65.33/65.64 (* PROOF-FOUND *) % 65.33/65.64 % SZS status Theorem % 65.33/65.64 (* BEGIN-PROOF *) % 65.33/65.64 % SZS output start Proof % 65.33/65.64 Theorem theorem_2 : (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)/\((smaller_or_equal (age X T0) (age X T1))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\(greater (age X T3) (age X T2)))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T3))/\((greater (hazard_of_mortality X T3) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))). % 65.33/65.64 Proof. % 65.33/65.64 assert (zenon_L1_ : (~((eta) = (eta))) -> False). % 65.33/65.64 do 0 intro. intros zenon_H11. % 65.33/65.64 apply zenon_H11. apply refl_equal. % 65.33/65.64 (* end of lemma zenon_L1_ *) % 65.33/65.64 assert (zenon_L2_ : forall (zenon_TT0_w : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TX_y : 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_y zenon_TT1_x) (age zenon_TX_y zenon_TT0_w)) -> (greater (eta) (age zenon_TX_y zenon_TT1_x)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT0_w) (eta))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H12 zenon_H13 zenon_H14 zenon_H15. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19. % 65.33/65.64 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20. % 65.33/65.64 generalize (zenon_H20 (eta)). zenon_intro zenon_H21. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ]. % 65.33/65.64 generalize (zenon_H12 (eta)). zenon_intro zenon_H25. % 65.33/65.64 generalize (zenon_H25 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H26. % 65.33/65.64 generalize (zenon_H26 (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H27. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 65.33/65.64 exact (zenon_H29 zenon_H14). % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H22 ]. % 65.33/65.64 exact (zenon_H2a zenon_H13). % 65.33/65.64 exact (zenon_H24 zenon_H22). % 65.33/65.64 exact (zenon_H1f zenon_H23). % 65.33/65.64 exact (zenon_H15 zenon_H1c). % 65.33/65.64 (* end of lemma zenon_L2_ *) % 65.33/65.64 assert (zenon_L3_ : forall (zenon_TT1_x : zenon_U) (zenon_TX_y : zenon_U), (greater (eta) (age zenon_TX_y zenon_TT1_x)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT1_x) (eta))) -> False). % 65.33/65.64 do 2 intro. intros zenon_H14 zenon_H2b. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c. % 65.33/65.64 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H33. % 65.33/65.64 generalize (zenon_H33 (eta)). zenon_intro zenon_H34. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H32; zenon_intro zenon_H29 | zenon_intro zenon_H35; zenon_intro zenon_H14 ]. % 65.33/65.64 exact (zenon_H29 zenon_H14). % 65.33/65.64 exact (zenon_H32 zenon_H35). % 65.33/65.64 exact (zenon_H2b zenon_H2f). % 65.33/65.64 (* end of lemma zenon_L3_ *) % 65.33/65.64 assert (zenon_L4_ : forall (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (~(smaller_or_equal (stock_of_knowledge zenon_TX_y zenon_TT2_cd) (stock_of_knowledge zenon_TX_y zenon_TT2_cd))) -> False). % 65.33/65.64 do 2 intro. intros zenon_H36. % 65.33/65.64 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H38. % 65.33/65.64 generalize (zenon_H38 (stock_of_knowledge zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H39. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H36; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H3a ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 65.33/65.64 apply zenon_H3d. apply refl_equal. % 65.33/65.64 exact (zenon_H36 zenon_H3b). % 65.33/65.64 (* end of lemma zenon_L4_ *) % 65.33/65.64 assert (zenon_L5_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (forall Y : zenon_U, ((smaller (internal_friction zenon_TX_y zenon_TT3_cp) Y)\/(((internal_friction zenon_TX_y zenon_TT3_cp) = Y)\/(greater (internal_friction zenon_TX_y zenon_TT3_cp) Y)))) -> (~(greater (internal_friction zenon_TX_y zenon_TT2_cd) (internal_friction zenon_TX_y zenon_TT3_cp))) -> (~((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT2_cd))) -> (~(greater (internal_friction zenon_TX_y zenon_TT3_cp) (internal_friction zenon_TX_y zenon_TT2_cd))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H3f zenon_H40 zenon_H41 zenon_H42. % 65.33/65.64 generalize (zenon_H3f (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H44. % 65.33/65.64 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 65.33/65.64 generalize (definition_smaller (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H47. % 65.33/65.64 generalize (zenon_H47 (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H48. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H4a; zenon_intro zenon_H40 | zenon_intro zenon_H46; zenon_intro zenon_H49 ]. % 65.33/65.64 exact (zenon_H4a zenon_H46). % 65.33/65.64 exact (zenon_H40 zenon_H49). % 65.33/65.64 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 65.33/65.64 exact (zenon_H41 zenon_H4c). % 65.33/65.64 exact (zenon_H42 zenon_H4b). % 65.33/65.64 (* end of lemma zenon_L5_ *) % 65.33/65.64 assert (zenon_L6_ : forall (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->((internal_friction zenon_TX_y T) = (internal_friction zenon_TX_y zenon_E)))) -> (organization zenon_TX_y) -> (~((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_E))) -> False). % 65.33/65.64 do 2 intro. intros zenon_H4d zenon_H4e zenon_H4f. % 65.33/65.64 generalize (zenon_H4d zenon_TT2_cd). zenon_intro zenon_H50. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 exact (zenon_H4f zenon_H51). % 65.33/65.64 (* end of lemma zenon_L6_ *) % 65.33/65.64 assert (zenon_L7_ : forall (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (greater (capability zenon_TX_y zenon_TT2_cd) (capability zenon_TX_y zenon_TT2_cd)) -> False). % 65.33/65.64 do 2 intro. intros zenon_H53. % 65.33/65.64 generalize (meaning_postulate_greater_strict (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H54. % 65.33/65.64 generalize (zenon_H54 (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H55. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 65.33/65.64 exact (zenon_H56 zenon_H53). % 65.33/65.64 exact (zenon_H56 zenon_H53). % 65.33/65.64 (* end of lemma zenon_L7_ *) % 65.33/65.64 assert (zenon_L8_ : forall (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (smaller (capability zenon_TX_y zenon_TT2_cd) (capability zenon_TX_y zenon_TT2_cd)) -> False). % 65.33/65.64 do 2 intro. intros zenon_H57. % 65.33/65.64 generalize (definition_smaller (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H58. % 65.33/65.64 generalize (zenon_H58 (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H59. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5a; zenon_intro zenon_H56 | zenon_intro zenon_H57; zenon_intro zenon_H53 ]. % 65.33/65.64 exact (zenon_H5a zenon_H57). % 65.33/65.64 apply (zenon_L7_ zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L8_ *) % 65.33/65.64 assert (zenon_L9_ : forall (zenon_TT3_cp : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->((((greater (stock_of_knowledge zenon_TX_y T) (stock_of_knowledge zenon_TX_y zenon_TT2_cd))/\(smaller_or_equal (internal_friction zenon_TX_y T) (internal_friction zenon_TX_y zenon_TT2_cd)))->(greater (capability zenon_TX_y T) (capability zenon_TX_y zenon_TT2_cd)))/\((((smaller_or_equal (stock_of_knowledge zenon_TX_y T) (stock_of_knowledge zenon_TX_y zenon_TT2_cd))/\(greater (internal_friction zenon_TX_y T) (internal_friction zenon_TX_y zenon_TT2_cd)))->(smaller (capability zenon_TX_y T) (capability zenon_TX_y zenon_TT2_cd)))/\((((stock_of_knowledge zenon_TX_y T) = (stock_of_knowledge zenon_TX_y zenon_TT2_cd))/\((internal_friction zenon_TX_y T) = (internal_friction zenon_TX_y zenon_TT2_cd)))->((capability zenon_TX_y T) = (capability zenon_TX_y zenon_TT2_cd))))))) -> (organization zenon_TX_y) -> ((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E)) -> (~((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT2_cd))) -> (~(greater (internal_friction zenon_TX_y zenon_TT2_cd) (internal_friction zenon_TX_y zenon_TT3_cp))) -> (forall Y : zenon_U, ((smaller (internal_friction zenon_TX_y zenon_TT3_cp) Y)\/(((internal_friction zenon_TX_y zenon_TT3_cp) = Y)\/(greater (internal_friction zenon_TX_y zenon_TT3_cp) Y)))) -> (forall T : zenon_U, ((organization zenon_TX_y)->((internal_friction zenon_TX_y T) = (internal_friction zenon_TX_y zenon_E)))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H5b zenon_H4e zenon_H5c zenon_H41 zenon_H40 zenon_H3f zenon_H4d. % 65.33/65.64 generalize (zenon_H5b zenon_TT2_cd). zenon_intro zenon_H5d. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H52 | zenon_intro zenon_H5e ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H62. zenon_intro zenon_H61. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H63 | zenon_intro zenon_H57 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H36 | zenon_intro zenon_H64 ]. % 65.33/65.64 apply (zenon_L4_ zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 elim (classic ((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT3_cp))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 65.33/65.64 elim (classic (greater (internal_friction zenon_TX_y zenon_TT3_cp) (internal_friction zenon_TX_y zenon_TT2_cd))); [ zenon_intro zenon_H4b | zenon_intro zenon_H42 ]. % 65.33/65.64 elim (classic (greater (internal_friction zenon_TX_y zenon_E) (internal_friction zenon_TX_y zenon_TT2_cd))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 65.33/65.64 cut ((greater (internal_friction zenon_TX_y zenon_E) (internal_friction zenon_TX_y zenon_TT2_cd)) = (greater (internal_friction zenon_TX_y zenon_TT2_cd) (internal_friction zenon_TX_y zenon_TT2_cd))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H64. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H67. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 65.33/65.64 congruence. % 65.33/65.64 elim (classic ((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [ zenon_intro zenon_H6b | zenon_intro zenon_H69 ]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd)) = ((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT2_cd))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H6a. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H6b. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 65.33/65.64 congruence. % 65.33/65.64 apply (zenon_L6_ zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 apply zenon_H69. apply refl_equal. % 65.33/65.64 apply zenon_H69. apply refl_equal. % 65.33/65.64 apply zenon_H69. apply refl_equal. % 65.33/65.64 cut ((greater (internal_friction zenon_TX_y zenon_TT3_cp) (internal_friction zenon_TX_y zenon_TT2_cd)) = (greater (internal_friction zenon_TX_y zenon_E) (internal_friction zenon_TX_y zenon_TT2_cd))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H68. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H4b. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 65.33/65.64 congruence. % 65.33/65.64 elim (classic ((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_E))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_E)) = ((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H6c. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H6d. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 65.33/65.64 congruence. % 65.33/65.64 exact (zenon_H66 zenon_H65). % 65.33/65.64 apply zenon_H6e. apply refl_equal. % 65.33/65.64 apply zenon_H6e. apply refl_equal. % 65.33/65.64 apply zenon_H69. apply refl_equal. % 65.33/65.64 apply (zenon_L5_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 elim (classic ((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT3_cp))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT3_cp)) = ((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT3_cp))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H66. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H6f. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 65.33/65.64 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 65.33/65.64 congruence. % 65.33/65.64 exact (zenon_H6c zenon_H5c). % 65.33/65.64 apply zenon_H70. apply refl_equal. % 65.33/65.64 apply zenon_H70. apply refl_equal. % 65.33/65.64 apply (zenon_L8_ zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L9_ *) % 65.33/65.64 assert (zenon_L10_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_y)->(((greater (external_ties zenon_TX_y T) (external_ties zenon_TX_y T0))->(greater (position zenon_TX_y T) (position zenon_TX_y T0)))/\(((external_ties zenon_TX_y T) = (external_ties zenon_TX_y T0))->((position zenon_TX_y T) = (position zenon_TX_y T0))))))) -> (~(greater (position zenon_TX_y zenon_TT3_cp) (position zenon_TX_y zenon_TT2_cd))) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (organization zenon_TX_y) -> False). % 65.33/65.64 do 3 intro. intros zenon_H71 zenon_H72 zenon_H73 zenon_H4e. % 65.33/65.64 generalize (zenon_H71 zenon_TT2_cd). zenon_intro zenon_H74. % 65.33/65.64 generalize (zenon_H74 zenon_TT3_cp). zenon_intro zenon_H75. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H52 | zenon_intro zenon_H76 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 65.33/65.64 generalize (assumption_8 zenon_TX_y). zenon_intro zenon_H7b. % 65.33/65.64 generalize (zenon_H7b zenon_TT2_cd). zenon_intro zenon_H7c. % 65.33/65.64 generalize (zenon_H7c zenon_TT3_cp). zenon_intro zenon_H7d. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H52 | zenon_intro zenon_H80 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 exact (zenon_H80 zenon_H73). % 65.33/65.64 exact (zenon_H7a zenon_H7e). % 65.33/65.64 exact (zenon_H72 zenon_H79). % 65.33/65.64 (* end of lemma zenon_L10_ *) % 65.33/65.64 assert (zenon_L11_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (~(greater (position zenon_TX_y zenon_TT3_cp) (position zenon_TX_y zenon_TT2_cd))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H4e zenon_H73 zenon_H72. % 65.33/65.64 generalize (assumption_6 zenon_TX_y). zenon_intro zenon_H71. % 65.33/65.64 apply (zenon_L10_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L11_ *) % 65.33/65.64 assert (zenon_L12_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (~(greater_or_equal (position zenon_TX_y zenon_TT3_cp) (position zenon_TX_y zenon_TT2_cd))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H4e zenon_H73 zenon_H81. % 65.33/65.64 generalize (definition_greater_or_equal (position zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H82. % 65.33/65.64 generalize (zenon_H82 (position zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H83. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H81; zenon_intro zenon_H86 | zenon_intro zenon_H85; zenon_intro zenon_H84 ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H72. zenon_intro zenon_H87. % 65.33/65.64 apply (zenon_L11_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 exact (zenon_H81 zenon_H85). % 65.33/65.64 (* end of lemma zenon_L12_ *) % 65.33/65.64 assert (zenon_L13_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (smaller (hazard_of_mortality zenon_TX_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT2_cd)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H88 zenon_H89. % 65.33/65.64 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H8a. % 65.33/65.64 generalize (zenon_H8a (hazard_of_mortality zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H8b. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H8b); [ zenon_intro zenon_H8d; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H8c ]. % 65.33/65.64 exact (zenon_H8d zenon_H88). % 65.33/65.64 exact (zenon_H89 zenon_H8c). % 65.33/65.64 (* end of lemma zenon_L13_ *) % 65.33/65.64 assert (zenon_L14_ : forall (zenon_TT3_cp : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((~(has_immunity zenon_TX_y T0))/\(~(has_immunity zenon_TX_y T))))->((((greater (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater_or_equal (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((greater_or_equal (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((capability zenon_TX_y T) = (capability zenon_TX_y T0))/\((position zenon_TX_y T) = (position zenon_TX_y T0)))->((hazard_of_mortality zenon_TX_y T) = (hazard_of_mortality zenon_TX_y T0)))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_y)->((((greater (stock_of_knowledge zenon_TX_y T) (stock_of_knowledge zenon_TX_y T0))/\(smaller_or_equal (internal_friction zenon_TX_y T) (internal_friction zenon_TX_y T0)))->(greater (capability zenon_TX_y T) (capability zenon_TX_y T0)))/\((((smaller_or_equal (stock_of_knowledge zenon_TX_y T) (stock_of_knowledge zenon_TX_y T0))/\(greater (internal_friction zenon_TX_y T) (internal_friction zenon_TX_y T0)))->(smaller (capability zenon_TX_y T) (capability zenon_TX_y T0)))/\((((stock_of_knowledge zenon_TX_y T) = (stock_of_knowledge zenon_TX_y T0))/\((internal_friction zenon_TX_y T) = (internal_friction zenon_TX_y T0)))->((capability zenon_TX_y T) = (capability zenon_TX_y T0)))))))) -> (~(has_immunity zenon_TX_y zenon_TT3_cp)) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> (organization zenon_TX_y) -> False). % 65.33/65.64 do 3 intro. intros zenon_H8e zenon_H89 zenon_H73 zenon_H8f zenon_H90 zenon_H91 zenon_H4e. % 65.33/65.64 generalize (assumption_9 zenon_TX_y). zenon_intro zenon_H0. % 65.33/65.64 generalize (zenon_H0 zenon_E). zenon_intro zenon_H4d. % 65.33/65.64 generalize (assumption_7 zenon_TX_y). zenon_intro zenon_H92. % 65.33/65.64 generalize (zenon_H4d zenon_TT3_cp). zenon_intro zenon_H93. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H52 | zenon_intro zenon_H5c ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 generalize (meaning_postulate_greater_comparable (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H3f. % 65.33/65.64 generalize (zenon_H8e zenon_TT2_cd). zenon_intro zenon_H94. % 65.33/65.64 generalize (zenon_H94 zenon_TT3_cp). zenon_intro zenon_H95. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H52 | zenon_intro zenon_H98 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 65.33/65.64 exact (zenon_H9a zenon_H91). % 65.33/65.64 exact (zenon_H99 zenon_H90). % 65.33/65.64 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H9c); [ zenon_intro zenon_H9d | zenon_intro zenon_H88 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_H9e | zenon_intro zenon_H81 ]. % 65.33/65.64 generalize (zenon_H8f zenon_TT2_cd). zenon_intro zenon_H5b. % 65.33/65.64 generalize (zenon_H5b zenon_TT3_cp). zenon_intro zenon_H9f. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H9f); [ zenon_intro zenon_H52 | zenon_intro zenon_Ha0 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ]. % 65.33/65.64 generalize (zenon_H92 zenon_TT2_cd). zenon_intro zenon_Ha7. % 65.33/65.64 generalize (zenon_Ha7 zenon_TT3_cp). zenon_intro zenon_Ha8. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_H7f | zenon_intro zenon_Ha9 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H52 | zenon_intro zenon_H80 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 exact (zenon_H80 zenon_H73). % 65.33/65.64 exact (zenon_Ha6 zenon_Ha9). % 65.33/65.64 generalize (definition_smaller_or_equal (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_Haa. % 65.33/65.64 generalize (zenon_Haa (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_Hab. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_Hab); [ zenon_intro zenon_Ha5; zenon_intro zenon_Hae | zenon_intro zenon_Had; zenon_intro zenon_Hac ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_Hae). zenon_intro zenon_H4a. zenon_intro zenon_H41. % 65.33/65.64 generalize (definition_smaller (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H47. % 65.33/65.64 generalize (zenon_H47 (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H48. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H4a; zenon_intro zenon_H40 | zenon_intro zenon_H46; zenon_intro zenon_H49 ]. % 65.33/65.64 apply (zenon_L9_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 exact (zenon_H4a zenon_H46). % 65.33/65.64 exact (zenon_Ha5 zenon_Had). % 65.33/65.64 exact (zenon_H9e zenon_Ha3). % 65.33/65.64 apply (zenon_L12_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L13_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L14_ *) % 65.33/65.64 assert (zenon_L15_ : forall (zenon_TT3_cp : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> (~(has_immunity zenon_TX_y zenon_TT3_cp)) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((~(has_immunity zenon_TX_y T0))/\(~(has_immunity zenon_TX_y T))))->((((greater (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater_or_equal (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((greater_or_equal (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((capability zenon_TX_y T) = (capability zenon_TX_y T0))/\((position zenon_TX_y T) = (position zenon_TX_y T0)))->((hazard_of_mortality zenon_TX_y T) = (hazard_of_mortality zenon_TX_y T0)))))))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H4e zenon_H91 zenon_H90 zenon_H73 zenon_H89 zenon_H8e. % 65.33/65.64 generalize (assumption_5 zenon_TX_y). zenon_intro zenon_H8f. % 65.33/65.64 apply (zenon_L14_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L15_ *) % 65.33/65.64 assert (zenon_L16_ : forall (zenon_TT3_cp : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((has_immunity zenon_TX_y zenon_TT0_w)/\(has_immunity zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y T)))) -> (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT0_w) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((~(has_immunity zenon_TX_y T0))/\(~(has_immunity zenon_TX_y T))))->((((greater (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater_or_equal (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((greater_or_equal (capability zenon_TX_y T) (capability zenon_TX_y T0))/\(greater (position zenon_TX_y T) (position zenon_TX_y T0)))->(smaller (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0)))/\((((capability zenon_TX_y T) = (capability zenon_TX_y T0))/\((position zenon_TX_y T) = (position zenon_TX_y T0)))->((hazard_of_mortality zenon_TX_y T) = (hazard_of_mortality zenon_TX_y T0)))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> False). % 65.33/65.64 do 4 intro. intros zenon_Haf zenon_H4e zenon_Hb0 zenon_H91 zenon_H73 zenon_H89 zenon_H8e zenon_Hb1. % 65.33/65.64 generalize (zenon_Haf zenon_TT3_cp). zenon_intro zenon_Hb2. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H52 | zenon_intro zenon_Hb5 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H90 ]. % 65.33/65.64 exact (zenon_Hb6 zenon_Hb0). % 65.33/65.64 apply (zenon_L15_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 exact (zenon_Hb1 zenon_Hb3). % 65.33/65.64 (* end of lemma zenon_L16_ *) % 65.33/65.64 assert (zenon_L17_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((has_immunity zenon_TX_y zenon_TT1_x)/\(~(has_immunity zenon_TX_y T))))->(greater (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y zenon_TT1_x)))) -> (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> False). % 65.33/65.64 do 3 intro. intros zenon_Hb7 zenon_H4e zenon_Hb8 zenon_H91 zenon_Hb9. % 65.33/65.64 generalize (zenon_Hb7 zenon_TT2_cd). zenon_intro zenon_Hba. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_H52 | zenon_intro zenon_Hbd ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbe | zenon_intro zenon_H9a ]. % 65.33/65.64 exact (zenon_Hbe zenon_Hb8). % 65.33/65.64 exact (zenon_H9a zenon_H91). % 65.33/65.64 exact (zenon_Hb9 zenon_Hbb). % 65.33/65.64 (* end of lemma zenon_L17_ *) % 65.33/65.64 assert (zenon_L18_ : forall (zenon_TT1_x : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TX_y : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((has_immunity zenon_TX_y T0)/\(~(has_immunity zenon_TX_y T))))->(greater (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (organization zenon_TX_y) -> False). % 65.33/65.64 do 3 intro. intros zenon_Hbf zenon_Hb9 zenon_H91 zenon_Hb8 zenon_H4e. % 65.33/65.64 generalize (zenon_Hbf zenon_TT1_x). zenon_intro zenon_Hb7. % 65.33/65.64 apply (zenon_L17_ zenon_TT2_cd zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L18_ *) % 65.33/65.64 assert (zenon_L19_ : forall (zenon_TT3_cp : zenon_U) (zenon_TT2_cd : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT0_w) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (~(has_immunity zenon_TX_y zenon_TT2_cd)) -> False). % 65.33/65.64 do 5 intro. intros zenon_H4e zenon_Hb0 zenon_Hb8 zenon_H89 zenon_H73 zenon_H91. % 65.33/65.64 generalize (assumption_3 zenon_TX_y). zenon_intro zenon_Hbf. % 65.33/65.64 generalize (assumption_4 zenon_TX_y). zenon_intro zenon_H8e. % 65.33/65.64 generalize (assumption_2 zenon_TX_y). zenon_intro zenon_Hc0. % 65.33/65.64 generalize (zenon_Hc0 zenon_TT0_w). zenon_intro zenon_Haf. % 65.33/65.64 generalize (zenon_Haf zenon_TT1_x). zenon_intro zenon_Hc1. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc4 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbe ]. % 65.33/65.64 exact (zenon_Hb6 zenon_Hb0). % 65.33/65.64 exact (zenon_Hbe zenon_Hb8). % 65.33/65.64 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc6 ]. % 65.33/65.64 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT1_x))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hb9 ]. % 65.33/65.64 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT0_w))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc8 ]. % 65.33/65.64 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT0_w)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT3_cp))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H89. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hc7. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_cd) = (hazard_of_mortality zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 65.33/65.64 congruence. % 65.33/65.64 apply zenon_Hc9. apply refl_equal. % 65.33/65.64 apply (zenon_L16_ zenon_TT3_cp zenon_TT2_cd zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT1_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y zenon_TT0_w))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_Hc8. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hbb. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_cd) = (hazard_of_mortality zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 65.33/65.64 congruence. % 65.33/65.64 apply zenon_Hc9. apply refl_equal. % 65.33/65.64 exact (zenon_Hc6 zenon_Hc5). % 65.33/65.64 apply (zenon_L18_ zenon_TT1_x zenon_TT2_cd zenon_TX_y); trivial. % 65.33/65.64 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT0_w)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_Hc6. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hca. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 65.33/65.64 cut (((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y zenon_TT1_x))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 65.33/65.64 congruence. % 65.33/65.64 exact (zenon_Hcc zenon_Hc2). % 65.33/65.64 apply zenon_Hcb. apply refl_equal. % 65.33/65.64 apply zenon_Hcb. apply refl_equal. % 65.33/65.64 (* end of lemma zenon_L19_ *) % 65.33/65.64 assert (zenon_L20_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : 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_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> (has_immunity zenon_TX_y zenon_TT3_cp) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> False). % 65.33/65.64 do 3 intro. intros zenon_H12 zenon_Hcd zenon_Hce zenon_H73 zenon_Hcf. % 65.33/65.64 generalize (zenon_Hcd zenon_TT3_cp). zenon_intro zenon_Hd0. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_H4e. zenon_intro zenon_Hd1. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hd2); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H90 ]. % 65.33/65.64 elim (classic ((~((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT2_cd)))/\(~(greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd))))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_Hd7. zenon_intro zenon_H80. % 65.33/65.64 exact (zenon_H80 zenon_H73). % 65.33/65.64 cut ((greater (age zenon_TX_y zenon_TT2_cd) (eta)) = (greater (age zenon_TX_y zenon_TT3_cp) (eta))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_Hd4. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hcf. % 65.33/65.64 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT2_cd) = (age zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 65.33/65.64 congruence. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hda | zenon_intro zenon_Hd9 ]. % 65.33/65.64 apply zenon_Hda. zenon_intro zenon_Hdb. % 65.33/65.64 elim (classic ((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT3_cp))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdd ]. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT3_cp)) = ((age zenon_TX_y zenon_TT2_cd) = (age zenon_TX_y zenon_TT3_cp))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_Hd8. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hdc. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 65.33/65.64 congruence. % 65.33/65.64 exact (zenon_Hd7 zenon_Hdb). % 65.33/65.64 apply zenon_Hdd. apply refl_equal. % 65.33/65.64 apply zenon_Hdd. apply refl_equal. % 65.33/65.64 apply zenon_Hd9. zenon_intro zenon_H73. % 65.33/65.64 generalize (zenon_H12 (age zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_Hde. % 65.33/65.64 generalize (zenon_Hde (age zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_Hdf. % 65.33/65.64 generalize (zenon_Hdf (eta)). zenon_intro zenon_He0. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_H80 | zenon_intro zenon_He1 ]. % 65.33/65.64 exact (zenon_H80 zenon_H73). % 65.33/65.64 apply (zenon_imply_s _ _ zenon_He1); [ zenon_intro zenon_He3 | zenon_intro zenon_He2 ]. % 65.33/65.64 exact (zenon_He3 zenon_Hcf). % 65.33/65.64 exact (zenon_Hd4 zenon_He2). % 65.33/65.64 apply zenon_H11. apply refl_equal. % 65.33/65.64 exact (zenon_H90 zenon_Hce). % 65.33/65.64 (* end of lemma zenon_L20_ *) % 65.33/65.64 assert (zenon_L21_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TX_y : 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_y)/\((has_immunity zenon_TX_y zenon_TT1_x)/\(~(has_immunity zenon_TX_y T))))->(greater (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y zenon_TT1_x)))) -> (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> False). % 65.33/65.64 do 4 intro. intros zenon_H12 zenon_Hb7 zenon_H4e zenon_Hb8 zenon_Hcd zenon_H73 zenon_Hcf zenon_He4. % 65.33/65.64 generalize (zenon_Hb7 zenon_TT3_cp). zenon_intro zenon_He5. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_He7); [ zenon_intro zenon_H52 | zenon_intro zenon_He8 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_He8); [ zenon_intro zenon_Hbe | zenon_intro zenon_H99 ]. % 65.33/65.64 exact (zenon_Hbe zenon_Hb8). % 65.33/65.64 apply zenon_H99. zenon_intro zenon_Hce. % 65.33/65.64 apply (zenon_L20_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 exact (zenon_He4 zenon_He6). % 65.33/65.64 (* end of lemma zenon_L21_ *) % 65.33/65.64 assert (zenon_L22_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((has_immunity zenon_TX_y T0)/\(~(has_immunity zenon_TX_y T))))->(greater (hazard_of_mortality zenon_TX_y T) (hazard_of_mortality zenon_TX_y T0))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (organization zenon_TX_y) -> False). % 65.33/65.64 do 4 intro. intros zenon_H12 zenon_Hbf zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_Hb8 zenon_H4e. % 65.33/65.64 generalize (zenon_Hbf zenon_TT1_x). zenon_intro zenon_Hb7. % 65.33/65.64 apply (zenon_L21_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L22_ *) % 65.33/65.64 assert (zenon_L23_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TX_y : 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_y) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> False). % 65.33/65.64 do 4 intro. intros zenon_H12 zenon_H4e zenon_Hb8 zenon_Hcd zenon_H73 zenon_Hcf zenon_He4. % 65.33/65.64 generalize (assumption_3 zenon_TX_y). zenon_intro zenon_Hbf. % 65.33/65.64 apply (zenon_L22_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L23_ *) % 65.33/65.64 assert (zenon_L24_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (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_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> (greater (eta) (age zenon_TX_y zenon_TT1_x)) -> False). % 65.33/65.64 do 4 intro. intros zenon_H12 zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_H14. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L23_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L24_ *) % 65.33/65.64 assert (zenon_L25_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((has_immunity zenon_TX_y zenon_TT0_w)/\(has_immunity zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y zenon_TT0_w) = (hazard_of_mortality zenon_TX_y T)))) -> (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT0_w) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))) -> False). % 65.33/65.64 do 3 intro. intros zenon_Haf zenon_H4e zenon_Hb0 zenon_Hb8 zenon_Hc6. % 65.33/65.64 generalize (zenon_Haf zenon_TT1_x). zenon_intro zenon_Hc1. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ]. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc4 ]. % 65.33/65.64 exact (zenon_H52 zenon_H4e). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbe ]. % 65.33/65.64 exact (zenon_Hb6 zenon_Hb0). % 65.33/65.64 exact (zenon_Hbe zenon_Hb8). % 65.33/65.64 apply zenon_Hc6. apply sym_equal. exact zenon_Hc2. % 65.33/65.64 (* end of lemma zenon_L25_ *) % 65.33/65.64 assert (zenon_L26_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (has_immunity zenon_TX_y zenon_TT0_w) -> (has_immunity zenon_TX_y zenon_TT1_x) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H4e zenon_Hb0 zenon_Hb8 zenon_Hc6. % 65.33/65.64 generalize (assumption_2 zenon_TX_y). zenon_intro zenon_Hc0. % 65.33/65.64 generalize (zenon_Hc0 zenon_TT0_w). zenon_intro zenon_Haf. % 65.33/65.64 apply (zenon_L25_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L26_ *) % 65.33/65.64 assert (zenon_L27_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) -> (greater (eta) (age zenon_TX_y zenon_TT1_x)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT0_w) (eta))) -> False). % 65.33/65.64 do 3 intro. intros zenon_Hed zenon_H14 zenon_H15. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19. % 65.33/65.64 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20. % 65.33/65.64 generalize (zenon_H20 (eta)). zenon_intro zenon_H21. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ]. % 65.33/65.64 cut ((greater (eta) (age zenon_TX_y zenon_TT1_x)) = (greater (eta) (age zenon_TX_y zenon_TT0_w))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H24. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H14. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT1_x) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 65.33/65.64 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 65.33/65.64 congruence. % 65.33/65.64 apply zenon_H11. apply refl_equal. % 65.33/65.64 apply zenon_Hee. apply sym_equal. exact zenon_Hed. % 65.33/65.64 exact (zenon_H1f zenon_H23). % 65.33/65.64 exact (zenon_H15 zenon_H1c). % 65.33/65.64 (* end of lemma zenon_L27_ *) % 65.33/65.64 assert (zenon_L28_ : forall (zenon_TT1_x : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_x) = (eta)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT1_x) (eta))) -> False). % 65.33/65.64 do 2 intro. intros zenon_Hef zenon_H2b. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c. % 65.33/65.64 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 65.33/65.64 exact (zenon_H31 zenon_Hef). % 65.33/65.64 exact (zenon_H2b zenon_H2f). % 65.33/65.64 (* end of lemma zenon_L28_ *) % 65.33/65.64 assert (zenon_L29_ : forall (zenon_TT0_w : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TX_y : 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_y zenon_TT1_x) = (eta)) -> (greater (age zenon_TX_y zenon_TT1_x) (age zenon_TX_y zenon_TT0_w)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT0_w) (eta))) -> False). % 65.33/65.64 do 3 intro. intros zenon_H12 zenon_Hef zenon_H13 zenon_H15. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19. % 65.33/65.64 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20. % 65.33/65.64 generalize (zenon_H20 (eta)). zenon_intro zenon_H21. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ]. % 65.33/65.64 elim (classic ((~((eta) = (age zenon_TX_y zenon_TT1_x)))/\(~(greater (eta) (age zenon_TX_y zenon_TT1_x))))); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf1 ]. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hf2. zenon_intro zenon_H29. % 65.33/65.64 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 65.33/65.64 cut ((greater (age zenon_TX_y zenon_TT1_x) (age zenon_TX_y zenon_TT0_w)) = (greater (eta) (age zenon_TX_y zenon_TT0_w))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H24. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_H13. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT1_x) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 65.33/65.64 congruence. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 65.33/65.64 apply zenon_Hf5. zenon_intro zenon_Hf6. % 65.33/65.64 elim (classic ((eta) = (eta))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H11 ]. % 65.33/65.64 cut (((eta) = (eta)) = ((age zenon_TX_y zenon_TT1_x) = (eta))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H31. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hf7. % 65.33/65.64 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 65.33/65.64 cut (((eta) = (age zenon_TX_y zenon_TT1_x))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 65.33/65.64 congruence. % 65.33/65.64 exact (zenon_Hf2 zenon_Hf6). % 65.33/65.64 apply zenon_H11. apply refl_equal. % 65.33/65.64 apply zenon_H11. apply refl_equal. % 65.33/65.64 apply zenon_Hf4. zenon_intro zenon_H14. % 65.33/65.64 generalize (zenon_H12 (eta)). zenon_intro zenon_H25. % 65.33/65.64 generalize (zenon_H25 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H26. % 65.33/65.64 generalize (zenon_H26 (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H27. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 65.33/65.64 exact (zenon_H29 zenon_H14). % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H22 ]. % 65.33/65.64 exact (zenon_H2a zenon_H13). % 65.33/65.64 exact (zenon_H24 zenon_H22). % 65.33/65.64 apply zenon_Hf3. apply refl_equal. % 65.33/65.64 exact (zenon_H1f zenon_H23). % 65.33/65.64 exact (zenon_H15 zenon_H1c). % 65.33/65.64 (* end of lemma zenon_L29_ *) % 65.33/65.64 assert (zenon_L30_ : forall (zenon_TT2_cd : zenon_U) (zenon_TT1_x : zenon_U) (zenon_TT3_cp : zenon_U) (zenon_TX_y : zenon_U), (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_y zenon_TT3_cp) (hazard_of_mortality zenon_TX_y zenon_TT1_x))) -> (greater (age zenon_TX_y zenon_TT2_cd) (eta)) -> (greater (age zenon_TX_y zenon_TT3_cp) (age zenon_TX_y zenon_TT2_cd)) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> ((age zenon_TX_y zenon_TT1_x) = (eta)) -> False). % 65.33/65.64 do 4 intro. intros zenon_H12 zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_Hef. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L23_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L30_ *) % 65.33/65.64 assert (zenon_L31_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), (~((age zenon_TX_y zenon_TT0_w) = (eta))) -> ((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) -> ((age zenon_TX_y zenon_TT1_x) = (eta)) -> False). % 65.33/65.64 do 3 intro. intros zenon_H1e zenon_Hed zenon_Hef. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) = ((age zenon_TX_y zenon_TT0_w) = (eta))). % 65.33/65.64 intro zenon_D_pnotp. % 65.33/65.64 apply zenon_H1e. % 65.33/65.64 rewrite <- zenon_D_pnotp. % 65.33/65.64 exact zenon_Hed. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT1_x) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 65.33/65.64 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 65.33/65.64 congruence. % 65.33/65.64 apply zenon_Hf3. apply refl_equal. % 65.33/65.64 exact (zenon_H31 zenon_Hef). % 65.33/65.64 (* end of lemma zenon_L31_ *) % 65.33/65.64 assert (zenon_L32_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) -> ((age zenon_TX_y zenon_TT1_x) = (eta)) -> (~(smaller_or_equal (age zenon_TX_y zenon_TT0_w) (eta))) -> False). % 65.33/65.64 do 3 intro. intros zenon_Hed zenon_Hef zenon_H15. % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19. % 65.33/65.64 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 65.33/65.64 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 65.33/65.64 apply (zenon_L31_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 exact (zenon_H15 zenon_H1c). % 65.33/65.64 (* end of lemma zenon_L32_ *) % 65.33/65.64 assert (zenon_L33_ : forall (zenon_TT1_x : zenon_U) (zenon_TT0_w : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))) -> (forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T)))))) -> ((age zenon_TX_y zenon_TT1_x) = (eta)) -> False). % 65.33/65.64 do 3 intro. intros zenon_Hed zenon_Hc6 zenon_Hcd zenon_Hef. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L32_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 (* end of lemma zenon_L33_ *) % 65.33/65.64 apply NNPP. intro zenon_G. % 65.33/65.64 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_H12 | zenon_intro zenon_Hfc ]. % 65.33/65.64 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)/\((smaller_or_equal (age X T0) (age X T1))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\(greater (age X T3) (age X T2)))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T3))/\((greater (hazard_of_mortality X T3) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))) zenon_G); [ zenon_intro zenon_Hfd; idtac ]. % 65.33/65.64 elim zenon_Hfd. zenon_intro zenon_TX_y. zenon_intro zenon_Hfe. % 65.33/65.64 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_y)/\((has_endowment zenon_TX_y)/\((smaller_or_equal (age zenon_TX_y T0) (age zenon_TX_y T1))/\((smaller_or_equal (age zenon_TX_y T1) (eta))/\((greater (age zenon_TX_y T2) (eta))/\(greater (age zenon_TX_y T3) (age zenon_TX_y T2)))))))->((greater (hazard_of_mortality zenon_TX_y T2) (hazard_of_mortality zenon_TX_y T3))/\((greater (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y T1))/\((hazard_of_mortality zenon_TX_y T1) = (hazard_of_mortality zenon_TX_y T0))))))))) zenon_Hfe); [ zenon_intro zenon_Hff; idtac ]. % 65.33/65.64 elim zenon_Hff. zenon_intro zenon_TT0_w. zenon_intro zenon_H100. % 65.33/65.64 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_y)/\((has_endowment zenon_TX_y)/\((smaller_or_equal (age zenon_TX_y zenon_TT0_w) (age zenon_TX_y T1))/\((smaller_or_equal (age zenon_TX_y T1) (eta))/\((greater (age zenon_TX_y T2) (eta))/\(greater (age zenon_TX_y T3) (age zenon_TX_y T2)))))))->((greater (hazard_of_mortality zenon_TX_y T2) (hazard_of_mortality zenon_TX_y T3))/\((greater (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y T1))/\((hazard_of_mortality zenon_TX_y T1) = (hazard_of_mortality zenon_TX_y zenon_TT0_w)))))))) zenon_H100); [ zenon_intro zenon_H101; idtac ]. % 65.33/65.64 elim zenon_H101. zenon_intro zenon_TT1_x. zenon_intro zenon_H102. % 65.33/65.64 apply (zenon_notallex_s (fun T2 : zenon_U => (forall T3 : zenon_U, (((organization zenon_TX_y)/\((has_endowment zenon_TX_y)/\((smaller_or_equal (age zenon_TX_y zenon_TT0_w) (age zenon_TX_y zenon_TT1_x))/\((smaller_or_equal (age zenon_TX_y zenon_TT1_x) (eta))/\((greater (age zenon_TX_y T2) (eta))/\(greater (age zenon_TX_y T3) (age zenon_TX_y T2)))))))->((greater (hazard_of_mortality zenon_TX_y T2) (hazard_of_mortality zenon_TX_y T3))/\((greater (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y zenon_TT1_x))/\((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w))))))) zenon_H102); [ zenon_intro zenon_H103; idtac ]. % 65.33/65.64 elim zenon_H103. zenon_intro zenon_TT2_cd. zenon_intro zenon_H104. % 65.33/65.64 apply (zenon_notallex_s (fun T3 : zenon_U => (((organization zenon_TX_y)/\((has_endowment zenon_TX_y)/\((smaller_or_equal (age zenon_TX_y zenon_TT0_w) (age zenon_TX_y zenon_TT1_x))/\((smaller_or_equal (age zenon_TX_y zenon_TT1_x) (eta))/\((greater (age zenon_TX_y zenon_TT2_cd) (eta))/\(greater (age zenon_TX_y T3) (age zenon_TX_y zenon_TT2_cd)))))))->((greater (hazard_of_mortality zenon_TX_y zenon_TT2_cd) (hazard_of_mortality zenon_TX_y T3))/\((greater (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y zenon_TT1_x))/\((hazard_of_mortality zenon_TX_y zenon_TT1_x) = (hazard_of_mortality zenon_TX_y zenon_TT0_w)))))) zenon_H104); [ zenon_intro zenon_H105; idtac ]. % 65.33/65.64 elim zenon_H105. zenon_intro zenon_TT3_cp. zenon_intro zenon_H106. % 65.33/65.64 apply (zenon_notimply_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H4e. zenon_intro zenon_H109. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H10a). zenon_intro zenon_H10d. zenon_intro zenon_H10c. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H10c). zenon_intro zenon_H2f. zenon_intro zenon_H10e. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H10e). zenon_intro zenon_Hcf. zenon_intro zenon_H73. % 65.33/65.64 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H10f. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H10f); [ zenon_intro zenon_H111; zenon_intro zenon_H110 | zenon_intro zenon_H10b; zenon_intro zenon_Hcd ]. % 65.33/65.64 exact (zenon_H111 zenon_H10b). % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19. % 65.33/65.64 generalize (zenon_H19 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H112. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H112); [ zenon_intro zenon_H115; zenon_intro zenon_H114 | zenon_intro zenon_H10d; zenon_intro zenon_H113 ]. % 65.33/65.64 exact (zenon_H115 zenon_H10d). % 65.33/65.64 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c. % 65.33/65.64 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 65.33/65.64 exact (zenon_H2b zenon_H2f). % 65.33/65.64 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H35 | zenon_intro zenon_Hef ]. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H33. % 65.33/65.64 generalize (zenon_H33 (eta)). zenon_intro zenon_H34. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H32; zenon_intro zenon_H29 | zenon_intro zenon_H35; zenon_intro zenon_H14 ]. % 65.33/65.64 exact (zenon_H32 zenon_H35). % 65.33/65.64 apply (zenon_or_s _ _ zenon_H113); [ zenon_intro zenon_H116 | zenon_intro zenon_Hed ]. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20. % 65.33/65.64 generalize (zenon_H20 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H117. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H117); [ zenon_intro zenon_H118; zenon_intro zenon_H2a | zenon_intro zenon_H116; zenon_intro zenon_H13 ]. % 65.33/65.64 exact (zenon_H118 zenon_H116). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ]. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L2_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ]. % 65.33/65.64 exact (zenon_He3 zenon_Hcf). % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ]. % 65.33/65.64 apply (zenon_L24_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L2_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ]. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L27_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ]. % 65.33/65.64 exact (zenon_He3 zenon_Hcf). % 65.33/65.64 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ]. % 65.33/65.64 apply (zenon_L24_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L27_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_or_s _ _ zenon_H113); [ zenon_intro zenon_H116 | zenon_intro zenon_Hed ]. % 65.33/65.64 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20. % 65.33/65.64 generalize (zenon_H20 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H117. % 65.33/65.64 apply (zenon_equiv_s _ _ zenon_H117); [ zenon_intro zenon_H118; zenon_intro zenon_H2a | zenon_intro zenon_H116; zenon_intro zenon_H13 ]. % 65.33/65.64 exact (zenon_H118 zenon_H116). % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ]. % 65.33/65.64 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ]. % 65.33/65.64 exact (zenon_He3 zenon_Hcf). % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L29_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ]. % 65.33/65.64 apply (zenon_L30_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.64 apply (zenon_L29_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.64 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ]. % 65.33/65.64 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9. % 65.33/65.64 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea. % 65.33/65.64 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ]. % 65.33/65.64 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial. % 65.33/65.64 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b. % 65.33/65.64 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 65.33/65.64 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ]. % 65.33/65.66 exact (zenon_He3 zenon_Hcf). % 65.33/65.66 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8. % 65.33/65.66 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9. % 65.33/65.66 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa. % 65.33/65.66 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ]. % 65.33/65.66 apply (zenon_L32_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.66 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.66 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ]. % 65.33/65.66 apply (zenon_L30_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial. % 65.33/65.66 apply (zenon_L33_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial. % 65.33/65.66 apply zenon_Hfc. zenon_intro zenon_Tx_la. apply NNPP. zenon_intro zenon_H11f. % 65.33/65.66 apply zenon_H11f. zenon_intro zenon_Ty_lc. apply NNPP. zenon_intro zenon_H121. % 65.33/65.66 apply zenon_H121. zenon_intro zenon_Tz_le. apply NNPP. zenon_intro zenon_H123. % 65.33/65.66 apply (zenon_notimply_s _ _ zenon_H123). zenon_intro zenon_H125. zenon_intro zenon_H124. % 65.33/65.66 apply (zenon_notimply_s _ _ zenon_H124). zenon_intro zenon_H127. zenon_intro zenon_H126. % 65.33/65.66 generalize (meaning_postulate_greater_transitive zenon_Tx_la). zenon_intro zenon_H128. % 65.33/65.66 generalize (zenon_H128 zenon_Ty_lc). zenon_intro zenon_H129. % 65.33/65.66 generalize (zenon_H129 zenon_Tz_le). zenon_intro zenon_H12a. % 65.33/65.66 apply (zenon_imply_s _ _ zenon_H12a); [ zenon_intro zenon_H12c | zenon_intro zenon_H12b ]. % 65.33/65.66 apply (zenon_notand_s _ _ zenon_H12c); [ zenon_intro zenon_H12e | zenon_intro zenon_H12d ]. % 65.33/65.66 exact (zenon_H12e zenon_H125). % 65.33/65.66 exact (zenon_H12d zenon_H127). % 65.33/65.66 exact (zenon_H126 zenon_H12b). % 65.33/65.66 Qed. % 65.33/65.66 % SZS output end Proof % 65.33/65.66 (* END-PROOF *) % 65.33/65.66 nodes searched: 2233391 % 65.33/65.66 max branch formulas: 6678 % 65.33/65.66 proof nodes created: 9790 % 65.33/65.66 formulas created: 433396 % 65.33/65.66 %------------------------------------------------------------------------------