%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT050+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 1.65s 1.92s % Output : Proof 1.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT050+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n017.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 13:12:24 UTC 2026 % 0.09/0.35 % CPUTime : % 1.65/1.92 (* PROOF-FOUND *) % 1.65/1.92 % SZS status Theorem % 1.65/1.92 (* BEGIN-PROOF *) % 1.65/1.92 % SZS output start Proof % 1.65/1.92 Theorem theorem_3 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_endowment X))/\(greater (age X T) (age X T0))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))). % 1.65/1.92 Proof. % 1.65/1.92 assert (zenon_L1_ : forall (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (has_immunity zenon_TX_t zenon_TT0_s) -> (~(has_endowment zenon_TX_t)) -> (organization zenon_TX_t) -> False). % 1.65/1.92 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11. % 1.65/1.92 generalize (assumption_1 zenon_TX_t). zenon_intro zenon_H14. % 1.65/1.92 generalize (zenon_H14 zenon_TT0_s). zenon_intro zenon_H15. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 exact (zenon_H18 zenon_H10). % 1.65/1.92 exact (zenon_H16 zenon_Hf). % 1.65/1.92 (* end of lemma zenon_L1_ *) % 1.65/1.92 assert (zenon_L2_ : forall (zenon_TT_bb : zenon_U) (zenon_TX_t : zenon_U), (has_immunity zenon_TX_t zenon_TT_bb) -> (~(has_endowment zenon_TX_t)) -> (organization zenon_TX_t) -> False). % 1.65/1.92 do 2 intro. intros zenon_H1a zenon_H10 zenon_H11. % 1.65/1.92 generalize (assumption_1 zenon_TX_t). zenon_intro zenon_H14. % 1.65/1.92 generalize (zenon_H14 zenon_TT_bb). zenon_intro zenon_H1c. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H17 | zenon_intro zenon_H1d ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 exact (zenon_H18 zenon_H10). % 1.65/1.92 exact (zenon_H1d zenon_H1a). % 1.65/1.92 (* end of lemma zenon_L2_ *) % 1.65/1.92 assert (zenon_L3_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, (((organization zenon_TX_t)/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s)))->(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))) -> (organization zenon_TX_t) -> (greater (age zenon_TX_t zenon_TT_bb) (age zenon_TX_t zenon_TT0_s)) -> (~(greater (internal_friction zenon_TX_t zenon_TT_bb) (internal_friction zenon_TX_t zenon_TT0_s))) -> False). % 1.65/1.92 do 3 intro. intros zenon_H1e zenon_H11 zenon_H1f zenon_H20. % 1.65/1.92 generalize (zenon_H1e zenon_TT_bb). zenon_intro zenon_H21. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H19 | zenon_intro zenon_H24 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 exact (zenon_H24 zenon_H1f). % 1.65/1.92 exact (zenon_H20 zenon_H22). % 1.65/1.92 (* end of lemma zenon_L3_ *) % 1.65/1.92 assert (zenon_L4_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, ((organization zenon_TX_t)->((((greater (stock_of_knowledge zenon_TX_t T) (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\(smaller_or_equal (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))->(greater (capability zenon_TX_t T) (capability zenon_TX_t zenon_TT0_s)))/\((((smaller_or_equal (stock_of_knowledge zenon_TX_t T) (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))->(smaller (capability zenon_TX_t T) (capability zenon_TX_t zenon_TT0_s)))/\((((stock_of_knowledge zenon_TX_t T) = (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\((internal_friction zenon_TX_t T) = (internal_friction zenon_TX_t zenon_TT0_s)))->((capability zenon_TX_t T) = (capability zenon_TX_t zenon_TT0_s))))))) -> (organization zenon_TX_t) -> (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_t)->((stock_of_knowledge zenon_TX_t T) = (stock_of_knowledge zenon_TX_t T0))))) -> (forall T : zenon_U, (((organization zenon_TX_t)/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s)))->(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))) -> (greater (age zenon_TX_t zenon_TT_bb) (age zenon_TX_t zenon_TT0_s)) -> (~(greater (capability zenon_TX_t zenon_TT0_s) (capability zenon_TX_t zenon_TT_bb))) -> False). % 1.65/1.92 do 3 intro. intros zenon_H25 zenon_H11 zenon_H26 zenon_H1e zenon_H1f zenon_H27. % 1.65/1.92 generalize (zenon_H25 zenon_TT_bb). zenon_intro zenon_H28. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H19 | zenon_intro zenon_H29 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H30 | zenon_intro zenon_H20 ]. % 1.65/1.92 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H31. % 1.65/1.92 generalize (zenon_H31 (stock_of_knowledge zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H32. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H30; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ]. % 1.65/1.92 apply (zenon_notor_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 1.65/1.92 generalize (zenon_H26 zenon_TT_bb). zenon_intro zenon_H38. % 1.65/1.92 generalize (zenon_H38 zenon_TT0_s). zenon_intro zenon_H39. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H19 | zenon_intro zenon_H3a ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply zenon_H36. apply sym_equal. exact zenon_H3a. % 1.65/1.92 exact (zenon_H30 zenon_H34). % 1.65/1.92 apply (zenon_L3_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 generalize (definition_smaller (capability zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H3b. % 1.65/1.92 generalize (zenon_H3b (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H3c. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3e; zenon_intro zenon_H27 | zenon_intro zenon_H2e; zenon_intro zenon_H3d ]. % 1.65/1.92 exact (zenon_H3e zenon_H2e). % 1.65/1.92 exact (zenon_H27 zenon_H3d). % 1.65/1.92 (* end of lemma zenon_L4_ *) % 1.65/1.92 assert (zenon_L5_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((smaller (external_ties zenon_TX_t zenon_TT0_s) Y)\/(((external_ties zenon_TX_t zenon_TT0_s) = Y)\/(greater (external_ties zenon_TX_t zenon_TT0_s) Y)))) -> (~(greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s))) -> (~((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT0_s))) -> (~(greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT_bb))) -> False). % 1.65/1.92 do 3 intro. intros zenon_H3f zenon_H40 zenon_H41 zenon_H42. % 1.65/1.92 generalize (zenon_H3f (external_ties zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H43. % 1.65/1.92 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 1.65/1.92 generalize (definition_smaller (external_ties zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H46. % 1.65/1.92 generalize (zenon_H46 (external_ties zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H47. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H49; zenon_intro zenon_H40 | zenon_intro zenon_H45; zenon_intro zenon_H48 ]. % 1.65/1.92 exact (zenon_H49 zenon_H45). % 1.65/1.92 exact (zenon_H40 zenon_H48). % 1.65/1.92 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 1.65/1.92 apply zenon_H41. apply sym_equal. exact zenon_H4b. % 1.65/1.92 exact (zenon_H42 zenon_H4a). % 1.65/1.92 (* end of lemma zenon_L5_ *) % 1.65/1.92 assert (zenon_L6_ : forall (zenon_TT0_s : zenon_U) (zenon_TT_bb : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, ((organization zenon_TX_t)->(((greater (external_ties zenon_TX_t T) (external_ties zenon_TX_t zenon_TT_bb))->(greater (position zenon_TX_t T) (position zenon_TX_t zenon_TT_bb)))/\(((external_ties zenon_TX_t T) = (external_ties zenon_TX_t zenon_TT_bb))->((position zenon_TX_t T) = (position zenon_TX_t zenon_TT_bb)))))) -> (organization zenon_TX_t) -> (forall T : zenon_U, ((organization zenon_TX_t)->((external_ties zenon_TX_t T) = (external_ties zenon_TX_t zenon_E)))) -> (~(greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT0_s))) -> (~((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT0_s))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_t zenon_TT0_s) Y)\/(((external_ties zenon_TX_t zenon_TT0_s) = Y)\/(greater (external_ties zenon_TX_t zenon_TT0_s) Y)))) -> ((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_E)) -> (~(greater (position zenon_TX_t zenon_TT0_s) (position zenon_TX_t zenon_TT_bb))) -> False). % 1.65/1.92 do 3 intro. intros zenon_H4c zenon_H11 zenon_H4d zenon_H4e zenon_H41 zenon_H3f zenon_H4f zenon_H50. % 1.65/1.92 generalize (zenon_H4c zenon_TT0_s). zenon_intro zenon_H51. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H19 | zenon_intro zenon_H52 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H42 | zenon_intro zenon_H55 ]. % 1.65/1.92 generalize (zenon_H4d zenon_TT_bb). zenon_intro zenon_H56. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H19 | zenon_intro zenon_H57 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 elim (classic ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 1.65/1.92 elim (classic (greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H48 | zenon_intro zenon_H40 ]. % 1.65/1.92 elim (classic (greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ]. % 1.65/1.92 cut ((greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s)) = (greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT0_s))). % 1.65/1.92 intro zenon_D_pnotp. % 1.65/1.92 apply zenon_H4e. % 1.65/1.92 rewrite <- zenon_D_pnotp. % 1.65/1.92 exact zenon_H5a. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 1.65/1.92 congruence. % 1.65/1.92 elim (classic ((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5c ]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s)) = ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT0_s))). % 1.65/1.92 intro zenon_D_pnotp. % 1.65/1.92 apply zenon_H5d. % 1.65/1.92 rewrite <- zenon_D_pnotp. % 1.65/1.92 exact zenon_H5e. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 1.65/1.92 congruence. % 1.65/1.92 exact (zenon_H5f zenon_H4f). % 1.65/1.92 apply zenon_H5c. apply refl_equal. % 1.65/1.92 apply zenon_H5c. apply refl_equal. % 1.65/1.92 apply zenon_H5c. apply refl_equal. % 1.65/1.92 cut ((greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s)) = (greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s))). % 1.65/1.92 intro zenon_D_pnotp. % 1.65/1.92 apply zenon_H5b. % 1.65/1.92 rewrite <- zenon_D_pnotp. % 1.65/1.92 exact zenon_H48. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 1.65/1.92 congruence. % 1.65/1.92 elim (classic ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E)) = ((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))). % 1.65/1.92 intro zenon_D_pnotp. % 1.65/1.92 apply zenon_H60. % 1.65/1.92 rewrite <- zenon_D_pnotp. % 1.65/1.92 exact zenon_H61. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 1.65/1.92 congruence. % 1.65/1.92 exact (zenon_H59 zenon_H58). % 1.65/1.92 apply zenon_H62. apply refl_equal. % 1.65/1.92 apply zenon_H62. apply refl_equal. % 1.65/1.92 apply zenon_H5c. apply refl_equal. % 1.65/1.92 apply (zenon_L5_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 elim (classic ((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb)) = ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))). % 1.65/1.92 intro zenon_D_pnotp. % 1.65/1.92 apply zenon_H59. % 1.65/1.92 rewrite <- zenon_D_pnotp. % 1.65/1.92 exact zenon_H63. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 1.65/1.92 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 1.65/1.92 congruence. % 1.65/1.92 exact (zenon_H60 zenon_H57). % 1.65/1.92 apply zenon_H64. apply refl_equal. % 1.65/1.92 apply zenon_H64. apply refl_equal. % 1.65/1.92 exact (zenon_H50 zenon_H55). % 1.65/1.92 (* end of lemma zenon_L6_ *) % 1.65/1.92 assert (zenon_L7_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s) (hazard_of_mortality zenon_TX_t zenon_TT_bb)) -> (~(greater (hazard_of_mortality zenon_TX_t zenon_TT_bb) (hazard_of_mortality zenon_TX_t zenon_TT0_s))) -> False). % 1.65/1.92 do 3 intro. intros zenon_H65 zenon_H66. % 1.65/1.92 generalize (definition_smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H67. % 1.65/1.92 generalize (zenon_H67 (hazard_of_mortality zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H68. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H6a; zenon_intro zenon_H66 | zenon_intro zenon_H65; zenon_intro zenon_H69 ]. % 1.65/1.92 exact (zenon_H6a zenon_H65). % 1.65/1.92 exact (zenon_H66 zenon_H69). % 1.65/1.92 (* end of lemma zenon_L7_ *) % 1.65/1.92 assert (zenon_L8_ : forall (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s) (hazard_of_mortality zenon_TX_t zenon_TT0_s)) -> False). % 1.65/1.92 do 2 intro. intros zenon_H6b. % 1.65/1.92 generalize (definition_smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H67. % 1.65/1.92 generalize (zenon_H67 (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H6c. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6f; zenon_intro zenon_H6e | zenon_intro zenon_H6b; zenon_intro zenon_H6d ]. % 1.65/1.92 exact (zenon_H6f zenon_H6b). % 1.65/1.92 generalize (meaning_postulate_greater_strict (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H70. % 1.65/1.92 generalize (zenon_H70 (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H71. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H6e | zenon_intro zenon_H6e ]. % 1.65/1.92 exact (zenon_H6e zenon_H6d). % 1.65/1.92 exact (zenon_H6e zenon_H6d). % 1.65/1.92 (* end of lemma zenon_L8_ *) % 1.65/1.92 apply NNPP. intro zenon_G. % 1.65/1.92 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_endowment X))/\(greater (age X T) (age X T0))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))) zenon_G); [ zenon_intro zenon_H72; idtac ]. % 1.65/1.92 elim zenon_H72. zenon_intro zenon_TX_t. zenon_intro zenon_H73. % 1.65/1.92 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_t)/\((~(has_endowment zenon_TX_t))/\(greater (age zenon_TX_t T) (age zenon_TX_t T0))))->(greater (hazard_of_mortality zenon_TX_t T) (hazard_of_mortality zenon_TX_t T0))))) zenon_H73); [ zenon_intro zenon_H74; idtac ]. % 1.65/1.92 elim zenon_H74. zenon_intro zenon_TT0_s. zenon_intro zenon_H75. % 1.65/1.92 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_t)/\((~(has_endowment zenon_TX_t))/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s))))->(greater (hazard_of_mortality zenon_TX_t T) (hazard_of_mortality zenon_TX_t zenon_TT0_s)))) zenon_H75); [ zenon_intro zenon_H76; idtac ]. % 1.65/1.92 elim zenon_H76. zenon_intro zenon_TT_bb. zenon_intro zenon_H77. % 1.65/1.92 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H78. zenon_intro zenon_H66. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H11. zenon_intro zenon_H79. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H10. zenon_intro zenon_H1f. % 1.65/1.92 generalize (assumption_4 zenon_TX_t). zenon_intro zenon_H7a. % 1.65/1.92 generalize (zenon_H7a zenon_TT0_s). zenon_intro zenon_H7b. % 1.65/1.92 generalize (zenon_H7b zenon_TT0_s). zenon_intro zenon_H7c. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H19 | zenon_intro zenon_H7f ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 1.65/1.92 apply zenon_H80. zenon_intro zenon_Hf. % 1.65/1.92 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 apply zenon_H80. zenon_intro zenon_Hf. % 1.65/1.92 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H82. zenon_intro zenon_H81. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H85 | zenon_intro zenon_H6b ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 1.65/1.92 generalize (definition_greater_or_equal (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H88. % 1.65/1.92 generalize (zenon_H88 (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H89. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_H89); [ zenon_intro zenon_H87; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H8a ]. % 1.65/1.92 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 1.65/1.92 apply zenon_H8d. apply refl_equal. % 1.65/1.92 exact (zenon_H87 zenon_H8b). % 1.65/1.92 generalize (assumption_6 zenon_TX_t). zenon_intro zenon_H8f. % 1.65/1.92 generalize (assumption_5 zenon_TX_t). zenon_intro zenon_H90. % 1.65/1.92 generalize (zenon_H8f zenon_TT0_s). zenon_intro zenon_H91. % 1.65/1.92 generalize (zenon_H90 zenon_TT0_s). zenon_intro zenon_H25. % 1.65/1.92 generalize (zenon_H91 zenon_TT0_s). zenon_intro zenon_H92. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H19 | zenon_intro zenon_H93 ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H95. zenon_intro zenon_H94. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H4e | zenon_intro zenon_H96 ]. % 1.65/1.92 generalize (assumption_11 zenon_TX_t). zenon_intro zenon_H0. % 1.65/1.92 generalize (zenon_H0 zenon_E). zenon_intro zenon_H4d. % 1.65/1.92 generalize (assumption_10 zenon_TX_t). zenon_intro zenon_H26. % 1.65/1.92 generalize (assumption_12 zenon_TX_t). zenon_intro zenon_H97. % 1.65/1.92 generalize (zenon_H97 zenon_TT0_s). zenon_intro zenon_H1e. % 1.65/1.92 generalize (zenon_H4d zenon_TT0_s). zenon_intro zenon_H98. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 generalize (meaning_postulate_greater_comparable (external_ties zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H3f. % 1.65/1.92 generalize (zenon_H7a zenon_TT_bb). zenon_intro zenon_H99. % 1.65/1.92 generalize (zenon_H99 zenon_TT0_s). zenon_intro zenon_H9a. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H9c); [ zenon_intro zenon_H19 | zenon_intro zenon_H9d ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_H9e | zenon_intro zenon_H80 ]. % 1.65/1.92 apply zenon_H9e. zenon_intro zenon_H1a. % 1.65/1.92 apply (zenon_L2_ zenon_TT_bb zenon_TX_t); trivial. % 1.65/1.92 apply zenon_H80. zenon_intro zenon_Hf. % 1.65/1.92 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_Ha0. zenon_intro zenon_H9f. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_Ha0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H65 ]. % 1.65/1.92 apply (zenon_notand_s _ _ zenon_Ha1); [ zenon_intro zenon_H27 | zenon_intro zenon_Ha2 ]. % 1.65/1.92 apply (zenon_L4_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 generalize (definition_greater_or_equal (position zenon_TX_t zenon_TT0_s)). zenon_intro zenon_Ha3. % 1.65/1.92 generalize (zenon_Ha3 (position zenon_TX_t zenon_TT_bb)). zenon_intro zenon_Ha4. % 1.65/1.92 apply (zenon_equiv_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha2; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha5 ]. % 1.65/1.92 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_H50. zenon_intro zenon_Ha8. % 1.65/1.92 generalize (zenon_H8f zenon_TT_bb). zenon_intro zenon_H4c. % 1.65/1.92 generalize (zenon_H91 zenon_TT_bb). zenon_intro zenon_Ha9. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H19 | zenon_intro zenon_Haa ]. % 1.65/1.92 exact (zenon_H19 zenon_H11). % 1.65/1.92 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Hac. zenon_intro zenon_Hab. % 1.65/1.92 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_H41 | zenon_intro zenon_Had ]. % 1.65/1.92 apply (zenon_L6_ zenon_TT0_s zenon_TT_bb zenon_TX_t); trivial. % 1.65/1.92 apply zenon_Ha8. apply sym_equal. exact zenon_Had. % 1.65/1.92 exact (zenon_Ha2 zenon_Ha6). % 1.65/1.92 apply (zenon_L7_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 exact (zenon_H86 zenon_H96). % 1.65/1.92 apply (zenon_L8_ zenon_TT0_s zenon_TX_t); trivial. % 1.65/1.92 Qed. % 1.65/1.92 % SZS output end Proof % 1.65/1.92 (* END-PROOF *) % 1.65/1.92 nodes searched: 111640 % 1.65/1.92 max branch formulas: 2448 % 1.65/1.92 proof nodes created: 1780 % 1.65/1.92 formulas created: 50671 % 1.65/1.92 %------------------------------------------------------------------------------