%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT054+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:24 AM UTC 2026 % Result : Theorem 0.39s 0.64s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT054+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.35 % Computer : n011.cluster.edu % 0.10/0.35 % Model : x86_64 x86_64 % 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.35 % Memory : 8046.5625MB % 0.10/0.35 % OS : Linux 6.8.0-71-generic % 0.10/0.35 % CPULimit : 300 % 0.10/0.35 % WCLimit : 300 % 0.10/0.35 % DateTime : Mon Sep 7 13:24:30 UTC 2026 % 0.10/0.36 % CPUTime : % 0.39/0.64 (* PROOF-FOUND *) % 0.39/0.64 % SZS status Theorem % 0.39/0.64 (* BEGIN-PROOF *) % 0.39/0.64 % SZS output start Proof % 0.39/0.64 Theorem theorem_5 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((smaller_or_equal (age X T1) (sigma))/\((greater (age X T2) (sigma))/\(greater (sigma) (zero)))))))->(greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))))))). % 0.39/0.64 Proof. % 0.39/0.64 assert (zenon_L1_ : forall (zenon_TT2_r : zenon_U) (zenon_TX_s : zenon_U), (has_immunity zenon_TX_s zenon_TT2_r) -> (~(has_endowment zenon_TX_s)) -> (organization zenon_TX_s) -> False). % 0.39/0.64 do 2 intro. intros zenon_He zenon_Hf zenon_H10. % 0.39/0.64 generalize (assumption_1 zenon_TX_s). zenon_intro zenon_H13. % 0.39/0.64 generalize (zenon_H13 zenon_TT2_r). zenon_intro zenon_H14. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H17 zenon_Hf). % 0.39/0.64 exact (zenon_H15 zenon_He). % 0.39/0.64 (* end of lemma zenon_L1_ *) % 0.39/0.64 assert (zenon_L2_ : forall (zenon_TT0_be : zenon_U) (zenon_TT2_r : zenon_U) (zenon_TX_s : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((age zenon_TX_s T0) = (zero)))->((greater (age zenon_TX_s T) (sigma))<->(dissimilar zenon_TX_s T0 T))))) -> (greater (age zenon_TX_s zenon_TT2_r) (sigma)) -> (is_aligned zenon_TX_s zenon_TT2_r) -> (is_aligned zenon_TX_s zenon_TT0_be) -> ((age zenon_TX_s zenon_TT0_be) = (zero)) -> (organization zenon_TX_s) -> False). % 0.39/0.64 do 3 intro. intros zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H10. % 0.39/0.64 generalize (zenon_H19 zenon_TT0_be). zenon_intro zenon_H1f. % 0.39/0.64 generalize (zenon_H1f zenon_TT2_r). zenon_intro zenon_H20. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H18 | zenon_intro zenon_H23 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H23 zenon_H1d). % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H1a; zenon_intro zenon_H24 ]. % 0.39/0.64 exact (zenon_H26 zenon_H1a). % 0.39/0.64 generalize (definition_2 zenon_TX_s). zenon_intro zenon_H27. % 0.39/0.64 generalize (zenon_H27 zenon_TT0_be). zenon_intro zenon_H28. % 0.39/0.64 generalize (zenon_H28 zenon_TT2_r). zenon_intro zenon_H29. % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H25; zenon_intro zenon_H2b | zenon_intro zenon_H24; zenon_intro zenon_H2a ]. % 0.39/0.64 exact (zenon_H25 zenon_H24). % 0.39/0.64 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H10. zenon_intro zenon_H2c. % 0.39/0.64 apply (zenon_notequiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2e; zenon_intro zenon_H1b | zenon_intro zenon_H1c; zenon_intro zenon_H2d ]. % 0.39/0.64 exact (zenon_H2e zenon_H1c). % 0.39/0.64 exact (zenon_H2d zenon_H1b). % 0.39/0.64 (* end of lemma zenon_L2_ *) % 0.39/0.64 assert (zenon_L3_ : forall (zenon_TT0_be : zenon_U) (zenon_TT2_r : zenon_U) (zenon_TT1_by : zenon_U) (zenon_TX_s : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((is_aligned zenon_TX_s T0)/\(~(is_aligned zenon_TX_s T))))->(greater (capability zenon_TX_s T0) (capability zenon_TX_s T))))) -> (~(greater (capability zenon_TX_s zenon_TT1_by) (capability zenon_TX_s zenon_TT2_r))) -> ((age zenon_TX_s zenon_TT0_be) = (zero)) -> (is_aligned zenon_TX_s zenon_TT0_be) -> (greater (age zenon_TX_s zenon_TT2_r) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((age zenon_TX_s T0) = (zero)))->((greater (age zenon_TX_s T) (sigma))<->(dissimilar zenon_TX_s T0 T))))) -> (is_aligned zenon_TX_s zenon_TT1_by) -> (organization zenon_TX_s) -> False). % 0.39/0.64 do 4 intro. intros zenon_H2f zenon_H30 zenon_H1d zenon_H1c zenon_H1a zenon_H19 zenon_H31 zenon_H10. % 0.39/0.64 generalize (zenon_H2f zenon_TT1_by). zenon_intro zenon_H33. % 0.39/0.64 generalize (zenon_H33 zenon_TT2_r). zenon_intro zenon_H34. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H18 | zenon_intro zenon_H37 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.39/0.64 exact (zenon_H39 zenon_H31). % 0.39/0.64 apply zenon_H38. zenon_intro zenon_H1b. % 0.39/0.64 apply (zenon_L2_ zenon_TT0_be zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H30 zenon_H35). % 0.39/0.64 (* end of lemma zenon_L3_ *) % 0.39/0.64 assert (zenon_L4_ : forall (zenon_TT2_r : zenon_U) (zenon_TT1_by : zenon_U) (zenon_TT0_be : zenon_U) (zenon_TX_s : zenon_U), (organization zenon_TX_s) -> (is_aligned zenon_TX_s zenon_TT0_be) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((is_aligned zenon_TX_s T0)/\(~(is_aligned zenon_TX_s T))))->(greater (capability zenon_TX_s T0) (capability zenon_TX_s T))))) -> (~(greater (capability zenon_TX_s zenon_TT1_by) (capability zenon_TX_s zenon_TT2_r))) -> ((age zenon_TX_s zenon_TT0_be) = (zero)) -> (greater (age zenon_TX_s zenon_TT2_r) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((age zenon_TX_s T0) = (zero)))->((greater (age zenon_TX_s T) (sigma))<->(dissimilar zenon_TX_s T0 T))))) -> (~(dissimilar zenon_TX_s zenon_TT0_be zenon_TT1_by)) -> False). % 0.39/0.64 do 4 intro. intros zenon_H10 zenon_H1c zenon_H2f zenon_H30 zenon_H1d zenon_H1a zenon_H19 zenon_H3a. % 0.39/0.64 generalize (definition_2 zenon_TX_s). zenon_intro zenon_H27. % 0.39/0.64 generalize (zenon_H27 zenon_TT0_be). zenon_intro zenon_H28. % 0.39/0.64 generalize (zenon_H28 zenon_TT1_by). zenon_intro zenon_H3b. % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H3c ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H18 | zenon_intro zenon_H3f ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 apply zenon_H3f. zenon_intro zenon_H40. % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H40); [ zenon_intro zenon_H2e; zenon_intro zenon_H39 | zenon_intro zenon_H1c; zenon_intro zenon_H31 ]. % 0.39/0.64 exact (zenon_H2e zenon_H1c). % 0.39/0.64 apply (zenon_L3_ zenon_TT0_be zenon_TT2_r zenon_TT1_by zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H3a zenon_H3d). % 0.39/0.64 (* end of lemma zenon_L4_ *) % 0.39/0.64 assert (zenon_L5_ : (~((sigma) = (sigma))) -> False). % 0.39/0.64 do 0 intro. intros zenon_H41. % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 (* end of lemma zenon_L5_ *) % 0.39/0.64 assert (zenon_L6_ : forall (zenon_TT1_by : zenon_U) (zenon_TX_s : zenon_U), (greater (sigma) (age zenon_TX_s zenon_TT1_by)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (sigma) (sigma))) -> (greater (age zenon_TX_s zenon_TT1_by) (sigma)) -> False). % 0.39/0.64 do 2 intro. intros zenon_H42 zenon_H43 zenon_H44 zenon_H45. % 0.39/0.64 elim (classic ((~((sigma) = (age zenon_TX_s zenon_TT1_by)))/\(~(greater (sigma) (age zenon_TX_s zenon_TT1_by))))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.39/0.64 exact (zenon_H48 zenon_H42). % 0.39/0.64 cut ((greater (age zenon_TX_s zenon_TT1_by) (sigma)) = (greater (sigma) (sigma))). % 0.39/0.64 intro zenon_D_pnotp. % 0.39/0.64 apply zenon_H44. % 0.39/0.64 rewrite <- zenon_D_pnotp. % 0.39/0.64 exact zenon_H45. % 0.39/0.64 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.39/0.64 cut (((age zenon_TX_s zenon_TT1_by) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 0.39/0.64 congruence. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.39/0.64 apply zenon_H4c. zenon_intro zenon_H4d. % 0.39/0.64 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_H4e | zenon_intro zenon_H41 ]. % 0.39/0.64 cut (((sigma) = (sigma)) = ((age zenon_TX_s zenon_TT1_by) = (sigma))). % 0.39/0.64 intro zenon_D_pnotp. % 0.39/0.64 apply zenon_H4a. % 0.39/0.64 rewrite <- zenon_D_pnotp. % 0.39/0.64 exact zenon_H4e. % 0.39/0.64 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.39/0.64 cut (((sigma) = (age zenon_TX_s zenon_TT1_by))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 0.39/0.64 congruence. % 0.39/0.64 exact (zenon_H49 zenon_H4d). % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 apply zenon_H4b. zenon_intro zenon_H42. % 0.39/0.64 generalize (zenon_H43 (sigma)). zenon_intro zenon_H4f. % 0.39/0.64 generalize (zenon_H4f (age zenon_TX_s zenon_TT1_by)). zenon_intro zenon_H50. % 0.39/0.64 generalize (zenon_H50 (sigma)). zenon_intro zenon_H51. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ]. % 0.39/0.64 exact (zenon_H48 zenon_H42). % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.39/0.64 exact (zenon_H54 zenon_H45). % 0.39/0.64 exact (zenon_H44 zenon_H53). % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 (* end of lemma zenon_L6_ *) % 0.39/0.64 assert (zenon_L7_ : forall (zenon_TT1_by : zenon_U) (zenon_TX_s : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, (~((greater (sigma) Y)/\(greater Y (sigma))))) -> (greater (age zenon_TX_s zenon_TT1_by) (sigma)) -> (greater (sigma) (age zenon_TX_s zenon_TT1_by)) -> False). % 0.39/0.64 do 2 intro. intros zenon_H43 zenon_H55 zenon_H45 zenon_H42. % 0.39/0.64 generalize (zenon_H55 (sigma)). zenon_intro zenon_H56. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H44 | zenon_intro zenon_H44 ]. % 0.39/0.64 apply (zenon_L6_ zenon_TT1_by zenon_TX_s); trivial. % 0.39/0.64 apply (zenon_L6_ zenon_TT1_by zenon_TX_s); trivial. % 0.39/0.64 (* end of lemma zenon_L7_ *) % 0.39/0.64 assert (zenon_L8_ : forall (zenon_TT2_r : zenon_U) (zenon_TT1_by : zenon_U) (zenon_TT0_be : zenon_U) (zenon_TX_s : zenon_U), (is_aligned zenon_TX_s zenon_TT0_be) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((is_aligned zenon_TX_s T0)/\(~(is_aligned zenon_TX_s T))))->(greater (capability zenon_TX_s T0) (capability zenon_TX_s T))))) -> (~(greater (capability zenon_TX_s zenon_TT1_by) (capability zenon_TX_s zenon_TT2_r))) -> (greater (age zenon_TX_s zenon_TT2_r) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_s)/\((age zenon_TX_s T0) = (zero)))->((greater (age zenon_TX_s T) (sigma))<->(dissimilar zenon_TX_s T0 T))))) -> (~(greater (age zenon_TX_s zenon_TT1_by) (sigma))) -> ((age zenon_TX_s zenon_TT0_be) = (zero)) -> (organization zenon_TX_s) -> False). % 0.39/0.64 do 4 intro. intros zenon_H1c zenon_H2f zenon_H30 zenon_H1a zenon_H19 zenon_H54 zenon_H1d zenon_H10. % 0.39/0.64 generalize (zenon_H19 zenon_TT0_be). zenon_intro zenon_H1f. % 0.39/0.64 generalize (zenon_H1f zenon_TT1_by). zenon_intro zenon_H57. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H22 | zenon_intro zenon_H58 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H18 | zenon_intro zenon_H23 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H23 zenon_H1d). % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H54; zenon_intro zenon_H3a | zenon_intro zenon_H45; zenon_intro zenon_H3d ]. % 0.39/0.64 apply (zenon_L4_ zenon_TT2_r zenon_TT1_by zenon_TT0_be zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H54 zenon_H45). % 0.39/0.64 (* end of lemma zenon_L8_ *) % 0.39/0.64 assert (zenon_L9_ : forall (zenon_TT0_be : zenon_U) (zenon_TT1_by : zenon_U) (zenon_TT2_r : zenon_U) (zenon_TX_s : zenon_U), (~(has_endowment zenon_TX_s)) -> (greater (age zenon_TX_s zenon_TT2_r) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_s zenon_TT2_r) (hazard_of_mortality zenon_TX_s zenon_TT1_by))) -> ((age zenon_TX_s zenon_TT0_be) = (zero)) -> (organization zenon_TX_s) -> (forall T : zenon_U, (((organization zenon_TX_s)/\((age zenon_TX_s T) = (zero)))->(is_aligned zenon_TX_s T))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_s zenon_TT1_by) = (sigma)) -> False). % 0.39/0.64 do 4 intro. intros zenon_Hf zenon_H1a zenon_H59 zenon_H1d zenon_H10 zenon_H5a zenon_H44 zenon_H5b. % 0.39/0.64 elim (classic ((sigma) = (age zenon_TX_s zenon_TT1_by))); [ zenon_intro zenon_H4d | zenon_intro zenon_H49 ]. % 0.39/0.64 elim (classic (greater (age zenon_TX_s zenon_TT1_by) (sigma))); [ zenon_intro zenon_H45 | zenon_intro zenon_H54 ]. % 0.39/0.64 cut ((greater (age zenon_TX_s zenon_TT1_by) (sigma)) = (greater (sigma) (sigma))). % 0.39/0.64 intro zenon_D_pnotp. % 0.39/0.64 apply zenon_H44. % 0.39/0.64 rewrite <- zenon_D_pnotp. % 0.39/0.64 exact zenon_H45. % 0.39/0.64 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.39/0.64 cut (((age zenon_TX_s zenon_TT1_by) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 0.39/0.64 congruence. % 0.39/0.64 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_H4e | zenon_intro zenon_H41 ]. % 0.39/0.64 cut (((sigma) = (sigma)) = ((age zenon_TX_s zenon_TT1_by) = (sigma))). % 0.39/0.64 intro zenon_D_pnotp. % 0.39/0.64 apply zenon_H4a. % 0.39/0.64 rewrite <- zenon_D_pnotp. % 0.39/0.64 exact zenon_H4e. % 0.39/0.64 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.39/0.64 cut (((sigma) = (age zenon_TX_s zenon_TT1_by))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 0.39/0.64 congruence. % 0.39/0.64 exact (zenon_H49 zenon_H4d). % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 apply zenon_H41. apply refl_equal. % 0.39/0.64 generalize (zenon_H5a zenon_TT0_be). zenon_intro zenon_H5c. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H22 | zenon_intro zenon_H1c ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H18 | zenon_intro zenon_H23 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H23 zenon_H1d). % 0.39/0.64 generalize (assumption_16 zenon_TX_s). zenon_intro zenon_H5d. % 0.39/0.64 generalize (assumption_15 zenon_TX_s). zenon_intro zenon_H19. % 0.39/0.64 generalize (zenon_H5d zenon_TT2_r). zenon_intro zenon_H5e. % 0.39/0.64 generalize (zenon_H5e zenon_TT1_by). zenon_intro zenon_H5f. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H18 | zenon_intro zenon_H62 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.39/0.64 apply zenon_H64. zenon_intro zenon_He. % 0.39/0.64 apply (zenon_L1_ zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H30 ]. % 0.39/0.64 apply zenon_H65. zenon_intro zenon_H66. % 0.39/0.64 generalize (assumption_1 zenon_TX_s). zenon_intro zenon_H13. % 0.39/0.64 generalize (zenon_H13 zenon_TT1_by). zenon_intro zenon_H67. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H16 | zenon_intro zenon_H68 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H17 zenon_Hf). % 0.39/0.64 exact (zenon_H68 zenon_H66). % 0.39/0.64 generalize (assumption_14 zenon_TX_s). zenon_intro zenon_H2f. % 0.39/0.64 apply (zenon_L8_ zenon_TT2_r zenon_TT1_by zenon_TT0_be zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H59 zenon_H60). % 0.39/0.64 elim (classic ((age zenon_TX_s zenon_TT1_by) = (age zenon_TX_s zenon_TT1_by))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 0.39/0.64 cut (((age zenon_TX_s zenon_TT1_by) = (age zenon_TX_s zenon_TT1_by)) = ((sigma) = (age zenon_TX_s zenon_TT1_by))). % 0.39/0.64 intro zenon_D_pnotp. % 0.39/0.64 apply zenon_H49. % 0.39/0.64 rewrite <- zenon_D_pnotp. % 0.39/0.64 exact zenon_H69. % 0.39/0.64 cut (((age zenon_TX_s zenon_TT1_by) = (age zenon_TX_s zenon_TT1_by))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 0.39/0.64 cut (((age zenon_TX_s zenon_TT1_by) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 0.39/0.64 congruence. % 0.39/0.64 exact (zenon_H4a zenon_H5b). % 0.39/0.64 apply zenon_H6a. apply refl_equal. % 0.39/0.64 apply zenon_H6a. apply refl_equal. % 0.39/0.64 (* end of lemma zenon_L9_ *) % 0.39/0.64 apply NNPP. intro zenon_G. % 0.39/0.64 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_H43 | zenon_intro zenon_H6b ]. % 0.39/0.64 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((smaller_or_equal (age X T1) (sigma))/\((greater (age X T2) (sigma))/\(greater (sigma) (zero)))))))->(greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))))))) zenon_G); [ zenon_intro zenon_H6c; idtac ]. % 0.39/0.64 elim zenon_H6c. zenon_intro zenon_TX_s. zenon_intro zenon_H6d. % 0.39/0.64 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization zenon_TX_s)/\((~(has_endowment zenon_TX_s))/\(((age zenon_TX_s T0) = (zero))/\((smaller_or_equal (age zenon_TX_s T1) (sigma))/\((greater (age zenon_TX_s T2) (sigma))/\(greater (sigma) (zero)))))))->(greater (hazard_of_mortality zenon_TX_s T2) (hazard_of_mortality zenon_TX_s T1)))))) zenon_H6d); [ zenon_intro zenon_H6e; idtac ]. % 0.39/0.64 elim zenon_H6e. zenon_intro zenon_TT0_be. zenon_intro zenon_H6f. % 0.39/0.64 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (((organization zenon_TX_s)/\((~(has_endowment zenon_TX_s))/\(((age zenon_TX_s zenon_TT0_be) = (zero))/\((smaller_or_equal (age zenon_TX_s T1) (sigma))/\((greater (age zenon_TX_s T2) (sigma))/\(greater (sigma) (zero)))))))->(greater (hazard_of_mortality zenon_TX_s T2) (hazard_of_mortality zenon_TX_s T1))))) zenon_H6f); [ zenon_intro zenon_H70; idtac ]. % 0.39/0.64 elim zenon_H70. zenon_intro zenon_TT1_by. zenon_intro zenon_H71. % 0.39/0.64 apply (zenon_notallex_s (fun T2 : zenon_U => (((organization zenon_TX_s)/\((~(has_endowment zenon_TX_s))/\(((age zenon_TX_s zenon_TT0_be) = (zero))/\((smaller_or_equal (age zenon_TX_s zenon_TT1_by) (sigma))/\((greater (age zenon_TX_s T2) (sigma))/\(greater (sigma) (zero)))))))->(greater (hazard_of_mortality zenon_TX_s T2) (hazard_of_mortality zenon_TX_s zenon_TT1_by)))) zenon_H71); [ zenon_intro zenon_H72; idtac ]. % 0.39/0.64 elim zenon_H72. zenon_intro zenon_TT2_r. zenon_intro zenon_H73. % 0.39/0.64 apply (zenon_notimply_s _ _ zenon_H73). zenon_intro zenon_H74. zenon_intro zenon_H59. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H10. zenon_intro zenon_H75. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_Hf. zenon_intro zenon_H76. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H1d. zenon_intro zenon_H77. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 0.39/0.64 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H1a. zenon_intro zenon_H7a. % 0.39/0.64 generalize (definition_smaller_or_equal (age zenon_TX_s zenon_TT1_by)). zenon_intro zenon_H7b. % 0.39/0.64 generalize (zenon_H7b (sigma)). zenon_intro zenon_H7c. % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7f; zenon_intro zenon_H7e | zenon_intro zenon_H79; zenon_intro zenon_H7d ]. % 0.39/0.64 exact (zenon_H7f zenon_H79). % 0.39/0.64 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H80 | zenon_intro zenon_H5b ]. % 0.39/0.64 generalize (definition_smaller (age zenon_TX_s zenon_TT1_by)). zenon_intro zenon_H81. % 0.39/0.64 generalize (zenon_H81 (sigma)). zenon_intro zenon_H82. % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H82); [ zenon_intro zenon_H83; zenon_intro zenon_H48 | zenon_intro zenon_H80; zenon_intro zenon_H42 ]. % 0.39/0.64 exact (zenon_H83 zenon_H80). % 0.39/0.64 generalize (assumption_13 zenon_TX_s). zenon_intro zenon_H5a. % 0.39/0.64 generalize (zenon_H5a zenon_TT0_be). zenon_intro zenon_H5c. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H22 | zenon_intro zenon_H1c ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H18 | zenon_intro zenon_H23 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H23 zenon_H1d). % 0.39/0.64 generalize (assumption_16 zenon_TX_s). zenon_intro zenon_H5d. % 0.39/0.64 generalize (assumption_3 zenon_TX_s). zenon_intro zenon_H84. % 0.39/0.64 generalize (zenon_H84 zenon_TT1_by). zenon_intro zenon_H85. % 0.39/0.64 generalize (assumption_15 zenon_TX_s). zenon_intro zenon_H19. % 0.39/0.64 generalize (zenon_H5d zenon_TT2_r). zenon_intro zenon_H5e. % 0.39/0.64 generalize (zenon_H85 zenon_TT2_r). zenon_intro zenon_H86. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H87 | zenon_intro zenon_H60 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H18 | zenon_intro zenon_H88 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H68 | zenon_intro zenon_H64 ]. % 0.39/0.64 generalize (zenon_H5e zenon_TT1_by). zenon_intro zenon_H5f. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H18 | zenon_intro zenon_H62 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.39/0.64 apply zenon_H64. zenon_intro zenon_He. % 0.39/0.64 apply (zenon_L1_ zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H30 ]. % 0.39/0.64 exact (zenon_H65 zenon_H68). % 0.39/0.64 generalize (assumption_14 zenon_TX_s). zenon_intro zenon_H2f. % 0.39/0.64 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_H55. % 0.39/0.64 generalize (zenon_H19 zenon_TT0_be). zenon_intro zenon_H1f. % 0.39/0.64 generalize (zenon_H1f zenon_TT1_by). zenon_intro zenon_H57. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H22 | zenon_intro zenon_H58 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H18 | zenon_intro zenon_H23 ]. % 0.39/0.64 exact (zenon_H18 zenon_H10). % 0.39/0.64 exact (zenon_H23 zenon_H1d). % 0.39/0.64 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H54; zenon_intro zenon_H3a | zenon_intro zenon_H45; zenon_intro zenon_H3d ]. % 0.39/0.64 apply (zenon_L4_ zenon_TT2_r zenon_TT1_by zenon_TT0_be zenon_TX_s); trivial. % 0.39/0.64 apply (zenon_L7_ zenon_TT1_by zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H59 zenon_H60). % 0.39/0.64 apply zenon_H64. zenon_intro zenon_He. % 0.39/0.64 apply (zenon_L1_ zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 exact (zenon_H59 zenon_H60). % 0.39/0.64 generalize (assumption_13 zenon_TX_s). zenon_intro zenon_H5a. % 0.39/0.64 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_H55. % 0.39/0.64 generalize (zenon_H55 (sigma)). zenon_intro zenon_H56. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H44 | zenon_intro zenon_H44 ]. % 0.39/0.64 apply (zenon_L9_ zenon_TT0_be zenon_TT1_by zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 apply (zenon_L9_ zenon_TT0_be zenon_TT1_by zenon_TT2_r zenon_TX_s); trivial. % 0.39/0.64 apply zenon_H6b. zenon_intro zenon_Tx_fh. apply NNPP. zenon_intro zenon_H8a. % 0.39/0.64 apply zenon_H8a. zenon_intro zenon_Ty_fj. apply NNPP. zenon_intro zenon_H8c. % 0.39/0.64 apply zenon_H8c. zenon_intro zenon_Tz_fl. apply NNPP. zenon_intro zenon_H8e. % 0.39/0.64 apply (zenon_notimply_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 0.39/0.64 apply (zenon_notimply_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91. % 0.39/0.64 generalize (meaning_postulate_greater_transitive zenon_Tx_fh). zenon_intro zenon_H93. % 0.39/0.64 generalize (zenon_H93 zenon_Ty_fj). zenon_intro zenon_H94. % 0.39/0.64 generalize (zenon_H94 zenon_Tz_fl). zenon_intro zenon_H95. % 0.39/0.64 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ]. % 0.39/0.64 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ]. % 0.39/0.64 exact (zenon_H99 zenon_H90). % 0.39/0.64 exact (zenon_H98 zenon_H92). % 0.39/0.64 exact (zenon_H91 zenon_H96). % 0.39/0.64 Qed. % 0.39/0.64 % SZS output end Proof % 0.39/0.64 (* END-PROOF *) % 0.39/0.64 nodes searched: 7758 % 0.39/0.64 max branch formulas: 506 % 0.39/0.64 proof nodes created: 298 % 0.39/0.64 formulas created: 8551 % 0.39/0.64 %------------------------------------------------------------------------------