%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT056+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 06:24:24 AM UTC 2026 % Result : Theorem 0.55s 0.82s % Output : Proof 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT056+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.11/0.35 % Computer : n017.cluster.edu % 0.11/0.35 % Model : x86_64 x86_64 % 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.35 % Memory : 8046.5625MB % 0.11/0.35 % OS : Linux 6.8.0-71-generic % 0.11/0.35 % CPULimit : 300 % 0.11/0.35 % WCLimit : 300 % 0.11/0.35 % DateTime : Mon Sep 7 13:23:09 UTC 2026 % 0.11/0.36 % CPUTime : % 0.55/0.82 (* PROOF-FOUND *) % 0.55/0.82 % SZS status Theorem % 0.55/0.82 (* BEGIN-PROOF *) % 0.55/0.82 % SZS output start Proof % 0.55/0.82 Theorem lemma_9 : (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) (eta))/\((greater (age X T2) (eta))/\((greater_or_equal (eta) (sigma))/\(greater (sigma) (zero))))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))). % 0.55/0.82 Proof. % 0.55/0.82 assert (zenon_L1_ : forall (zenon_TT1_m : zenon_U) (zenon_TX_n : zenon_U), (greater (eta) (age zenon_TX_n zenon_TT1_m)) -> (~(smaller_or_equal (age zenon_TX_n zenon_TT1_m) (eta))) -> False). % 0.55/0.82 do 2 intro. intros zenon_Ha zenon_Hb. % 0.55/0.82 generalize (definition_smaller_or_equal (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_He. % 0.55/0.82 generalize (zenon_He (eta)). zenon_intro zenon_Hf. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_Hb; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_H10 ]. % 0.55/0.82 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.55/0.82 generalize (definition_smaller (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_H15. % 0.55/0.82 generalize (zenon_H15 (eta)). zenon_intro zenon_H16. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_Ha ]. % 0.55/0.82 exact (zenon_H18 zenon_Ha). % 0.55/0.82 exact (zenon_H14 zenon_H17). % 0.55/0.82 exact (zenon_Hb zenon_H11). % 0.55/0.82 (* end of lemma zenon_L1_ *) % 0.55/0.82 assert (zenon_L2_ : forall (zenon_TT2_bc : zenon_U) (zenon_TX_n : zenon_U), ((greater (age zenon_TX_n zenon_TT2_bc) (eta))->(~(has_immunity zenon_TX_n zenon_TT2_bc))) -> (has_immunity zenon_TX_n zenon_TT2_bc) -> (greater (age zenon_TX_n zenon_TT2_bc) (eta)) -> False). % 0.55/0.82 do 2 intro. intros zenon_H19 zenon_H1a zenon_H1b. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.55/0.82 exact (zenon_H1e zenon_H1b). % 0.55/0.82 exact (zenon_H1d zenon_H1a). % 0.55/0.82 (* end of lemma zenon_L2_ *) % 0.55/0.82 assert (zenon_L3_ : forall (zenon_TT2_bc : zenon_U) (zenon_TT1_m : zenon_U) (zenon_TX_n : zenon_U), (organization zenon_TX_n) -> (has_immunity zenon_TX_n zenon_TT1_m) -> (forall T : zenon_U, ((organization zenon_TX_n)/\(((smaller_or_equal (age zenon_TX_n T) (eta))->(has_immunity zenon_TX_n T))/\((greater (age zenon_TX_n T) (eta))->(~(has_immunity zenon_TX_n T)))))) -> (greater (age zenon_TX_n zenon_TT2_bc) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_n zenon_TT2_bc) (hazard_of_mortality zenon_TX_n zenon_TT1_m))) -> False). % 0.55/0.82 do 3 intro. intros zenon_H1f zenon_H20 zenon_H21 zenon_H1b zenon_H22. % 0.55/0.82 generalize (assumption_3 zenon_TX_n). zenon_intro zenon_H23. % 0.55/0.82 generalize (zenon_H23 zenon_TT1_m). zenon_intro zenon_H24. % 0.55/0.82 generalize (zenon_H24 zenon_TT2_bc). zenon_intro zenon_H25. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.55/0.82 exact (zenon_H29 zenon_H1f). % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.55/0.82 exact (zenon_H2b zenon_H20). % 0.55/0.82 apply zenon_H2a. zenon_intro zenon_H1a. % 0.55/0.82 generalize (zenon_H21 zenon_TT2_bc). zenon_intro zenon_H2c. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H1f. zenon_intro zenon_H2d. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H2e. zenon_intro zenon_H19. % 0.55/0.82 apply (zenon_L2_ zenon_TT2_bc zenon_TX_n); trivial. % 0.55/0.82 exact (zenon_H22 zenon_H26). % 0.55/0.82 (* end of lemma zenon_L3_ *) % 0.55/0.82 assert (zenon_L4_ : forall (zenon_TT1_m : zenon_U) (zenon_TT2_bc : zenon_U) (zenon_TX_n : zenon_U), (~(greater (hazard_of_mortality zenon_TX_n zenon_TT2_bc) (hazard_of_mortality zenon_TX_n zenon_TT1_m))) -> (greater (age zenon_TX_n zenon_TT2_bc) (eta)) -> (forall T : zenon_U, ((organization zenon_TX_n)/\(((smaller_or_equal (age zenon_TX_n T) (eta))->(has_immunity zenon_TX_n T))/\((greater (age zenon_TX_n T) (eta))->(~(has_immunity zenon_TX_n T)))))) -> (greater (eta) (age zenon_TX_n zenon_TT1_m)) -> False). % 0.55/0.82 do 3 intro. intros zenon_H22 zenon_H1b zenon_H21 zenon_Ha. % 0.55/0.82 generalize (zenon_H21 zenon_TT1_m). zenon_intro zenon_H2f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H1f. zenon_intro zenon_H30. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_Hb | zenon_intro zenon_H20 ]. % 0.55/0.82 apply (zenon_L1_ zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L3_ zenon_TT2_bc zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 (* end of lemma zenon_L4_ *) % 0.55/0.82 assert (zenon_L5_ : (~((eta) = (eta))) -> False). % 0.55/0.82 do 0 intro. intros zenon_H33. % 0.55/0.82 apply zenon_H33. apply refl_equal. % 0.55/0.82 (* end of lemma zenon_L5_ *) % 0.55/0.82 assert (zenon_L6_ : (~((sigma) = (sigma))) -> False). % 0.55/0.82 do 0 intro. intros zenon_H34. % 0.55/0.82 apply zenon_H34. apply refl_equal. % 0.55/0.82 (* end of lemma zenon_L6_ *) % 0.55/0.82 assert (zenon_L7_ : forall (zenon_TT0_ce : zenon_U) (zenon_TX_n : zenon_U), (~(greater (sigma) (age zenon_TX_n zenon_TT0_ce))) -> (greater (sigma) (zero)) -> ((age zenon_TX_n zenon_TT0_ce) = (zero)) -> False). % 0.55/0.82 do 2 intro. intros zenon_H35 zenon_H36 zenon_H37. % 0.55/0.82 elim (classic ((zero) = (age zenon_TX_n zenon_TT0_ce))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 0.55/0.82 cut ((greater (sigma) (zero)) = (greater (sigma) (age zenon_TX_n zenon_TT0_ce))). % 0.55/0.82 intro zenon_D_pnotp. % 0.55/0.82 apply zenon_H35. % 0.55/0.82 rewrite <- zenon_D_pnotp. % 0.55/0.82 exact zenon_H36. % 0.55/0.82 cut (((zero) = (age zenon_TX_n zenon_TT0_ce))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 0.55/0.82 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 0.55/0.82 congruence. % 0.55/0.82 apply zenon_H34. apply refl_equal. % 0.55/0.82 exact (zenon_H3a zenon_H39). % 0.55/0.82 apply zenon_H3a. apply sym_equal. exact zenon_H37. % 0.55/0.82 (* end of lemma zenon_L7_ *) % 0.55/0.82 assert (zenon_L8_ : forall (zenon_TT0_ce : zenon_U) (zenon_TX_n : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (sigma) (zero)) -> ((age zenon_TX_n zenon_TT0_ce) = (zero)) -> (greater (eta) (sigma)) -> (~(smaller_or_equal (age zenon_TX_n zenon_TT0_ce) (eta))) -> False). % 0.55/0.82 do 2 intro. intros zenon_H3b zenon_H36 zenon_H37 zenon_H3c zenon_H3d. % 0.55/0.82 generalize (definition_smaller_or_equal (age zenon_TX_n zenon_TT0_ce)). zenon_intro zenon_H3e. % 0.55/0.82 generalize (zenon_H3e (eta)). zenon_intro zenon_H3f. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 0.55/0.82 apply (zenon_notor_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.55/0.82 generalize (definition_smaller (age zenon_TX_n zenon_TT0_ce)). zenon_intro zenon_H45. % 0.55/0.82 generalize (zenon_H45 (eta)). zenon_intro zenon_H46. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H44; zenon_intro zenon_H49 | zenon_intro zenon_H48; zenon_intro zenon_H47 ]. % 0.55/0.82 elim (classic (greater (sigma) (age zenon_TX_n zenon_TT0_ce))); [ zenon_intro zenon_H4a | zenon_intro zenon_H35 ]. % 0.55/0.82 generalize (zenon_H3b (eta)). zenon_intro zenon_H4b. % 0.55/0.82 generalize (zenon_H4b (sigma)). zenon_intro zenon_H4c. % 0.55/0.82 generalize (zenon_H4c (age zenon_TX_n zenon_TT0_ce)). zenon_intro zenon_H4d. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.55/0.82 exact (zenon_H4f zenon_H3c). % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H35 | zenon_intro zenon_H47 ]. % 0.55/0.82 exact (zenon_H35 zenon_H4a). % 0.55/0.82 exact (zenon_H49 zenon_H47). % 0.55/0.82 apply (zenon_L7_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 exact (zenon_H44 zenon_H48). % 0.55/0.82 exact (zenon_H3d zenon_H41). % 0.55/0.82 (* end of lemma zenon_L8_ *) % 0.55/0.82 assert (zenon_L9_ : forall (zenon_TT1_m : zenon_U) (zenon_TT0_ce : zenon_U) (zenon_TX_n : zenon_U), (organization zenon_TX_n) -> (has_immunity zenon_TX_n zenon_TT0_ce) -> (has_immunity zenon_TX_n zenon_TT1_m) -> (~((hazard_of_mortality zenon_TX_n zenon_TT1_m) = (hazard_of_mortality zenon_TX_n zenon_TT0_ce))) -> False). % 0.55/0.82 do 3 intro. intros zenon_H1f zenon_H50 zenon_H20 zenon_H51. % 0.55/0.82 generalize (assumption_2 zenon_TX_n). zenon_intro zenon_H52. % 0.55/0.82 generalize (zenon_H52 zenon_TT0_ce). zenon_intro zenon_H53. % 0.55/0.82 generalize (zenon_H53 zenon_TT1_m). zenon_intro zenon_H54. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H29 | zenon_intro zenon_H57 ]. % 0.55/0.82 exact (zenon_H29 zenon_H1f). % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H2b ]. % 0.55/0.82 exact (zenon_H58 zenon_H50). % 0.55/0.82 exact (zenon_H2b zenon_H20). % 0.55/0.82 apply zenon_H51. apply sym_equal. exact zenon_H55. % 0.55/0.82 (* end of lemma zenon_L9_ *) % 0.55/0.82 assert (zenon_L10_ : forall (zenon_TT0_ce : zenon_U) (zenon_TT1_m : zenon_U) (zenon_TX_n : zenon_U), (forall T : zenon_U, ((organization zenon_TX_n)/\(((smaller_or_equal (age zenon_TX_n T) (eta))->(has_immunity zenon_TX_n T))/\((greater (age zenon_TX_n T) (eta))->(~(has_immunity zenon_TX_n T)))))) -> (~((hazard_of_mortality zenon_TX_n zenon_TT1_m) = (hazard_of_mortality zenon_TX_n zenon_TT0_ce))) -> (has_immunity zenon_TX_n zenon_TT0_ce) -> (greater (eta) (age zenon_TX_n zenon_TT1_m)) -> False). % 0.55/0.82 do 3 intro. intros zenon_H21 zenon_H51 zenon_H50 zenon_Ha. % 0.55/0.82 generalize (zenon_H21 zenon_TT1_m). zenon_intro zenon_H2f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H1f. zenon_intro zenon_H30. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_Hb | zenon_intro zenon_H20 ]. % 0.55/0.82 apply (zenon_L1_ zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L9_ zenon_TT1_m zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 (* end of lemma zenon_L10_ *) % 0.55/0.82 assert (zenon_L11_ : forall (zenon_TT1_m : zenon_U) (zenon_TX_n : zenon_U), ((age zenon_TX_n zenon_TT1_m) = (eta)) -> (~(smaller_or_equal (age zenon_TX_n zenon_TT1_m) (eta))) -> False). % 0.55/0.82 do 2 intro. intros zenon_H59 zenon_Hb. % 0.55/0.82 generalize (definition_smaller_or_equal (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_He. % 0.55/0.82 generalize (zenon_He (eta)). zenon_intro zenon_Hf. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_Hb; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_H10 ]. % 0.55/0.82 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.55/0.82 exact (zenon_H13 zenon_H59). % 0.55/0.82 exact (zenon_Hb zenon_H11). % 0.55/0.82 (* end of lemma zenon_L11_ *) % 0.55/0.82 assert (zenon_L12_ : forall (zenon_TT1_m : zenon_U) (zenon_TT2_bc : zenon_U) (zenon_TX_n : zenon_U), (~(greater (hazard_of_mortality zenon_TX_n zenon_TT2_bc) (hazard_of_mortality zenon_TX_n zenon_TT1_m))) -> (greater (age zenon_TX_n zenon_TT2_bc) (eta)) -> (forall T : zenon_U, ((organization zenon_TX_n)/\(((smaller_or_equal (age zenon_TX_n T) (eta))->(has_immunity zenon_TX_n T))/\((greater (age zenon_TX_n T) (eta))->(~(has_immunity zenon_TX_n T)))))) -> ((age zenon_TX_n zenon_TT1_m) = (eta)) -> False). % 0.55/0.82 do 3 intro. intros zenon_H22 zenon_H1b zenon_H21 zenon_H59. % 0.55/0.82 generalize (zenon_H21 zenon_TT1_m). zenon_intro zenon_H2f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H1f. zenon_intro zenon_H30. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_Hb | zenon_intro zenon_H20 ]. % 0.55/0.82 apply (zenon_L11_ zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L3_ zenon_TT2_bc zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 (* end of lemma zenon_L12_ *) % 0.55/0.82 assert (zenon_L13_ : forall (zenon_TT0_ce : zenon_U) (zenon_TT1_m : zenon_U) (zenon_TX_n : zenon_U), ((smaller_or_equal (age zenon_TX_n zenon_TT1_m) (eta))->(has_immunity zenon_TX_n zenon_TT1_m)) -> (~((hazard_of_mortality zenon_TX_n zenon_TT1_m) = (hazard_of_mortality zenon_TX_n zenon_TT0_ce))) -> (has_immunity zenon_TX_n zenon_TT0_ce) -> (organization zenon_TX_n) -> ((age zenon_TX_n zenon_TT1_m) = (eta)) -> False). % 0.55/0.82 do 3 intro. intros zenon_H32 zenon_H51 zenon_H50 zenon_H1f zenon_H59. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_Hb | zenon_intro zenon_H20 ]. % 0.55/0.82 apply (zenon_L11_ zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L9_ zenon_TT1_m zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 (* end of lemma zenon_L13_ *) % 0.55/0.82 assert (zenon_L14_ : forall (zenon_TT0_ce : zenon_U) (zenon_TX_n : zenon_U), ((eta) = (sigma)) -> (~(greater (eta) (age zenon_TX_n zenon_TT0_ce))) -> (greater (sigma) (zero)) -> ((age zenon_TX_n zenon_TT0_ce) = (zero)) -> False). % 0.55/0.82 do 2 intro. intros zenon_H5a zenon_H49 zenon_H36 zenon_H37. % 0.55/0.82 elim (classic (greater (sigma) (age zenon_TX_n zenon_TT0_ce))); [ zenon_intro zenon_H4a | zenon_intro zenon_H35 ]. % 0.55/0.82 cut ((greater (sigma) (age zenon_TX_n zenon_TT0_ce)) = (greater (eta) (age zenon_TX_n zenon_TT0_ce))). % 0.55/0.82 intro zenon_D_pnotp. % 0.55/0.82 apply zenon_H49. % 0.55/0.82 rewrite <- zenon_D_pnotp. % 0.55/0.82 exact zenon_H4a. % 0.55/0.82 cut (((age zenon_TX_n zenon_TT0_ce) = (age zenon_TX_n zenon_TT0_ce))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 0.55/0.82 cut (((sigma) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 0.55/0.82 congruence. % 0.55/0.82 elim (classic ((eta) = (eta))); [ zenon_intro zenon_H5d | zenon_intro zenon_H33 ]. % 0.55/0.82 cut (((eta) = (eta)) = ((sigma) = (eta))). % 0.55/0.82 intro zenon_D_pnotp. % 0.55/0.82 apply zenon_H5c. % 0.55/0.82 rewrite <- zenon_D_pnotp. % 0.55/0.82 exact zenon_H5d. % 0.55/0.82 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.55/0.82 cut (((eta) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 0.55/0.82 congruence. % 0.55/0.82 exact (zenon_H5e zenon_H5a). % 0.55/0.82 apply zenon_H33. apply refl_equal. % 0.55/0.82 apply zenon_H33. apply refl_equal. % 0.55/0.82 apply zenon_H5b. apply refl_equal. % 0.55/0.82 apply (zenon_L7_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 (* end of lemma zenon_L14_ *) % 0.55/0.82 assert (zenon_L15_ : forall (zenon_TT0_ce : zenon_U) (zenon_TX_n : zenon_U), (greater (sigma) (zero)) -> ((age zenon_TX_n zenon_TT0_ce) = (zero)) -> ((eta) = (sigma)) -> (~(smaller_or_equal (age zenon_TX_n zenon_TT0_ce) (eta))) -> False). % 0.55/0.82 do 2 intro. intros zenon_H36 zenon_H37 zenon_H5a zenon_H3d. % 0.55/0.82 generalize (definition_smaller_or_equal (age zenon_TX_n zenon_TT0_ce)). zenon_intro zenon_H3e. % 0.55/0.82 generalize (zenon_H3e (eta)). zenon_intro zenon_H3f. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 0.55/0.82 apply (zenon_notor_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.55/0.82 generalize (definition_smaller (age zenon_TX_n zenon_TT0_ce)). zenon_intro zenon_H45. % 0.55/0.82 generalize (zenon_H45 (eta)). zenon_intro zenon_H46. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H44; zenon_intro zenon_H49 | zenon_intro zenon_H48; zenon_intro zenon_H47 ]. % 0.55/0.82 apply (zenon_L14_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 exact (zenon_H44 zenon_H48). % 0.55/0.82 exact (zenon_H3d zenon_H41). % 0.55/0.82 (* end of lemma zenon_L15_ *) % 0.55/0.82 apply NNPP. intro zenon_G. % 0.55/0.82 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_H3b | zenon_intro zenon_H5f ]. % 0.55/0.82 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) (eta))/\((greater (age X T2) (eta))/\((greater_or_equal (eta) (sigma))/\(greater (sigma) (zero))))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))) zenon_G); [ zenon_intro zenon_H60; idtac ]. % 0.55/0.82 elim zenon_H60. zenon_intro zenon_TX_n. zenon_intro zenon_H61. % 0.55/0.82 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization zenon_TX_n)/\((has_endowment zenon_TX_n)/\(((age zenon_TX_n T0) = (zero))/\((smaller_or_equal (age zenon_TX_n T1) (eta))/\((greater (age zenon_TX_n T2) (eta))/\((greater_or_equal (eta) (sigma))/\(greater (sigma) (zero))))))))->((greater (hazard_of_mortality zenon_TX_n T2) (hazard_of_mortality zenon_TX_n T1))/\((hazard_of_mortality zenon_TX_n T1) = (hazard_of_mortality zenon_TX_n T0))))))) zenon_H61); [ zenon_intro zenon_H62; idtac ]. % 0.55/0.82 elim zenon_H62. zenon_intro zenon_TT0_ce. zenon_intro zenon_H63. % 0.55/0.82 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (((organization zenon_TX_n)/\((has_endowment zenon_TX_n)/\(((age zenon_TX_n zenon_TT0_ce) = (zero))/\((smaller_or_equal (age zenon_TX_n T1) (eta))/\((greater (age zenon_TX_n T2) (eta))/\((greater_or_equal (eta) (sigma))/\(greater (sigma) (zero))))))))->((greater (hazard_of_mortality zenon_TX_n T2) (hazard_of_mortality zenon_TX_n T1))/\((hazard_of_mortality zenon_TX_n T1) = (hazard_of_mortality zenon_TX_n zenon_TT0_ce)))))) zenon_H63); [ zenon_intro zenon_H64; idtac ]. % 0.55/0.82 elim zenon_H64. zenon_intro zenon_TT1_m. zenon_intro zenon_H65. % 0.55/0.82 apply (zenon_notallex_s (fun T2 : zenon_U => (((organization zenon_TX_n)/\((has_endowment zenon_TX_n)/\(((age zenon_TX_n zenon_TT0_ce) = (zero))/\((smaller_or_equal (age zenon_TX_n zenon_TT1_m) (eta))/\((greater (age zenon_TX_n T2) (eta))/\((greater_or_equal (eta) (sigma))/\(greater (sigma) (zero))))))))->((greater (hazard_of_mortality zenon_TX_n T2) (hazard_of_mortality zenon_TX_n zenon_TT1_m))/\((hazard_of_mortality zenon_TX_n zenon_TT1_m) = (hazard_of_mortality zenon_TX_n zenon_TT0_ce))))) zenon_H65); [ zenon_intro zenon_H66; idtac ]. % 0.55/0.82 elim zenon_H66. zenon_intro zenon_TT2_bc. zenon_intro zenon_H67. % 0.55/0.82 apply (zenon_notimply_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H1f. zenon_intro zenon_H6a. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H37. zenon_intro zenon_H6d. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H11. zenon_intro zenon_H6e. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H1b. zenon_intro zenon_H6f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H70. zenon_intro zenon_H36. % 0.55/0.82 generalize (definition_1 zenon_TX_n). zenon_intro zenon_H71. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H71); [ zenon_intro zenon_H73; zenon_intro zenon_H72 | zenon_intro zenon_H6c; zenon_intro zenon_H21 ]. % 0.55/0.82 exact (zenon_H73 zenon_H6c). % 0.55/0.82 generalize (definition_smaller_or_equal (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_He. % 0.55/0.82 generalize (zenon_He (eta)). zenon_intro zenon_Hf. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_Hb; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_H10 ]. % 0.55/0.82 exact (zenon_Hb zenon_H11). % 0.55/0.82 generalize (definition_greater_or_equal (eta)). zenon_intro zenon_H74. % 0.55/0.82 generalize (zenon_H74 (sigma)). zenon_intro zenon_H75. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H75); [ zenon_intro zenon_H78; zenon_intro zenon_H77 | zenon_intro zenon_H70; zenon_intro zenon_H76 ]. % 0.55/0.82 exact (zenon_H78 zenon_H70). % 0.55/0.82 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H3c | zenon_intro zenon_H5a ]. % 0.55/0.82 apply (zenon_or_s _ _ zenon_H10); [ zenon_intro zenon_H17 | zenon_intro zenon_H59 ]. % 0.55/0.82 generalize (definition_smaller (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_H15. % 0.55/0.82 generalize (zenon_H15 (eta)). zenon_intro zenon_H16. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_Ha ]. % 0.55/0.82 exact (zenon_H14 zenon_H17). % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H22 | zenon_intro zenon_H51 ]. % 0.55/0.82 apply (zenon_L4_ zenon_TT1_m zenon_TT2_bc zenon_TX_n); trivial. % 0.55/0.82 generalize (zenon_H21 zenon_TT0_ce). zenon_intro zenon_H79. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H1f. zenon_intro zenon_H7a. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H3d | zenon_intro zenon_H50 ]. % 0.55/0.82 apply (zenon_L8_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L10_ zenon_TT0_ce zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H22 | zenon_intro zenon_H51 ]. % 0.55/0.82 apply (zenon_L12_ zenon_TT1_m zenon_TT2_bc zenon_TX_n); trivial. % 0.55/0.82 generalize (zenon_H21 zenon_TT1_m). zenon_intro zenon_H2f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H1f. zenon_intro zenon_H30. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.55/0.82 generalize (zenon_H21 zenon_TT0_ce). zenon_intro zenon_H79. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H1f. zenon_intro zenon_H7a. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H3d | zenon_intro zenon_H50 ]. % 0.55/0.82 apply (zenon_L8_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L13_ zenon_TT0_ce zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_or_s _ _ zenon_H10); [ zenon_intro zenon_H17 | zenon_intro zenon_H59 ]. % 0.55/0.82 generalize (definition_smaller (age zenon_TX_n zenon_TT1_m)). zenon_intro zenon_H15. % 0.55/0.82 generalize (zenon_H15 (eta)). zenon_intro zenon_H16. % 0.55/0.82 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_Ha ]. % 0.55/0.82 exact (zenon_H14 zenon_H17). % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H22 | zenon_intro zenon_H51 ]. % 0.55/0.82 apply (zenon_L4_ zenon_TT1_m zenon_TT2_bc zenon_TX_n); trivial. % 0.55/0.82 generalize (zenon_H21 zenon_TT0_ce). zenon_intro zenon_H79. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H1f. zenon_intro zenon_H7a. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H3d | zenon_intro zenon_H50 ]. % 0.55/0.82 apply (zenon_L15_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_L10_ zenon_TT0_ce zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H22 | zenon_intro zenon_H51 ]. % 0.55/0.82 apply (zenon_L12_ zenon_TT1_m zenon_TT2_bc zenon_TX_n); trivial. % 0.55/0.82 generalize (zenon_H21 zenon_TT0_ce). zenon_intro zenon_H79. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H1f. zenon_intro zenon_H7a. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H3d | zenon_intro zenon_H50 ]. % 0.55/0.82 apply (zenon_L15_ zenon_TT0_ce zenon_TX_n); trivial. % 0.55/0.82 generalize (zenon_H21 zenon_TT1_m). zenon_intro zenon_H2f. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H1f. zenon_intro zenon_H30. % 0.55/0.82 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.55/0.82 apply (zenon_L13_ zenon_TT0_ce zenon_TT1_m zenon_TX_n); trivial. % 0.55/0.82 apply zenon_H5f. zenon_intro zenon_Tx_ev. apply NNPP. zenon_intro zenon_H7e. % 0.55/0.82 apply zenon_H7e. zenon_intro zenon_Ty_ex. apply NNPP. zenon_intro zenon_H80. % 0.55/0.82 apply zenon_H80. zenon_intro zenon_Tz_ez. apply NNPP. zenon_intro zenon_H82. % 0.55/0.82 apply (zenon_notimply_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83. % 0.55/0.82 apply (zenon_notimply_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 0.55/0.82 generalize (meaning_postulate_greater_transitive zenon_Tx_ev). zenon_intro zenon_H87. % 0.55/0.82 generalize (zenon_H87 zenon_Ty_ex). zenon_intro zenon_H88. % 0.55/0.82 generalize (zenon_H88 zenon_Tz_ez). zenon_intro zenon_H89. % 0.55/0.82 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 0.55/0.82 apply (zenon_notand_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ]. % 0.55/0.82 exact (zenon_H8d zenon_H84). % 0.55/0.82 exact (zenon_H8c zenon_H86). % 0.55/0.82 exact (zenon_H85 zenon_H8a). % 0.55/0.82 Qed. % 0.55/0.82 % SZS output end Proof % 0.55/0.82 (* END-PROOF *) % 0.55/0.82 nodes searched: 42875 % 0.55/0.82 max branch formulas: 1139 % 0.55/0.82 proof nodes created: 536 % 0.55/0.82 formulas created: 22561 % 0.55/0.82 %------------------------------------------------------------------------------