TSTP Solution File: MGT047+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT047+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:31:10 EDT 2022
% Result : Theorem 35.76s 35.93s
% Output : Proof 35.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : MGT047+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.13 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 9 12:13:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 35.76/35.93 (* PROOF-FOUND *)
% 35.76/35.93 % SZS status Theorem
% 35.76/35.93 (* BEGIN-PROOF *)
% 35.76/35.93 % SZS output start Proof
% 35.76/35.93 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)))))))))).
% 35.76/35.93 Proof.
% 35.76/35.93 assert (zenon_L1_ : (~((eta) = (eta))) -> False).
% 35.76/35.93 do 0 intro. intros zenon_H11.
% 35.76/35.93 apply zenon_H11. apply refl_equal.
% 35.76/35.93 (* end of lemma zenon_L1_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H12 zenon_H13 zenon_H14 zenon_H15.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19.
% 35.76/35.93 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20.
% 35.76/35.93 generalize (zenon_H20 (eta)). zenon_intro zenon_H21.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 35.76/35.93 generalize (zenon_H12 (eta)). zenon_intro zenon_H25.
% 35.76/35.93 generalize (zenon_H25 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H26.
% 35.76/35.93 generalize (zenon_H26 (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H27.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 35.76/35.93 exact (zenon_H29 zenon_H14).
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H22 ].
% 35.76/35.93 exact (zenon_H2a zenon_H13).
% 35.76/35.93 exact (zenon_H24 zenon_H22).
% 35.76/35.93 exact (zenon_H1f zenon_H23).
% 35.76/35.93 exact (zenon_H15 zenon_H1c).
% 35.76/35.93 (* end of lemma zenon_L2_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_H14 zenon_H2b.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c.
% 35.76/35.93 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H33.
% 35.76/35.93 generalize (zenon_H33 (eta)). zenon_intro zenon_H34.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H32; zenon_intro zenon_H29 | zenon_intro zenon_H35; zenon_intro zenon_H14 ].
% 35.76/35.93 exact (zenon_H29 zenon_H14).
% 35.76/35.93 exact (zenon_H32 zenon_H35).
% 35.76/35.93 exact (zenon_H2b zenon_H2f).
% 35.76/35.93 (* end of lemma zenon_L3_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_H36.
% 35.76/35.93 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H38.
% 35.76/35.93 generalize (zenon_H38 (stock_of_knowledge zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H39.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H36; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H3a ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 35.76/35.93 apply zenon_H3d. apply refl_equal.
% 35.76/35.93 exact (zenon_H36 zenon_H3b).
% 35.76/35.93 (* end of lemma zenon_L4_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H3f zenon_H40 zenon_H41 zenon_H42.
% 35.76/35.93 generalize (zenon_H3f (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H44.
% 35.76/35.93 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 35.76/35.93 generalize (definition_smaller (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H47.
% 35.76/35.93 generalize (zenon_H47 (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H48.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H4a; zenon_intro zenon_H40 | zenon_intro zenon_H46; zenon_intro zenon_H49 ].
% 35.76/35.93 exact (zenon_H4a zenon_H46).
% 35.76/35.93 exact (zenon_H40 zenon_H49).
% 35.76/35.93 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 35.76/35.93 exact (zenon_H41 zenon_H4c).
% 35.76/35.93 exact (zenon_H42 zenon_H4b).
% 35.76/35.93 (* end of lemma zenon_L5_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_H4d zenon_H4e zenon_H4f.
% 35.76/35.93 generalize (zenon_H4d zenon_TT2_cd). zenon_intro zenon_H50.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 exact (zenon_H4f zenon_H51).
% 35.76/35.93 (* end of lemma zenon_L6_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_H53.
% 35.76/35.93 generalize (meaning_postulate_greater_strict (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H54.
% 35.76/35.93 generalize (zenon_H54 (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H55.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ].
% 35.76/35.93 exact (zenon_H56 zenon_H53).
% 35.76/35.93 exact (zenon_H56 zenon_H53).
% 35.76/35.93 (* end of lemma zenon_L7_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_H57.
% 35.76/35.93 generalize (definition_smaller (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H58.
% 35.76/35.93 generalize (zenon_H58 (capability zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H59.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5a; zenon_intro zenon_H56 | zenon_intro zenon_H57; zenon_intro zenon_H53 ].
% 35.76/35.93 exact (zenon_H5a zenon_H57).
% 35.76/35.93 apply (zenon_L7_ zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L8_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H5b zenon_H4e zenon_H5c zenon_H41 zenon_H40 zenon_H3f zenon_H4d.
% 35.76/35.93 generalize (zenon_H5b zenon_TT2_cd). zenon_intro zenon_H5d.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H52 | zenon_intro zenon_H5e ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H5f.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H63 | zenon_intro zenon_H57 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H36 | zenon_intro zenon_H64 ].
% 35.76/35.93 apply (zenon_L4_ zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 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 ].
% 35.76/35.93 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 ].
% 35.76/35.93 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 ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H64.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H67.
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 35.76/35.93 congruence.
% 35.76/35.93 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 ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H6a.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H6b.
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 35.76/35.93 congruence.
% 35.76/35.93 apply (zenon_L6_ zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 apply zenon_H69. apply refl_equal.
% 35.76/35.93 apply zenon_H69. apply refl_equal.
% 35.76/35.93 apply zenon_H69. apply refl_equal.
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H68.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H4b.
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT2_cd) = (internal_friction zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 35.76/35.93 congruence.
% 35.76/35.93 elim (classic ((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_E))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H6c.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H6d.
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6e].
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_E) = (internal_friction zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 35.76/35.93 congruence.
% 35.76/35.93 exact (zenon_H66 zenon_H65).
% 35.76/35.93 apply zenon_H6e. apply refl_equal.
% 35.76/35.93 apply zenon_H6e. apply refl_equal.
% 35.76/35.93 apply zenon_H69. apply refl_equal.
% 35.76/35.93 apply (zenon_L5_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 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 ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H66.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H6f.
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 35.76/35.93 cut (((internal_friction zenon_TX_y zenon_TT3_cp) = (internal_friction zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 35.76/35.93 congruence.
% 35.76/35.93 exact (zenon_H6c zenon_H5c).
% 35.76/35.93 apply zenon_H70. apply refl_equal.
% 35.76/35.93 apply zenon_H70. apply refl_equal.
% 35.76/35.93 apply (zenon_L8_ zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L9_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H71 zenon_H72 zenon_H73 zenon_H4e.
% 35.76/35.93 generalize (zenon_H71 zenon_TT2_cd). zenon_intro zenon_H74.
% 35.76/35.93 generalize (zenon_H74 zenon_TT3_cp). zenon_intro zenon_H75.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H52 | zenon_intro zenon_H76 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ].
% 35.76/35.93 generalize (assumption_8 zenon_TX_y). zenon_intro zenon_H7b.
% 35.76/35.93 generalize (zenon_H7b zenon_TT2_cd). zenon_intro zenon_H7c.
% 35.76/35.93 generalize (zenon_H7c zenon_TT3_cp). zenon_intro zenon_H7d.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H52 | zenon_intro zenon_H80 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 exact (zenon_H80 zenon_H73).
% 35.76/35.93 exact (zenon_H7a zenon_H7e).
% 35.76/35.93 exact (zenon_H72 zenon_H79).
% 35.76/35.93 (* end of lemma zenon_L10_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H4e zenon_H73 zenon_H72.
% 35.76/35.93 generalize (assumption_6 zenon_TX_y). zenon_intro zenon_H71.
% 35.76/35.93 apply (zenon_L10_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L11_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H4e zenon_H73 zenon_H81.
% 35.76/35.93 generalize (definition_greater_or_equal (position zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H82.
% 35.76/35.93 generalize (zenon_H82 (position zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H83.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H81; zenon_intro zenon_H86 | zenon_intro zenon_H85; zenon_intro zenon_H84 ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H72. zenon_intro zenon_H87.
% 35.76/35.93 apply (zenon_L11_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 exact (zenon_H81 zenon_H85).
% 35.76/35.93 (* end of lemma zenon_L12_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H88 zenon_H89.
% 35.76/35.93 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H8a.
% 35.76/35.93 generalize (zenon_H8a (hazard_of_mortality zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H8b.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H8b); [ zenon_intro zenon_H8d; zenon_intro zenon_H89 | zenon_intro zenon_H88; zenon_intro zenon_H8c ].
% 35.76/35.93 exact (zenon_H8d zenon_H88).
% 35.76/35.93 exact (zenon_H89 zenon_H8c).
% 35.76/35.93 (* end of lemma zenon_L13_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H8e zenon_H89 zenon_H73 zenon_H8f zenon_H90 zenon_H91 zenon_H4e.
% 35.76/35.93 generalize (assumption_9 zenon_TX_y). zenon_intro zenon_H0.
% 35.76/35.93 generalize (zenon_H0 zenon_E). zenon_intro zenon_H4d.
% 35.76/35.93 generalize (assumption_7 zenon_TX_y). zenon_intro zenon_H92.
% 35.76/35.93 generalize (zenon_H4d zenon_TT3_cp). zenon_intro zenon_H93.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H52 | zenon_intro zenon_H5c ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 generalize (meaning_postulate_greater_comparable (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H3f.
% 35.76/35.93 generalize (zenon_H8e zenon_TT2_cd). zenon_intro zenon_H94.
% 35.76/35.93 generalize (zenon_H94 zenon_TT3_cp). zenon_intro zenon_H95.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H52 | zenon_intro zenon_H98 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ].
% 35.76/35.93 exact (zenon_H9a zenon_H91).
% 35.76/35.93 exact (zenon_H99 zenon_H90).
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H9c. zenon_intro zenon_H9b.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H9c); [ zenon_intro zenon_H9d | zenon_intro zenon_H88 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_H9e | zenon_intro zenon_H81 ].
% 35.76/35.93 generalize (zenon_H8f zenon_TT2_cd). zenon_intro zenon_H5b.
% 35.76/35.93 generalize (zenon_H5b zenon_TT3_cp). zenon_intro zenon_H9f.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H9f); [ zenon_intro zenon_H52 | zenon_intro zenon_Ha0 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ].
% 35.76/35.93 generalize (zenon_H92 zenon_TT2_cd). zenon_intro zenon_Ha7.
% 35.76/35.93 generalize (zenon_Ha7 zenon_TT3_cp). zenon_intro zenon_Ha8.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_H7f | zenon_intro zenon_Ha9 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H52 | zenon_intro zenon_H80 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 exact (zenon_H80 zenon_H73).
% 35.76/35.93 exact (zenon_Ha6 zenon_Ha9).
% 35.76/35.93 generalize (definition_smaller_or_equal (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_Haa.
% 35.76/35.93 generalize (zenon_Haa (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_Hab.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_Hab); [ zenon_intro zenon_Ha5; zenon_intro zenon_Hae | zenon_intro zenon_Had; zenon_intro zenon_Hac ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_Hae). zenon_intro zenon_H4a. zenon_intro zenon_H41.
% 35.76/35.93 generalize (definition_smaller (internal_friction zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_H47.
% 35.76/35.93 generalize (zenon_H47 (internal_friction zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_H48.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H4a; zenon_intro zenon_H40 | zenon_intro zenon_H46; zenon_intro zenon_H49 ].
% 35.76/35.93 apply (zenon_L9_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 exact (zenon_H4a zenon_H46).
% 35.76/35.93 exact (zenon_Ha5 zenon_Had).
% 35.76/35.93 exact (zenon_H9e zenon_Ha3).
% 35.76/35.93 apply (zenon_L12_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L13_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L14_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H4e zenon_H91 zenon_H90 zenon_H73 zenon_H89 zenon_H8e.
% 35.76/35.93 generalize (assumption_5 zenon_TX_y). zenon_intro zenon_H8f.
% 35.76/35.93 apply (zenon_L14_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L15_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_Haf zenon_H4e zenon_Hb0 zenon_H91 zenon_H73 zenon_H89 zenon_H8e zenon_Hb1.
% 35.76/35.93 generalize (zenon_Haf zenon_TT3_cp). zenon_intro zenon_Hb2.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H52 | zenon_intro zenon_Hb5 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H90 ].
% 35.76/35.93 exact (zenon_Hb6 zenon_Hb0).
% 35.76/35.93 apply (zenon_L15_ zenon_TT3_cp zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 exact (zenon_Hb1 zenon_Hb3).
% 35.76/35.93 (* end of lemma zenon_L16_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Hb7 zenon_H4e zenon_Hb8 zenon_H91 zenon_Hb9.
% 35.76/35.93 generalize (zenon_Hb7 zenon_TT2_cd). zenon_intro zenon_Hba.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_H52 | zenon_intro zenon_Hbd ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbe | zenon_intro zenon_H9a ].
% 35.76/35.93 exact (zenon_Hbe zenon_Hb8).
% 35.76/35.93 exact (zenon_H9a zenon_H91).
% 35.76/35.93 exact (zenon_Hb9 zenon_Hbb).
% 35.76/35.93 (* end of lemma zenon_L17_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Hbf zenon_Hb9 zenon_H91 zenon_Hb8 zenon_H4e.
% 35.76/35.93 generalize (zenon_Hbf zenon_TT1_x). zenon_intro zenon_Hb7.
% 35.76/35.93 apply (zenon_L17_ zenon_TT2_cd zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L18_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 5 intro. intros zenon_H4e zenon_Hb0 zenon_Hb8 zenon_H89 zenon_H73 zenon_H91.
% 35.76/35.93 generalize (assumption_3 zenon_TX_y). zenon_intro zenon_Hbf.
% 35.76/35.93 generalize (assumption_4 zenon_TX_y). zenon_intro zenon_H8e.
% 35.76/35.93 generalize (assumption_2 zenon_TX_y). zenon_intro zenon_Hc0.
% 35.76/35.93 generalize (zenon_Hc0 zenon_TT0_w). zenon_intro zenon_Haf.
% 35.76/35.93 generalize (zenon_Haf zenon_TT1_x). zenon_intro zenon_Hc1.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc4 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbe ].
% 35.76/35.93 exact (zenon_Hb6 zenon_Hb0).
% 35.76/35.93 exact (zenon_Hbe zenon_Hb8).
% 35.76/35.93 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 ].
% 35.76/35.93 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 ].
% 35.76/35.93 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 ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H89.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hc7.
% 35.76/35.93 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].
% 35.76/35.93 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].
% 35.76/35.93 congruence.
% 35.76/35.93 apply zenon_Hc9. apply refl_equal.
% 35.76/35.93 apply (zenon_L16_ zenon_TT3_cp zenon_TT2_cd zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_Hc8.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hbb.
% 35.76/35.93 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].
% 35.76/35.93 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].
% 35.76/35.93 congruence.
% 35.76/35.93 apply zenon_Hc9. apply refl_equal.
% 35.76/35.93 exact (zenon_Hc6 zenon_Hc5).
% 35.76/35.93 apply (zenon_L18_ zenon_TT1_x zenon_TT2_cd zenon_TX_y); trivial.
% 35.76/35.93 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 ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_Hc6.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hca.
% 35.76/35.93 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].
% 35.76/35.93 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].
% 35.76/35.93 congruence.
% 35.76/35.93 exact (zenon_Hcc zenon_Hc2).
% 35.76/35.93 apply zenon_Hcb. apply refl_equal.
% 35.76/35.93 apply zenon_Hcb. apply refl_equal.
% 35.76/35.93 (* end of lemma zenon_L19_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H12 zenon_Hcd zenon_Hce zenon_H73 zenon_Hcf.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT3_cp). zenon_intro zenon_Hd0.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_H4e. zenon_intro zenon_Hd1.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hd2); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H90 ].
% 35.76/35.93 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 ].
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_Hd7. zenon_intro zenon_H80.
% 35.76/35.93 exact (zenon_H80 zenon_H73).
% 35.76/35.93 cut ((greater (age zenon_TX_y zenon_TT2_cd) (eta)) = (greater (age zenon_TX_y zenon_TT3_cp) (eta))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_Hd4.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hcf.
% 35.76/35.93 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11].
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT2_cd) = (age zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_Hd8].
% 35.76/35.93 congruence.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hda | zenon_intro zenon_Hd9 ].
% 35.76/35.93 apply zenon_Hda. zenon_intro zenon_Hdb.
% 35.76/35.93 elim (classic ((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT3_cp))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdd ].
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_Hd8.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hdc.
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT3_cp))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT3_cp) = (age zenon_TX_y zenon_TT2_cd))); [idtac | apply NNPP; zenon_intro zenon_Hd7].
% 35.76/35.93 congruence.
% 35.76/35.93 exact (zenon_Hd7 zenon_Hdb).
% 35.76/35.93 apply zenon_Hdd. apply refl_equal.
% 35.76/35.93 apply zenon_Hdd. apply refl_equal.
% 35.76/35.93 apply zenon_Hd9. zenon_intro zenon_H73.
% 35.76/35.93 generalize (zenon_H12 (age zenon_TX_y zenon_TT3_cp)). zenon_intro zenon_Hde.
% 35.76/35.93 generalize (zenon_Hde (age zenon_TX_y zenon_TT2_cd)). zenon_intro zenon_Hdf.
% 35.76/35.93 generalize (zenon_Hdf (eta)). zenon_intro zenon_He0.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_H80 | zenon_intro zenon_He1 ].
% 35.76/35.93 exact (zenon_H80 zenon_H73).
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_He1); [ zenon_intro zenon_He3 | zenon_intro zenon_He2 ].
% 35.76/35.93 exact (zenon_He3 zenon_Hcf).
% 35.76/35.93 exact (zenon_Hd4 zenon_He2).
% 35.76/35.93 apply zenon_H11. apply refl_equal.
% 35.76/35.93 exact (zenon_H90 zenon_Hce).
% 35.76/35.93 (* end of lemma zenon_L20_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_H12 zenon_Hb7 zenon_H4e zenon_Hb8 zenon_Hcd zenon_H73 zenon_Hcf zenon_He4.
% 35.76/35.93 generalize (zenon_Hb7 zenon_TT3_cp). zenon_intro zenon_He5.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_He7); [ zenon_intro zenon_H52 | zenon_intro zenon_He8 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_He8); [ zenon_intro zenon_Hbe | zenon_intro zenon_H99 ].
% 35.76/35.93 exact (zenon_Hbe zenon_Hb8).
% 35.76/35.93 apply zenon_H99. zenon_intro zenon_Hce.
% 35.76/35.93 apply (zenon_L20_ zenon_TT2_cd zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 exact (zenon_He4 zenon_He6).
% 35.76/35.93 (* end of lemma zenon_L21_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_H12 zenon_Hbf zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_Hb8 zenon_H4e.
% 35.76/35.93 generalize (zenon_Hbf zenon_TT1_x). zenon_intro zenon_Hb7.
% 35.76/35.93 apply (zenon_L21_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L22_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_H12 zenon_H4e zenon_Hb8 zenon_Hcd zenon_H73 zenon_Hcf zenon_He4.
% 35.76/35.93 generalize (assumption_3 zenon_TX_y). zenon_intro zenon_Hbf.
% 35.76/35.93 apply (zenon_L22_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L23_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_H12 zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_H14.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L23_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L24_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Haf zenon_H4e zenon_Hb0 zenon_Hb8 zenon_Hc6.
% 35.76/35.93 generalize (zenon_Haf zenon_TT1_x). zenon_intro zenon_Hc1.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc4 ].
% 35.76/35.93 exact (zenon_H52 zenon_H4e).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hbe ].
% 35.76/35.93 exact (zenon_Hb6 zenon_Hb0).
% 35.76/35.93 exact (zenon_Hbe zenon_Hb8).
% 35.76/35.93 apply zenon_Hc6. apply sym_equal. exact zenon_Hc2.
% 35.76/35.93 (* end of lemma zenon_L25_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H4e zenon_Hb0 zenon_Hb8 zenon_Hc6.
% 35.76/35.93 generalize (assumption_2 zenon_TX_y). zenon_intro zenon_Hc0.
% 35.76/35.93 generalize (zenon_Hc0 zenon_TT0_w). zenon_intro zenon_Haf.
% 35.76/35.93 apply (zenon_L25_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L26_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Hed zenon_H14 zenon_H15.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19.
% 35.76/35.93 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20.
% 35.76/35.93 generalize (zenon_H20 (eta)). zenon_intro zenon_H21.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 35.76/35.93 cut ((greater (eta) (age zenon_TX_y zenon_TT1_x)) = (greater (eta) (age zenon_TX_y zenon_TT0_w))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H24.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H14.
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT1_x) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hee].
% 35.76/35.93 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11].
% 35.76/35.93 congruence.
% 35.76/35.93 apply zenon_H11. apply refl_equal.
% 35.76/35.93 apply zenon_Hee. apply sym_equal. exact zenon_Hed.
% 35.76/35.93 exact (zenon_H1f zenon_H23).
% 35.76/35.93 exact (zenon_H15 zenon_H1c).
% 35.76/35.93 (* end of lemma zenon_L27_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 2 intro. intros zenon_Hef zenon_H2b.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c.
% 35.76/35.93 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 35.76/35.93 exact (zenon_H31 zenon_Hef).
% 35.76/35.93 exact (zenon_H2b zenon_H2f).
% 35.76/35.93 (* end of lemma zenon_L28_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H12 zenon_Hef zenon_H13 zenon_H15.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19.
% 35.76/35.93 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20.
% 35.76/35.93 generalize (zenon_H20 (eta)). zenon_intro zenon_H21.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 35.76/35.93 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 ].
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hf2. zenon_intro zenon_H29.
% 35.76/35.93 apply zenon_Hf2. apply sym_equal. exact zenon_Hef.
% 35.76/35.93 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))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H24.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_H13.
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hf3].
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT1_x) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 35.76/35.93 congruence.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ].
% 35.76/35.93 apply zenon_Hf5. zenon_intro zenon_Hf6.
% 35.76/35.93 elim (classic ((eta) = (eta))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H11 ].
% 35.76/35.93 cut (((eta) = (eta)) = ((age zenon_TX_y zenon_TT1_x) = (eta))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H31.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hf7.
% 35.76/35.93 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H11].
% 35.76/35.93 cut (((eta) = (age zenon_TX_y zenon_TT1_x))); [idtac | apply NNPP; zenon_intro zenon_Hf2].
% 35.76/35.93 congruence.
% 35.76/35.93 exact (zenon_Hf2 zenon_Hf6).
% 35.76/35.93 apply zenon_H11. apply refl_equal.
% 35.76/35.93 apply zenon_H11. apply refl_equal.
% 35.76/35.93 apply zenon_Hf4. zenon_intro zenon_H14.
% 35.76/35.93 generalize (zenon_H12 (eta)). zenon_intro zenon_H25.
% 35.76/35.93 generalize (zenon_H25 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H26.
% 35.76/35.93 generalize (zenon_H26 (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H27.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 35.76/35.93 exact (zenon_H29 zenon_H14).
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H22 ].
% 35.76/35.93 exact (zenon_H2a zenon_H13).
% 35.76/35.93 exact (zenon_H24 zenon_H22).
% 35.76/35.93 apply zenon_Hf3. apply refl_equal.
% 35.76/35.93 exact (zenon_H1f zenon_H23).
% 35.76/35.93 exact (zenon_H15 zenon_H1c).
% 35.76/35.93 (* end of lemma zenon_L29_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 4 intro. intros zenon_H12 zenon_He4 zenon_Hcf zenon_H73 zenon_Hcd zenon_Hef.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L23_ zenon_TT2_cd zenon_TT3_cp zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L30_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_H1e zenon_Hed zenon_Hef.
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT1_x)) = ((age zenon_TX_y zenon_TT0_w) = (eta))).
% 35.76/35.93 intro zenon_D_pnotp.
% 35.76/35.93 apply zenon_H1e.
% 35.76/35.93 rewrite <- zenon_D_pnotp.
% 35.76/35.93 exact zenon_Hed.
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT1_x) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 35.76/35.93 cut (((age zenon_TX_y zenon_TT0_w) = (age zenon_TX_y zenon_TT0_w))); [idtac | apply NNPP; zenon_intro zenon_Hf3].
% 35.76/35.93 congruence.
% 35.76/35.93 apply zenon_Hf3. apply refl_equal.
% 35.76/35.93 exact (zenon_H31 zenon_Hef).
% 35.76/35.93 (* end of lemma zenon_L31_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Hed zenon_Hef zenon_H15.
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19.
% 35.76/35.93 generalize (zenon_H19 (eta)). zenon_intro zenon_H1a.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ].
% 35.76/35.93 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 35.76/35.93 apply (zenon_L31_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 exact (zenon_H15 zenon_H1c).
% 35.76/35.93 (* end of lemma zenon_L32_ *)
% 35.76/35.93 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).
% 35.76/35.93 do 3 intro. intros zenon_Hed zenon_Hc6 zenon_Hcd zenon_Hef.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L32_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 (* end of lemma zenon_L33_ *)
% 35.76/35.93 apply NNPP. intro zenon_G.
% 35.76/35.93 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 ].
% 35.76/35.93 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 ].
% 35.76/35.93 elim zenon_Hfd. zenon_intro zenon_TX_y. zenon_intro zenon_Hfe.
% 35.76/35.93 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 ].
% 35.76/35.93 elim zenon_Hff. zenon_intro zenon_TT0_w. zenon_intro zenon_H100.
% 35.76/35.93 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 ].
% 35.76/35.93 elim zenon_H101. zenon_intro zenon_TT1_x. zenon_intro zenon_H102.
% 35.76/35.93 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 ].
% 35.76/35.93 elim zenon_H103. zenon_intro zenon_TT2_cd. zenon_intro zenon_H104.
% 35.76/35.93 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 ].
% 35.76/35.93 elim zenon_H105. zenon_intro zenon_TT3_cp. zenon_intro zenon_H106.
% 35.76/35.93 apply (zenon_notimply_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H4e. zenon_intro zenon_H109.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10b. zenon_intro zenon_H10a.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H10a). zenon_intro zenon_H10d. zenon_intro zenon_H10c.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H10c). zenon_intro zenon_H2f. zenon_intro zenon_H10e.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H10e). zenon_intro zenon_Hcf. zenon_intro zenon_H73.
% 35.76/35.93 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H10f.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H10f); [ zenon_intro zenon_H111; zenon_intro zenon_H110 | zenon_intro zenon_H10b; zenon_intro zenon_Hcd ].
% 35.76/35.93 exact (zenon_H111 zenon_H10b).
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H19.
% 35.76/35.93 generalize (zenon_H19 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H112.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H112); [ zenon_intro zenon_H115; zenon_intro zenon_H114 | zenon_intro zenon_H10d; zenon_intro zenon_H113 ].
% 35.76/35.93 exact (zenon_H115 zenon_H10d).
% 35.76/35.93 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H2c.
% 35.76/35.93 generalize (zenon_H2c (eta)). zenon_intro zenon_H2d.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ].
% 35.76/35.93 exact (zenon_H2b zenon_H2f).
% 35.76/35.93 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H35 | zenon_intro zenon_Hef ].
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H33.
% 35.76/35.93 generalize (zenon_H33 (eta)). zenon_intro zenon_H34.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H32; zenon_intro zenon_H29 | zenon_intro zenon_H35; zenon_intro zenon_H14 ].
% 35.76/35.93 exact (zenon_H32 zenon_H35).
% 35.76/35.93 apply (zenon_or_s _ _ zenon_H113); [ zenon_intro zenon_H116 | zenon_intro zenon_Hed ].
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20.
% 35.76/35.93 generalize (zenon_H20 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H117.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H117); [ zenon_intro zenon_H118; zenon_intro zenon_H2a | zenon_intro zenon_H116; zenon_intro zenon_H13 ].
% 35.76/35.93 exact (zenon_H118 zenon_H116).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ].
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L2_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ].
% 35.76/35.93 exact (zenon_He3 zenon_Hcf).
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ].
% 35.76/35.93 apply (zenon_L24_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L2_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ].
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L27_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ].
% 35.76/35.93 exact (zenon_He3 zenon_Hcf).
% 35.76/35.93 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ].
% 35.76/35.93 apply (zenon_L24_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L3_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L27_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_or_s _ _ zenon_H113); [ zenon_intro zenon_H116 | zenon_intro zenon_Hed ].
% 35.76/35.93 generalize (definition_smaller (age zenon_TX_y zenon_TT0_w)). zenon_intro zenon_H20.
% 35.76/35.93 generalize (zenon_H20 (age zenon_TX_y zenon_TT1_x)). zenon_intro zenon_H117.
% 35.76/35.93 apply (zenon_equiv_s _ _ zenon_H117); [ zenon_intro zenon_H118; zenon_intro zenon_H2a | zenon_intro zenon_H116; zenon_intro zenon_H13 ].
% 35.76/35.93 exact (zenon_H118 zenon_H116).
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ].
% 35.76/35.93 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ].
% 35.76/35.93 exact (zenon_He3 zenon_Hcf).
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L29_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ].
% 35.76/35.93 apply (zenon_L30_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L29_ zenon_TT0_w zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L26_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H107); [ zenon_intro zenon_H89 | zenon_intro zenon_H119 ].
% 35.76/35.93 generalize (zenon_Hcd zenon_TT1_x). zenon_intro zenon_He9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_H4e. zenon_intro zenon_Hea.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hea). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb8 ].
% 35.76/35.93 apply (zenon_L28_ zenon_TT1_x zenon_TX_y); trivial.
% 35.76/35.93 generalize (zenon_Hcd zenon_TT2_cd). zenon_intro zenon_H11a.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_H4e. zenon_intro zenon_H11b.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H11c); [ zenon_intro zenon_He3 | zenon_intro zenon_H91 ].
% 35.76/35.93 exact (zenon_He3 zenon_Hcf).
% 35.76/35.93 generalize (zenon_Hcd zenon_TT0_w). zenon_intro zenon_Hf8.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H4e. zenon_intro zenon_Hf9.
% 35.76/35.93 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfb. zenon_intro zenon_Hfa.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H15 | zenon_intro zenon_Hb0 ].
% 35.76/35.93 apply (zenon_L32_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L19_ zenon_TT3_cp zenon_TT2_cd zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_He4 | zenon_intro zenon_Hc6 ].
% 35.76/35.93 apply (zenon_L30_ zenon_TT2_cd zenon_TT1_x zenon_TT3_cp zenon_TX_y); trivial.
% 35.76/35.93 apply (zenon_L33_ zenon_TT1_x zenon_TT0_w zenon_TX_y); trivial.
% 35.76/35.93 apply zenon_Hfc. zenon_intro zenon_Tx_la. apply NNPP. zenon_intro zenon_H11f.
% 35.76/35.93 apply zenon_H11f. zenon_intro zenon_Ty_lc. apply NNPP. zenon_intro zenon_H121.
% 35.76/35.93 apply zenon_H121. zenon_intro zenon_Tz_le. apply NNPP. zenon_intro zenon_H123.
% 35.76/35.93 apply (zenon_notimply_s _ _ zenon_H123). zenon_intro zenon_H125. zenon_intro zenon_H124.
% 35.76/35.93 apply (zenon_notimply_s _ _ zenon_H124). zenon_intro zenon_H127. zenon_intro zenon_H126.
% 35.76/35.93 generalize (meaning_postulate_greater_transitive zenon_Tx_la). zenon_intro zenon_H128.
% 35.76/35.93 generalize (zenon_H128 zenon_Ty_lc). zenon_intro zenon_H129.
% 35.76/35.93 generalize (zenon_H129 zenon_Tz_le). zenon_intro zenon_H12a.
% 35.76/35.93 apply (zenon_imply_s _ _ zenon_H12a); [ zenon_intro zenon_H12c | zenon_intro zenon_H12b ].
% 35.76/35.93 apply (zenon_notand_s _ _ zenon_H12c); [ zenon_intro zenon_H12e | zenon_intro zenon_H12d ].
% 35.76/35.93 exact (zenon_H12e zenon_H125).
% 35.76/35.93 exact (zenon_H12d zenon_H127).
% 35.76/35.93 exact (zenon_H126 zenon_H12b).
% 35.76/35.93 Qed.
% 35.76/35.93 % SZS output end Proof
% 35.76/35.93 (* END-PROOF *)
% 35.76/35.93 nodes searched: 2233391
% 35.76/35.93 max branch formulas: 6678
% 35.76/35.93 proof nodes created: 9790
% 35.76/35.93 formulas created: 430650
% 35.76/35.93
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