TSTP Solution File: MGT061+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT061+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n019.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 22:31:15 EDT 2022
% Result : Theorem 12.48s 12.65s
% Output : Proof 12.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT061+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 11:51:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 12.48/12.65 (* PROOF-FOUND *)
% 12.48/12.65 % SZS status Theorem
% 12.48/12.65 (* BEGIN-PROOF *)
% 12.48/12.65 % SZS output start Proof
% 12.48/12.65 Theorem theorem_7 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((fragile_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age X T1) (sigma))/\(greater (age X T2) (sigma))))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))).
% 12.48/12.65 Proof.
% 12.48/12.65 assert (zenon_L1_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (greater (sigma) (age zenon_TX_v zenon_TT1_u)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H12 zenon_H13.
% 12.48/12.65 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16.
% 12.48/12.65 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 12.48/12.65 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 12.48/12.65 generalize (definition_smaller (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H1d.
% 12.48/12.65 generalize (zenon_H1d (sigma)). zenon_intro zenon_H1e.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H1c; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H12 ].
% 12.48/12.65 exact (zenon_H20 zenon_H12).
% 12.48/12.65 exact (zenon_H1c zenon_H1f).
% 12.48/12.65 exact (zenon_H13 zenon_H19).
% 12.48/12.65 (* end of lemma zenon_L1_ *)
% 12.48/12.65 assert (zenon_L2_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT1_u))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H21 zenon_H22 zenon_H23.
% 12.48/12.65 apply zenon_H21. zenon_intro zenon_H24.
% 12.48/12.65 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25.
% 12.48/12.65 generalize (zenon_H25 zenon_TT1_u). zenon_intro zenon_H26.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H29 zenon_H23).
% 12.48/12.65 exact (zenon_H27 zenon_H24).
% 12.48/12.65 (* end of lemma zenon_L2_ *)
% 12.48/12.65 assert (zenon_L3_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(is_aligned zenon_TX_v zenon_TT1_u)) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H2b zenon_H2c zenon_H2d zenon_H2e zenon_H2f zenon_H22.
% 12.48/12.65 generalize (zenon_H2b zenon_TT0_bw). zenon_intro zenon_H31.
% 12.48/12.65 generalize (zenon_H31 zenon_TT1_u). zenon_intro zenon_H32.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H2e; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ].
% 12.48/12.65 generalize (definition_2 zenon_TX_v). zenon_intro zenon_H39.
% 12.48/12.65 generalize (zenon_H39 zenon_TT0_bw). zenon_intro zenon_H3a.
% 12.48/12.65 generalize (zenon_H3a zenon_TT1_u). zenon_intro zenon_H3b.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H38; zenon_intro zenon_H3d | zenon_intro zenon_H36; zenon_intro zenon_H3c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H2a | zenon_intro zenon_H3e ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply zenon_H3e. zenon_intro zenon_H3f.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H41; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H40 ].
% 12.48/12.65 exact (zenon_H41 zenon_H2c).
% 12.48/12.65 exact (zenon_H2d zenon_H40).
% 12.48/12.65 exact (zenon_H38 zenon_H36).
% 12.48/12.65 exact (zenon_H2e zenon_H37).
% 12.48/12.65 (* end of lemma zenon_L3_ *)
% 12.48/12.65 assert (zenon_L4_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT2_cp))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H42 zenon_H22 zenon_H23.
% 12.48/12.65 apply zenon_H42. zenon_intro zenon_H44.
% 12.48/12.65 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25.
% 12.48/12.65 generalize (zenon_H25 zenon_TT2_cp). zenon_intro zenon_H45.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H28 | zenon_intro zenon_H46 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H29 zenon_H23).
% 12.48/12.65 exact (zenon_H46 zenon_H44).
% 12.48/12.65 (* end of lemma zenon_L4_ *)
% 12.48/12.65 assert (zenon_L5_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), ((greater (age zenon_TX_v zenon_TT2_cp) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT2_cp))) -> (positional_advantage zenon_TX_v zenon_TT2_cp) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H47 zenon_H48 zenon_H49.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 12.48/12.65 exact (zenon_H4b zenon_H49).
% 12.48/12.65 exact (zenon_H4a zenon_H48).
% 12.48/12.65 (* end of lemma zenon_L5_ *)
% 12.48/12.65 assert (zenon_L6_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (((smaller_or_equal (age zenon_TX_v zenon_TT2_cp) (sigma))->(positional_advantage zenon_TX_v zenon_TT2_cp))/\((greater (age zenon_TX_v zenon_TT2_cp) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT2_cp)))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (positional_advantage zenon_TX_v zenon_TT2_cp) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H4c zenon_H49 zenon_H48.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4d. zenon_intro zenon_H47.
% 12.48/12.65 apply (zenon_L5_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L6_ *)
% 12.48/12.65 assert (zenon_L7_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (((is_aligned zenon_TX_v zenon_TT2_cp)/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> (~(positional_advantage zenon_TX_v zenon_TT2_cp)) -> (((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H4e zenon_H4a zenon_H4f zenon_H50 zenon_H51.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H54 ].
% 12.48/12.65 exact (zenon_H58 zenon_H55).
% 12.48/12.65 exact (zenon_H54 zenon_H4a).
% 12.48/12.65 exact (zenon_H50 zenon_H56).
% 12.48/12.65 exact (zenon_H54 zenon_H4a).
% 12.48/12.65 exact (zenon_H51 zenon_H52).
% 12.48/12.65 (* end of lemma zenon_L7_ *)
% 12.48/12.65 assert (zenon_L8_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT2_cp)/\(positional_advantage zenon_TX_v zenon_TT2_cp))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(positional_advantage zenon_TX_v zenon_TT2_cp))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT2_cp)/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT2_cp))/\(~(positional_advantage zenon_TX_v zenon_TT2_cp)))->((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high)))))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))) -> (~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H59 zenon_H51 zenon_H50 zenon_H49 zenon_H5a zenon_H5b.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H4e. zenon_intro zenon_H4f.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H58 | zenon_intro zenon_H4a ].
% 12.48/12.65 apply zenon_H58. zenon_intro zenon_H62.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 12.48/12.65 exact (zenon_H55 zenon_H62).
% 12.48/12.65 apply zenon_H54. zenon_intro zenon_H48.
% 12.48/12.65 generalize (zenon_H5a zenon_TT2_cp). zenon_intro zenon_H4c.
% 12.48/12.65 apply (zenon_L6_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H51 zenon_H52).
% 12.48/12.65 apply (zenon_L7_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 apply zenon_H5b. apply sym_equal. exact zenon_H60.
% 12.48/12.65 (* end of lemma zenon_L8_ *)
% 12.48/12.65 assert (zenon_L9_ : (~((mod2) = (mod2))) -> False).
% 12.48/12.65 do 0 intro. intros zenon_H63.
% 12.48/12.65 apply zenon_H63. apply refl_equal.
% 12.48/12.65 (* end of lemma zenon_L9_ *)
% 12.48/12.65 assert (zenon_L10_ : (~((low) = (low))) -> False).
% 12.48/12.65 do 0 intro. intros zenon_H64.
% 12.48/12.65 apply zenon_H64. apply refl_equal.
% 12.48/12.65 (* end of lemma zenon_L10_ *)
% 12.48/12.65 assert (zenon_L11_ : forall (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (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_v zenon_TT2_cp) (low))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H49 zenon_H5a zenon_H5b zenon_H66 zenon_H67.
% 12.48/12.65 elim (classic ((~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (mod2))))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ].
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H51. zenon_intro zenon_H6a.
% 12.48/12.65 elim (classic ((~((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (high))))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H50. zenon_intro zenon_H6d.
% 12.48/12.65 generalize (zenon_H65 zenon_TT2_cp). zenon_intro zenon_H6e.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H2a | zenon_intro zenon_H6f ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H42 | zenon_intro zenon_H59 ].
% 12.48/12.65 apply (zenon_L4_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L8_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (mod2))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H6a.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact assumption_18d.
% 12.48/12.65 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 12.48/12.65 cut (((high) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 12.48/12.65 congruence.
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ].
% 12.48/12.65 apply zenon_H74. zenon_intro zenon_H56.
% 12.48/12.65 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp)) = ((high) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H72.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H75.
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (high))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 12.48/12.65 congruence.
% 12.48/12.65 exact (zenon_H50 zenon_H56).
% 12.48/12.65 apply zenon_H76. apply refl_equal.
% 12.48/12.65 apply zenon_H76. apply refl_equal.
% 12.48/12.65 apply zenon_H73. zenon_intro zenon_H77.
% 12.48/12.65 generalize (zenon_H66 (hazard_of_mortality zenon_TX_v zenon_TT2_cp)). zenon_intro zenon_H78.
% 12.48/12.65 generalize (zenon_H78 (high)). zenon_intro zenon_H79.
% 12.48/12.65 generalize (zenon_H79 (mod2)). zenon_intro zenon_H7a.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H6d | zenon_intro zenon_H7b ].
% 12.48/12.65 exact (zenon_H6d zenon_H77).
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 12.48/12.65 exact (zenon_H7d assumption_18d).
% 12.48/12.65 exact (zenon_H6a zenon_H7c).
% 12.48/12.65 apply zenon_H63. apply refl_equal.
% 12.48/12.65 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H67.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact assumption_18e.
% 12.48/12.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 12.48/12.65 cut (((mod2) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H7e].
% 12.48/12.65 congruence.
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ].
% 12.48/12.65 apply zenon_H80. zenon_intro zenon_H52.
% 12.48/12.65 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp)) = ((mod2) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H7e.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H75.
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 12.48/12.65 congruence.
% 12.48/12.65 exact (zenon_H51 zenon_H52).
% 12.48/12.65 apply zenon_H76. apply refl_equal.
% 12.48/12.65 apply zenon_H76. apply refl_equal.
% 12.48/12.65 apply zenon_H7f. zenon_intro zenon_H7c.
% 12.48/12.65 generalize (zenon_H66 (hazard_of_mortality zenon_TX_v zenon_TT2_cp)). zenon_intro zenon_H78.
% 12.48/12.65 generalize (zenon_H78 (mod2)). zenon_intro zenon_H81.
% 12.48/12.65 generalize (zenon_H81 (low)). zenon_intro zenon_H82.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H6a | zenon_intro zenon_H83 ].
% 12.48/12.65 exact (zenon_H6a zenon_H7c).
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ].
% 12.48/12.65 exact (zenon_H85 assumption_18e).
% 12.48/12.65 exact (zenon_H67 zenon_H84).
% 12.48/12.65 apply zenon_H64. apply refl_equal.
% 12.48/12.65 (* end of lemma zenon_L11_ *)
% 12.48/12.65 assert (zenon_L12_ : forall (zenon_TT1_u : zenon_U) (zenon_TT2_cp : zenon_U) (zenon_TX_v : zenon_U), (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (~(has_endowment zenon_TX_v)) -> (organization zenon_TX_v) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H5b zenon_H5a zenon_H49 zenon_H23 zenon_H22 zenon_H65 zenon_H86 zenon_H66 zenon_H87.
% 12.48/12.65 elim (classic ((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ].
% 12.48/12.65 elim (classic (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low))); [ zenon_intro zenon_H84 | zenon_intro zenon_H67 ].
% 12.48/12.65 cut ((greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H86.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H84.
% 12.48/12.65 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT2_cp) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 12.48/12.65 congruence.
% 12.48/12.65 apply zenon_H76. apply refl_equal.
% 12.48/12.65 exact (zenon_H89 zenon_H88).
% 12.48/12.65 apply (zenon_L11_ zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 elim (classic ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u)) = ((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H89.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H8a.
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H8b].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 12.48/12.65 congruence.
% 12.48/12.65 exact (zenon_H8c zenon_H87).
% 12.48/12.65 apply zenon_H8b. apply refl_equal.
% 12.48/12.65 apply zenon_H8b. apply refl_equal.
% 12.48/12.65 (* end of lemma zenon_L12_ *)
% 12.48/12.65 assert (zenon_L13_ : forall (zenon_TT2_cp : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (~(has_endowment zenon_TX_v)) -> (organization zenon_TX_v) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False).
% 12.48/12.65 do 4 intro. intros zenon_H8d zenon_H8e zenon_H2b zenon_H2c zenon_H2e zenon_H2f zenon_H5b zenon_H5a zenon_H49 zenon_H23 zenon_H22 zenon_H65 zenon_H86 zenon_H66.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L3_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 apply (zenon_L12_ zenon_TT1_u zenon_TT2_cp zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L13_ *)
% 12.48/12.65 assert (zenon_L14_ : forall (zenon_TT2_cp : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : 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_v) -> (~(has_endowment zenon_TX_v)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> False).
% 12.48/12.65 do 4 intro. intros zenon_H66 zenon_H22 zenon_H23 zenon_H2b zenon_H2c zenon_H2e zenon_H2f zenon_H8e zenon_H86 zenon_H5b zenon_H5a zenon_H49 zenon_H65.
% 12.48/12.65 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ].
% 12.48/12.65 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L13_ zenon_TT2_cp zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L14_ *)
% 12.48/12.65 assert (zenon_L15_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (is_aligned zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H8d zenon_H8e zenon_H40 zenon_H89.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ].
% 12.48/12.65 exact (zenon_H2d zenon_H40).
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 apply zenon_H89. apply sym_equal. exact zenon_H87.
% 12.48/12.65 (* end of lemma zenon_L15_ *)
% 12.48/12.65 assert (zenon_L16_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT1_u) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H40 zenon_H8e zenon_H89.
% 12.48/12.65 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ].
% 12.48/12.65 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L15_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L16_ *)
% 12.48/12.65 assert (zenon_L17_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (~(has_endowment zenon_TX_v)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H2b zenon_H2c zenon_H65 zenon_H23 zenon_H8e zenon_H89 zenon_H2e zenon_H2f zenon_H22.
% 12.48/12.65 generalize (zenon_H2b zenon_TT0_bw). zenon_intro zenon_H31.
% 12.48/12.65 generalize (zenon_H31 zenon_TT1_u). zenon_intro zenon_H32.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H2e; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ].
% 12.48/12.65 generalize (definition_2 zenon_TX_v). zenon_intro zenon_H39.
% 12.48/12.65 generalize (zenon_H39 zenon_TT0_bw). zenon_intro zenon_H3a.
% 12.48/12.65 generalize (zenon_H3a zenon_TT1_u). zenon_intro zenon_H3b.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H38; zenon_intro zenon_H3d | zenon_intro zenon_H36; zenon_intro zenon_H3c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H2a | zenon_intro zenon_H3e ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply zenon_H3e. zenon_intro zenon_H3f.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H41; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H40 ].
% 12.48/12.65 exact (zenon_H41 zenon_H2c).
% 12.48/12.65 apply (zenon_L16_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H38 zenon_H36).
% 12.48/12.65 exact (zenon_H2e zenon_H37).
% 12.48/12.65 (* end of lemma zenon_L17_ *)
% 12.48/12.65 assert (zenon_L18_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), (~(has_endowment zenon_TX_v)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H23 zenon_H8e zenon_H89 zenon_H2e zenon_H2f zenon_H22 zenon_H97.
% 12.48/12.65 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b.
% 12.48/12.65 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65.
% 12.48/12.65 apply (zenon_L17_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L18_ *)
% 12.48/12.65 assert (zenon_L19_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((greater (age zenon_TX_v zenon_TT1_u) (sigma))->(~(positional_advantage zenon_TX_v zenon_TT1_u))) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> (organization zenon_TX_v) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(has_endowment zenon_TX_v)) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H99 zenon_H97 zenon_H22 zenon_H2f zenon_H89 zenon_H8e zenon_H23.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L18_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 (* end of lemma zenon_L19_ *)
% 12.48/12.65 assert (zenon_L20_ : (~((sigma) = (sigma))) -> False).
% 12.48/12.65 do 0 intro. intros zenon_H9a.
% 12.48/12.65 apply zenon_H9a. apply refl_equal.
% 12.48/12.65 (* end of lemma zenon_L20_ *)
% 12.48/12.65 assert (zenon_L21_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (~(greater (sigma) (age zenon_TX_v zenon_TT0_bw))) -> (greater (sigma) (zero)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H9b zenon_H9c zenon_H2f.
% 12.48/12.65 elim (classic ((zero) = (age zenon_TX_v zenon_TT0_bw))); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ].
% 12.48/12.65 cut ((greater (sigma) (zero)) = (greater (sigma) (age zenon_TX_v zenon_TT0_bw))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H9b.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H9c.
% 12.48/12.65 cut (((zero) = (age zenon_TX_v zenon_TT0_bw))); [idtac | apply NNPP; zenon_intro zenon_H9e].
% 12.48/12.65 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H9a].
% 12.48/12.65 congruence.
% 12.48/12.65 apply zenon_H9a. apply refl_equal.
% 12.48/12.65 exact (zenon_H9e zenon_H9d).
% 12.48/12.65 apply zenon_H9e. apply sym_equal. exact zenon_H2f.
% 12.48/12.65 (* end of lemma zenon_L21_ *)
% 12.48/12.65 assert (zenon_L22_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (greater (sigma) (zero)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT0_bw) (sigma))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_H2f zenon_H9c zenon_H9f.
% 12.48/12.65 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT0_bw)). zenon_intro zenon_Ha0.
% 12.48/12.65 generalize (zenon_Ha0 (sigma)). zenon_intro zenon_Ha1.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_Ha1); [ zenon_intro zenon_H9f; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3; zenon_intro zenon_Ha2 ].
% 12.48/12.65 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5.
% 12.48/12.65 generalize (definition_smaller (age zenon_TX_v zenon_TT0_bw)). zenon_intro zenon_Ha7.
% 12.48/12.65 generalize (zenon_Ha7 (sigma)). zenon_intro zenon_Ha8.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_Ha8); [ zenon_intro zenon_Ha6; zenon_intro zenon_H9b | zenon_intro zenon_Haa; zenon_intro zenon_Ha9 ].
% 12.48/12.65 apply (zenon_L21_ zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_Ha6 zenon_Haa).
% 12.48/12.65 exact (zenon_H9f zenon_Ha3).
% 12.48/12.65 (* end of lemma zenon_L22_ *)
% 12.48/12.65 assert (zenon_L23_ : forall (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (~(~(has_immunity zenon_TX_v zenon_TT0_bw))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> False).
% 12.48/12.65 do 2 intro. intros zenon_Hab zenon_H22 zenon_H23.
% 12.48/12.65 apply zenon_Hab. zenon_intro zenon_Hac.
% 12.48/12.65 generalize (assumption_1 zenon_TX_v). zenon_intro zenon_H25.
% 12.48/12.65 generalize (zenon_H25 zenon_TT0_bw). zenon_intro zenon_Had.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_H28 | zenon_intro zenon_Hae ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H29 zenon_H23).
% 12.48/12.65 exact (zenon_Hae zenon_Hac).
% 12.48/12.65 (* end of lemma zenon_L23_ *)
% 12.48/12.65 assert (zenon_L24_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT0_bw)/\(positional_advantage zenon_TX_v zenon_TT0_bw))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT0_bw))/\(positional_advantage zenon_TX_v zenon_TT0_bw))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT0_bw)/\(~(positional_advantage zenon_TX_v zenon_TT0_bw)))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT0_bw))/\(~(positional_advantage zenon_TX_v zenon_TT0_bw)))->((hazard_of_mortality zenon_TX_v zenon_TT0_bw) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False).
% 12.48/12.65 do 3 intro. intros zenon_Haf zenon_Hb0 zenon_H2c zenon_Hb1 zenon_H87.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Haf). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hb4 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H41 | zenon_intro zenon_Hb6 ].
% 12.48/12.65 exact (zenon_H41 zenon_H2c).
% 12.48/12.65 exact (zenon_Hb6 zenon_Hb0).
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) = ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_Hb1.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact zenon_H87.
% 12.48/12.65 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 12.48/12.65 cut (((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H8b].
% 12.48/12.65 congruence.
% 12.48/12.65 apply zenon_H8b. apply refl_equal.
% 12.48/12.65 apply zenon_Hb7. apply sym_equal. exact zenon_Hb4.
% 12.48/12.65 (* end of lemma zenon_L24_ *)
% 12.48/12.65 assert (zenon_L25_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> ((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H65 zenon_H22 zenon_H23 zenon_H2c zenon_Hb0 zenon_Hb1 zenon_H87.
% 12.48/12.65 generalize (zenon_H65 zenon_TT0_bw). zenon_intro zenon_Hb8.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb9 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_Hbb. zenon_intro zenon_Hba.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hab | zenon_intro zenon_Haf ].
% 12.48/12.65 apply (zenon_L23_ zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L24_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L25_ *)
% 12.48/12.65 assert (zenon_L26_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((((is_aligned zenon_TX_v zenon_TT1_u)/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (low)))/\((((~(is_aligned zenon_TX_v zenon_TT1_u))/\(positional_advantage zenon_TX_v zenon_TT1_u))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod1)))/\((((is_aligned zenon_TX_v zenon_TT1_u)/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (mod2)))/\(((~(is_aligned zenon_TX_v zenon_TT1_u))/\(~(positional_advantage zenon_TX_v zenon_TT1_u)))->((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (high)))))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T0) = (zero)))->((greater (age zenon_TX_v T) (sigma))<->(dissimilar zenon_TX_v T0 T))))) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_v)->(((has_immunity zenon_TX_v T)->((hazard_of_mortality zenon_TX_v T) = (very_low)))/\((~(has_immunity zenon_TX_v T))->((((is_aligned zenon_TX_v T)/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (low)))/\((((~(is_aligned zenon_TX_v T))/\(positional_advantage zenon_TX_v T))->((hazard_of_mortality zenon_TX_v T) = (mod1)))/\((((is_aligned zenon_TX_v T)/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (mod2)))/\(((~(is_aligned zenon_TX_v T))/\(~(positional_advantage zenon_TX_v T)))->((hazard_of_mortality zenon_TX_v T) = (high)))))))))) -> (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H8d zenon_H8e zenon_H2b zenon_H2e zenon_H2f zenon_H65 zenon_H22 zenon_H23 zenon_H2c zenon_Hb0 zenon_Hb1.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H91 | zenon_intro zenon_H87 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2d | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L3_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 apply (zenon_L25_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L26_ *)
% 12.48/12.65 assert (zenon_L27_ : forall (zenon_TT1_u : zenon_U) (zenon_TT0_bw : zenon_U) (zenon_TX_v : zenon_U), (organization zenon_TX_v) -> (~(has_endowment zenon_TX_v)) -> (is_aligned zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> False).
% 12.48/12.65 do 3 intro. intros zenon_H22 zenon_H23 zenon_H2c zenon_H2e zenon_H2f zenon_H8e zenon_Hb0 zenon_Hb1.
% 12.48/12.65 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b.
% 12.48/12.65 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65.
% 12.48/12.65 generalize (zenon_H65 zenon_TT1_u). zenon_intro zenon_H93.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H2a | zenon_intro zenon_H94 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H21 | zenon_intro zenon_H8d ].
% 12.48/12.65 apply (zenon_L2_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L26_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L27_ *)
% 12.48/12.65 assert (zenon_L28_ : forall (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> (~(smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))) -> False).
% 12.48/12.65 do 2 intro. intros zenon_Hbc zenon_H13.
% 12.48/12.65 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16.
% 12.48/12.65 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 12.48/12.65 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 12.48/12.65 exact (zenon_H1b zenon_Hbc).
% 12.48/12.65 exact (zenon_H13 zenon_H19).
% 12.48/12.65 (* end of lemma zenon_L28_ *)
% 12.48/12.65 assert (zenon_L29_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> (organization zenon_TX_v) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (~(has_endowment zenon_TX_v)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> False).
% 12.48/12.65 do 3 intro. intros zenon_Hbc zenon_H22 zenon_H2f zenon_H89 zenon_H23 zenon_H5a.
% 12.48/12.65 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97.
% 12.48/12.65 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L19_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L29_ *)
% 12.48/12.65 assert (zenon_L30_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT2_cp : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : 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_v zenon_TT1_u) = (sigma)) -> (greater (age zenon_TX_v zenon_TT2_cp) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_v T) (sigma))->(positional_advantage zenon_TX_v T))/\((greater (age zenon_TX_v T) (sigma))->(~(positional_advantage zenon_TX_v T))))) -> (~(greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))) -> (positional_advantage zenon_TX_v zenon_TT1_u) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> (~(has_endowment zenon_TX_v)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> False).
% 12.48/12.65 do 4 intro. intros zenon_H66 zenon_Hbc zenon_H49 zenon_H5a zenon_H86 zenon_H8e zenon_H2e zenon_H23 zenon_H2f zenon_H22 zenon_H97.
% 12.48/12.65 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65.
% 12.48/12.65 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b.
% 12.48/12.65 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H86.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact assumption_18b.
% 12.48/12.65 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89].
% 12.48/12.65 cut (((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 12.48/12.65 congruence.
% 12.48/12.65 apply (zenon_L14_ zenon_TT2_cp zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L29_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L30_ *)
% 12.48/12.65 assert (zenon_L31_ : forall (zenon_TT0_bw : zenon_U) (zenon_TT1_u : zenon_U) (zenon_TX_v : zenon_U), ((smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))->(positional_advantage zenon_TX_v zenon_TT1_u)) -> (~((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))) -> (positional_advantage zenon_TX_v zenon_TT0_bw) -> (~(greater (age zenon_TX_v zenon_TT1_u) (sigma))) -> (~(has_endowment zenon_TX_v)) -> ((age zenon_TX_v zenon_TT0_bw) = (zero)) -> (organization zenon_TX_v) -> (forall T : zenon_U, (((organization zenon_TX_v)/\((age zenon_TX_v T) = (zero)))->(is_aligned zenon_TX_v T))) -> ((age zenon_TX_v zenon_TT1_u) = (sigma)) -> False).
% 12.48/12.65 do 3 intro. intros zenon_Hbe zenon_Hb1 zenon_Hb0 zenon_H2e zenon_H23 zenon_H2f zenon_H22 zenon_H97 zenon_Hbc.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 apply (zenon_L27_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 (* end of lemma zenon_L31_ *)
% 12.48/12.65 apply NNPP. intro zenon_G.
% 12.48/12.65 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_H66 | zenon_intro zenon_Hbf ].
% 12.48/12.65 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\((fragile_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age X T1) (sigma))/\(greater (age X T2) (sigma))))))))->((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_Hc0; idtac ].
% 12.48/12.65 elim zenon_Hc0. zenon_intro zenon_TX_v. zenon_intro zenon_Hc1.
% 12.48/12.65 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v T0) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v T1) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v T1))/\((hazard_of_mortality zenon_TX_v T1) = (hazard_of_mortality zenon_TX_v T0))))))) zenon_Hc1); [ zenon_intro zenon_Hc2; idtac ].
% 12.48/12.65 elim zenon_Hc2. zenon_intro zenon_TT0_bw. zenon_intro zenon_Hc3.
% 12.48/12.65 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v zenon_TT0_bw) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v T1) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v T1))/\((hazard_of_mortality zenon_TX_v T1) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw)))))) zenon_Hc3); [ zenon_intro zenon_Hc4; idtac ].
% 12.48/12.65 elim zenon_Hc4. zenon_intro zenon_TT1_u. zenon_intro zenon_Hc5.
% 12.48/12.65 apply (zenon_notallex_s (fun T2 : zenon_U => (((organization zenon_TX_v)/\((fragile_position zenon_TX_v)/\((~(has_endowment zenon_TX_v))/\(((age zenon_TX_v zenon_TT0_bw) = (zero))/\((greater (sigma) (zero))/\((smaller_or_equal (age zenon_TX_v zenon_TT1_u) (sigma))/\(greater (age zenon_TX_v T2) (sigma))))))))->((greater (hazard_of_mortality zenon_TX_v T2) (hazard_of_mortality zenon_TX_v zenon_TT1_u))/\((hazard_of_mortality zenon_TX_v zenon_TT1_u) = (hazard_of_mortality zenon_TX_v zenon_TT0_bw))))) zenon_Hc5); [ zenon_intro zenon_Hc6; idtac ].
% 12.48/12.65 elim zenon_Hc6. zenon_intro zenon_TT2_cp. zenon_intro zenon_Hc7.
% 12.48/12.65 apply (zenon_notimply_s _ _ zenon_Hc7). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H22. zenon_intro zenon_Hca.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcc. zenon_intro zenon_Hcb.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_H23. zenon_intro zenon_Hcd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_H2f. zenon_intro zenon_Hce.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_H9c. zenon_intro zenon_Hcf.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_H19. zenon_intro zenon_H49.
% 12.48/12.65 generalize (definition_3 zenon_TX_v). zenon_intro zenon_Hd0.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd2; zenon_intro zenon_Hd1 | zenon_intro zenon_Hcc; zenon_intro zenon_H5a ].
% 12.48/12.65 exact (zenon_Hd2 zenon_Hcc).
% 12.48/12.65 generalize (definition_smaller_or_equal (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H16.
% 12.48/12.65 generalize (zenon_H16 (sigma)). zenon_intro zenon_H17.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H13; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 12.48/12.65 exact (zenon_H13 zenon_H19).
% 12.48/12.65 apply (zenon_or_s _ _ zenon_H18); [ zenon_intro zenon_H1f | zenon_intro zenon_Hbc ].
% 12.48/12.65 generalize (definition_smaller (age zenon_TX_v zenon_TT1_u)). zenon_intro zenon_H1d.
% 12.48/12.65 generalize (zenon_H1d (sigma)). zenon_intro zenon_H1e.
% 12.48/12.65 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H1c; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H12 ].
% 12.48/12.65 exact (zenon_H1c zenon_H1f).
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H86 | zenon_intro zenon_Hb1 ].
% 12.48/12.65 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97.
% 12.48/12.65 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L1_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ].
% 12.48/12.65 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 generalize (assumption_15 zenon_TX_v). zenon_intro zenon_H2b.
% 12.48/12.65 generalize (assumption_17 zenon_TX_v). zenon_intro zenon_H65.
% 12.48/12.65 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_v zenon_TT2_cp) (hazard_of_mortality zenon_TX_v zenon_TT1_u))).
% 12.48/12.65 intro zenon_D_pnotp.
% 12.48/12.65 apply zenon_H86.
% 12.48/12.65 rewrite <- zenon_D_pnotp.
% 12.48/12.65 exact assumption_18b.
% 12.48/12.65 cut (((low) = (hazard_of_mortality zenon_TX_v zenon_TT1_u))); [idtac | apply NNPP; zenon_intro zenon_H89].
% 12.48/12.65 cut (((mod1) = (hazard_of_mortality zenon_TX_v zenon_TT2_cp))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 12.48/12.65 congruence.
% 12.48/12.65 apply (zenon_L14_ zenon_TT2_cp zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_L19_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97.
% 12.48/12.65 generalize (zenon_H5a zenon_TT0_bw). zenon_intro zenon_Hd3.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hd5); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb0 ].
% 12.48/12.65 apply (zenon_L22_ zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 generalize (zenon_H97 zenon_TT0_bw). zenon_intro zenon_H98.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H34 | zenon_intro zenon_H2c ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2a | zenon_intro zenon_H35 ].
% 12.48/12.65 exact (zenon_H2a zenon_H22).
% 12.48/12.65 exact (zenon_H35 zenon_H2f).
% 12.48/12.65 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L1_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L27_ zenon_TT1_u zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H86 | zenon_intro zenon_Hb1 ].
% 12.48/12.65 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97.
% 12.48/12.65 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L30_ zenon_TT0_bw zenon_TT2_cp zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 generalize (assumption_13 zenon_TX_v). zenon_intro zenon_H97.
% 12.48/12.65 generalize (zenon_H5a zenon_TT0_bw). zenon_intro zenon_Hd3.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hd5); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb0 ].
% 12.48/12.65 apply (zenon_L22_ zenon_TT0_bw zenon_TX_v); trivial.
% 12.48/12.65 generalize (zenon_H5a zenon_TT1_u). zenon_intro zenon_Hbd.
% 12.48/12.65 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hbe. zenon_intro zenon_H99.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_H13 | zenon_intro zenon_H8e ].
% 12.48/12.65 apply (zenon_L28_ zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H2e | zenon_intro zenon_H92 ].
% 12.48/12.65 apply (zenon_L31_ zenon_TT0_bw zenon_TT1_u zenon_TX_v); trivial.
% 12.48/12.65 exact (zenon_H92 zenon_H8e).
% 12.48/12.65 apply zenon_Hbf. zenon_intro zenon_Tx_ig. apply NNPP. zenon_intro zenon_Hd7.
% 12.48/12.65 apply zenon_Hd7. zenon_intro zenon_Ty_ii. apply NNPP. zenon_intro zenon_Hd9.
% 12.48/12.65 apply zenon_Hd9. zenon_intro zenon_Tz_ik. apply NNPP. zenon_intro zenon_Hdb.
% 12.48/12.65 apply (zenon_notimply_s _ _ zenon_Hdb). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc.
% 12.48/12.65 apply (zenon_notimply_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde.
% 12.48/12.65 generalize (meaning_postulate_greater_transitive zenon_Tx_ig). zenon_intro zenon_He0.
% 12.48/12.65 generalize (zenon_He0 zenon_Ty_ii). zenon_intro zenon_He1.
% 12.48/12.65 generalize (zenon_He1 zenon_Tz_ik). zenon_intro zenon_He2.
% 12.48/12.65 apply (zenon_imply_s _ _ zenon_He2); [ zenon_intro zenon_He4 | zenon_intro zenon_He3 ].
% 12.48/12.65 apply (zenon_notand_s _ _ zenon_He4); [ zenon_intro zenon_He6 | zenon_intro zenon_He5 ].
% 12.48/12.65 exact (zenon_He6 zenon_Hdd).
% 12.48/12.65 exact (zenon_He5 zenon_Hdf).
% 12.48/12.65 exact (zenon_Hde zenon_He3).
% 12.48/12.65 Qed.
% 12.48/12.65 % SZS output end Proof
% 12.48/12.65 (* END-PROOF *)
% 12.48/12.65 nodes searched: 714138
% 12.48/12.65 max branch formulas: 1260
% 12.48/12.65 proof nodes created: 12573
% 12.48/12.65 formulas created: 327610
% 12.48/12.65
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