TSTP Solution File: MGT050+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT050+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n025.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 22:31:11 EDT 2022
% Result : Theorem 1.91s 2.08s
% Output : Proof 1.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT050+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 11:02:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.91/2.08 (* PROOF-FOUND *)
% 1.91/2.08 % SZS status Theorem
% 1.91/2.08 (* BEGIN-PROOF *)
% 1.91/2.08 % SZS output start Proof
% 1.91/2.08 Theorem theorem_3 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_endowment X))/\(greater (age X T) (age X T0))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))).
% 1.91/2.08 Proof.
% 1.91/2.08 assert (zenon_L1_ : forall (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (has_immunity zenon_TX_t zenon_TT0_s) -> (~(has_endowment zenon_TX_t)) -> (organization zenon_TX_t) -> False).
% 1.91/2.08 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11.
% 1.91/2.08 generalize (assumption_1 zenon_TX_t). zenon_intro zenon_H14.
% 1.91/2.08 generalize (zenon_H14 zenon_TT0_s). zenon_intro zenon_H15.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 exact (zenon_H18 zenon_H10).
% 1.91/2.08 exact (zenon_H16 zenon_Hf).
% 1.91/2.08 (* end of lemma zenon_L1_ *)
% 1.91/2.08 assert (zenon_L2_ : forall (zenon_TT_bb : zenon_U) (zenon_TX_t : zenon_U), (has_immunity zenon_TX_t zenon_TT_bb) -> (~(has_endowment zenon_TX_t)) -> (organization zenon_TX_t) -> False).
% 1.91/2.08 do 2 intro. intros zenon_H1a zenon_H10 zenon_H11.
% 1.91/2.08 generalize (assumption_1 zenon_TX_t). zenon_intro zenon_H14.
% 1.91/2.08 generalize (zenon_H14 zenon_TT_bb). zenon_intro zenon_H1c.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H17 | zenon_intro zenon_H1d ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 exact (zenon_H18 zenon_H10).
% 1.91/2.08 exact (zenon_H1d zenon_H1a).
% 1.91/2.08 (* end of lemma zenon_L2_ *)
% 1.91/2.08 assert (zenon_L3_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, (((organization zenon_TX_t)/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s)))->(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))) -> (organization zenon_TX_t) -> (greater (age zenon_TX_t zenon_TT_bb) (age zenon_TX_t zenon_TT0_s)) -> (~(greater (internal_friction zenon_TX_t zenon_TT_bb) (internal_friction zenon_TX_t zenon_TT0_s))) -> False).
% 1.91/2.08 do 3 intro. intros zenon_H1e zenon_H11 zenon_H1f zenon_H20.
% 1.91/2.08 generalize (zenon_H1e zenon_TT_bb). zenon_intro zenon_H21.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H19 | zenon_intro zenon_H24 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 exact (zenon_H24 zenon_H1f).
% 1.91/2.08 exact (zenon_H20 zenon_H22).
% 1.91/2.08 (* end of lemma zenon_L3_ *)
% 1.91/2.08 assert (zenon_L4_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, ((organization zenon_TX_t)->((((greater (stock_of_knowledge zenon_TX_t T) (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\(smaller_or_equal (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))->(greater (capability zenon_TX_t T) (capability zenon_TX_t zenon_TT0_s)))/\((((smaller_or_equal (stock_of_knowledge zenon_TX_t T) (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))->(smaller (capability zenon_TX_t T) (capability zenon_TX_t zenon_TT0_s)))/\((((stock_of_knowledge zenon_TX_t T) = (stock_of_knowledge zenon_TX_t zenon_TT0_s))/\((internal_friction zenon_TX_t T) = (internal_friction zenon_TX_t zenon_TT0_s)))->((capability zenon_TX_t T) = (capability zenon_TX_t zenon_TT0_s))))))) -> (organization zenon_TX_t) -> (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_t)->((stock_of_knowledge zenon_TX_t T) = (stock_of_knowledge zenon_TX_t T0))))) -> (forall T : zenon_U, (((organization zenon_TX_t)/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s)))->(greater (internal_friction zenon_TX_t T) (internal_friction zenon_TX_t zenon_TT0_s)))) -> (greater (age zenon_TX_t zenon_TT_bb) (age zenon_TX_t zenon_TT0_s)) -> (~(greater (capability zenon_TX_t zenon_TT0_s) (capability zenon_TX_t zenon_TT_bb))) -> False).
% 1.91/2.08 do 3 intro. intros zenon_H25 zenon_H11 zenon_H26 zenon_H1e zenon_H1f zenon_H27.
% 1.91/2.08 generalize (zenon_H25 zenon_TT_bb). zenon_intro zenon_H28.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H19 | zenon_intro zenon_H29 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H30 | zenon_intro zenon_H20 ].
% 1.91/2.08 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H31.
% 1.91/2.08 generalize (zenon_H31 (stock_of_knowledge zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H32.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H30; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ].
% 1.91/2.08 apply (zenon_notor_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 1.91/2.08 generalize (zenon_H26 zenon_TT_bb). zenon_intro zenon_H38.
% 1.91/2.08 generalize (zenon_H38 zenon_TT0_s). zenon_intro zenon_H39.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H19 | zenon_intro zenon_H3a ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply zenon_H36. apply sym_equal. exact zenon_H3a.
% 1.91/2.08 exact (zenon_H30 zenon_H34).
% 1.91/2.08 apply (zenon_L3_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 generalize (definition_smaller (capability zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H3b.
% 1.91/2.08 generalize (zenon_H3b (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H3c.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3e; zenon_intro zenon_H27 | zenon_intro zenon_H2e; zenon_intro zenon_H3d ].
% 1.91/2.08 exact (zenon_H3e zenon_H2e).
% 1.91/2.08 exact (zenon_H27 zenon_H3d).
% 1.91/2.08 (* end of lemma zenon_L4_ *)
% 1.91/2.08 assert (zenon_L5_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((smaller (external_ties zenon_TX_t zenon_TT0_s) Y)\/(((external_ties zenon_TX_t zenon_TT0_s) = Y)\/(greater (external_ties zenon_TX_t zenon_TT0_s) Y)))) -> (~(greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s))) -> (~((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT0_s))) -> (~(greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT_bb))) -> False).
% 1.91/2.08 do 3 intro. intros zenon_H3f zenon_H40 zenon_H41 zenon_H42.
% 1.91/2.08 generalize (zenon_H3f (external_ties zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H43.
% 1.91/2.08 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 1.91/2.08 generalize (definition_smaller (external_ties zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H46.
% 1.91/2.08 generalize (zenon_H46 (external_ties zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H47.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H49; zenon_intro zenon_H40 | zenon_intro zenon_H45; zenon_intro zenon_H48 ].
% 1.91/2.08 exact (zenon_H49 zenon_H45).
% 1.91/2.08 exact (zenon_H40 zenon_H48).
% 1.91/2.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 1.91/2.08 apply zenon_H41. apply sym_equal. exact zenon_H4b.
% 1.91/2.08 exact (zenon_H42 zenon_H4a).
% 1.91/2.08 (* end of lemma zenon_L5_ *)
% 1.91/2.08 assert (zenon_L6_ : forall (zenon_TT0_s : zenon_U) (zenon_TT_bb : zenon_U) (zenon_TX_t : zenon_U), (forall T : zenon_U, ((organization zenon_TX_t)->(((greater (external_ties zenon_TX_t T) (external_ties zenon_TX_t zenon_TT_bb))->(greater (position zenon_TX_t T) (position zenon_TX_t zenon_TT_bb)))/\(((external_ties zenon_TX_t T) = (external_ties zenon_TX_t zenon_TT_bb))->((position zenon_TX_t T) = (position zenon_TX_t zenon_TT_bb)))))) -> (organization zenon_TX_t) -> (forall T : zenon_U, ((organization zenon_TX_t)->((external_ties zenon_TX_t T) = (external_ties zenon_TX_t zenon_E)))) -> (~(greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT0_s))) -> (~((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT0_s))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_t zenon_TT0_s) Y)\/(((external_ties zenon_TX_t zenon_TT0_s) = Y)\/(greater (external_ties zenon_TX_t zenon_TT0_s) Y)))) -> ((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_E)) -> (~(greater (position zenon_TX_t zenon_TT0_s) (position zenon_TX_t zenon_TT_bb))) -> False).
% 1.91/2.08 do 3 intro. intros zenon_H4c zenon_H11 zenon_H4d zenon_H4e zenon_H41 zenon_H3f zenon_H4f zenon_H50.
% 1.91/2.08 generalize (zenon_H4c zenon_TT0_s). zenon_intro zenon_H51.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H19 | zenon_intro zenon_H52 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H42 | zenon_intro zenon_H55 ].
% 1.91/2.08 generalize (zenon_H4d zenon_TT_bb). zenon_intro zenon_H56.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H19 | zenon_intro zenon_H57 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 elim (classic ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ].
% 1.91/2.08 elim (classic (greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H48 | zenon_intro zenon_H40 ].
% 1.91/2.08 elim (classic (greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 1.91/2.08 cut ((greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s)) = (greater (external_ties zenon_TX_t zenon_TT0_s) (external_ties zenon_TX_t zenon_TT0_s))).
% 1.91/2.08 intro zenon_D_pnotp.
% 1.91/2.08 apply zenon_H4e.
% 1.91/2.08 rewrite <- zenon_D_pnotp.
% 1.91/2.08 exact zenon_H5a.
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5d].
% 1.91/2.08 congruence.
% 1.91/2.08 elim (classic ((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5c ].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s)) = ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT0_s))).
% 1.91/2.08 intro zenon_D_pnotp.
% 1.91/2.08 apply zenon_H5d.
% 1.91/2.08 rewrite <- zenon_D_pnotp.
% 1.91/2.08 exact zenon_H5e.
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 1.91/2.08 congruence.
% 1.91/2.08 exact (zenon_H5f zenon_H4f).
% 1.91/2.08 apply zenon_H5c. apply refl_equal.
% 1.91/2.08 apply zenon_H5c. apply refl_equal.
% 1.91/2.08 apply zenon_H5c. apply refl_equal.
% 1.91/2.08 cut ((greater (external_ties zenon_TX_t zenon_TT_bb) (external_ties zenon_TX_t zenon_TT0_s)) = (greater (external_ties zenon_TX_t zenon_E) (external_ties zenon_TX_t zenon_TT0_s))).
% 1.91/2.08 intro zenon_D_pnotp.
% 1.91/2.08 apply zenon_H5b.
% 1.91/2.08 rewrite <- zenon_D_pnotp.
% 1.91/2.08 exact zenon_H48.
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT0_s) = (external_ties zenon_TX_t zenon_TT0_s))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 1.91/2.08 congruence.
% 1.91/2.08 elim (classic ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E)) = ((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))).
% 1.91/2.08 intro zenon_D_pnotp.
% 1.91/2.08 apply zenon_H60.
% 1.91/2.08 rewrite <- zenon_D_pnotp.
% 1.91/2.08 exact zenon_H61.
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H62].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 1.91/2.08 congruence.
% 1.91/2.08 exact (zenon_H59 zenon_H58).
% 1.91/2.08 apply zenon_H62. apply refl_equal.
% 1.91/2.08 apply zenon_H62. apply refl_equal.
% 1.91/2.08 apply zenon_H5c. apply refl_equal.
% 1.91/2.08 apply (zenon_L5_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 elim (classic ((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb)) = ((external_ties zenon_TX_t zenon_E) = (external_ties zenon_TX_t zenon_TT_bb))).
% 1.91/2.08 intro zenon_D_pnotp.
% 1.91/2.08 apply zenon_H59.
% 1.91/2.08 rewrite <- zenon_D_pnotp.
% 1.91/2.08 exact zenon_H63.
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_TT_bb))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 1.91/2.08 cut (((external_ties zenon_TX_t zenon_TT_bb) = (external_ties zenon_TX_t zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 1.91/2.08 congruence.
% 1.91/2.08 exact (zenon_H60 zenon_H57).
% 1.91/2.08 apply zenon_H64. apply refl_equal.
% 1.91/2.08 apply zenon_H64. apply refl_equal.
% 1.91/2.08 exact (zenon_H50 zenon_H55).
% 1.91/2.08 (* end of lemma zenon_L6_ *)
% 1.91/2.08 assert (zenon_L7_ : forall (zenon_TT_bb : zenon_U) (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s) (hazard_of_mortality zenon_TX_t zenon_TT_bb)) -> (~(greater (hazard_of_mortality zenon_TX_t zenon_TT_bb) (hazard_of_mortality zenon_TX_t zenon_TT0_s))) -> False).
% 1.91/2.08 do 3 intro. intros zenon_H65 zenon_H66.
% 1.91/2.08 generalize (definition_smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H67.
% 1.91/2.08 generalize (zenon_H67 (hazard_of_mortality zenon_TX_t zenon_TT_bb)). zenon_intro zenon_H68.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H68); [ zenon_intro zenon_H6a; zenon_intro zenon_H66 | zenon_intro zenon_H65; zenon_intro zenon_H69 ].
% 1.91/2.08 exact (zenon_H6a zenon_H65).
% 1.91/2.08 exact (zenon_H66 zenon_H69).
% 1.91/2.08 (* end of lemma zenon_L7_ *)
% 1.91/2.08 assert (zenon_L8_ : forall (zenon_TT0_s : zenon_U) (zenon_TX_t : zenon_U), (smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s) (hazard_of_mortality zenon_TX_t zenon_TT0_s)) -> False).
% 1.91/2.08 do 2 intro. intros zenon_H6b.
% 1.91/2.08 generalize (definition_smaller (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H67.
% 1.91/2.08 generalize (zenon_H67 (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H6c.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6f; zenon_intro zenon_H6e | zenon_intro zenon_H6b; zenon_intro zenon_H6d ].
% 1.91/2.08 exact (zenon_H6f zenon_H6b).
% 1.91/2.08 generalize (meaning_postulate_greater_strict (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H70.
% 1.91/2.08 generalize (zenon_H70 (hazard_of_mortality zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H71.
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H6e | zenon_intro zenon_H6e ].
% 1.91/2.08 exact (zenon_H6e zenon_H6d).
% 1.91/2.08 exact (zenon_H6e zenon_H6d).
% 1.91/2.08 (* end of lemma zenon_L8_ *)
% 1.91/2.08 apply NNPP. intro zenon_G.
% 1.91/2.08 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_endowment X))/\(greater (age X T) (age X T0))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))) zenon_G); [ zenon_intro zenon_H72; idtac ].
% 1.91/2.08 elim zenon_H72. zenon_intro zenon_TX_t. zenon_intro zenon_H73.
% 1.91/2.08 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_t)/\((~(has_endowment zenon_TX_t))/\(greater (age zenon_TX_t T) (age zenon_TX_t T0))))->(greater (hazard_of_mortality zenon_TX_t T) (hazard_of_mortality zenon_TX_t T0))))) zenon_H73); [ zenon_intro zenon_H74; idtac ].
% 1.91/2.08 elim zenon_H74. zenon_intro zenon_TT0_s. zenon_intro zenon_H75.
% 1.91/2.08 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_t)/\((~(has_endowment zenon_TX_t))/\(greater (age zenon_TX_t T) (age zenon_TX_t zenon_TT0_s))))->(greater (hazard_of_mortality zenon_TX_t T) (hazard_of_mortality zenon_TX_t zenon_TT0_s)))) zenon_H75); [ zenon_intro zenon_H76; idtac ].
% 1.91/2.08 elim zenon_H76. zenon_intro zenon_TT_bb. zenon_intro zenon_H77.
% 1.91/2.08 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H78. zenon_intro zenon_H66.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H11. zenon_intro zenon_H79.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H10. zenon_intro zenon_H1f.
% 1.91/2.08 generalize (assumption_4 zenon_TX_t). zenon_intro zenon_H7a.
% 1.91/2.08 generalize (zenon_H7a zenon_TT0_s). zenon_intro zenon_H7b.
% 1.91/2.08 generalize (zenon_H7b zenon_TT0_s). zenon_intro zenon_H7c.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H19 | zenon_intro zenon_H7f ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ].
% 1.91/2.08 apply zenon_H80. zenon_intro zenon_Hf.
% 1.91/2.08 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 apply zenon_H80. zenon_intro zenon_Hf.
% 1.91/2.08 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H82. zenon_intro zenon_H81.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H85 | zenon_intro zenon_H6b ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ].
% 1.91/2.08 generalize (definition_greater_or_equal (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H88.
% 1.91/2.08 generalize (zenon_H88 (capability zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H89.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_H89); [ zenon_intro zenon_H87; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H8a ].
% 1.91/2.08 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 1.91/2.08 apply zenon_H8d. apply refl_equal.
% 1.91/2.08 exact (zenon_H87 zenon_H8b).
% 1.91/2.08 generalize (assumption_6 zenon_TX_t). zenon_intro zenon_H8f.
% 1.91/2.08 generalize (assumption_5 zenon_TX_t). zenon_intro zenon_H90.
% 1.91/2.08 generalize (zenon_H8f zenon_TT0_s). zenon_intro zenon_H91.
% 1.91/2.08 generalize (zenon_H90 zenon_TT0_s). zenon_intro zenon_H25.
% 1.91/2.08 generalize (zenon_H91 zenon_TT0_s). zenon_intro zenon_H92.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H19 | zenon_intro zenon_H93 ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H95. zenon_intro zenon_H94.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H4e | zenon_intro zenon_H96 ].
% 1.91/2.08 generalize (assumption_11 zenon_TX_t). zenon_intro zenon_H0.
% 1.91/2.08 generalize (zenon_H0 zenon_E). zenon_intro zenon_H4d.
% 1.91/2.08 generalize (assumption_10 zenon_TX_t). zenon_intro zenon_H26.
% 1.91/2.08 generalize (assumption_12 zenon_TX_t). zenon_intro zenon_H97.
% 1.91/2.08 generalize (zenon_H97 zenon_TT0_s). zenon_intro zenon_H1e.
% 1.91/2.08 generalize (zenon_H4d zenon_TT0_s). zenon_intro zenon_H98.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 generalize (meaning_postulate_greater_comparable (external_ties zenon_TX_t zenon_TT0_s)). zenon_intro zenon_H3f.
% 1.91/2.08 generalize (zenon_H7a zenon_TT_bb). zenon_intro zenon_H99.
% 1.91/2.08 generalize (zenon_H99 zenon_TT0_s). zenon_intro zenon_H9a.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H9c); [ zenon_intro zenon_H19 | zenon_intro zenon_H9d ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_H9e | zenon_intro zenon_H80 ].
% 1.91/2.08 apply zenon_H9e. zenon_intro zenon_H1a.
% 1.91/2.08 apply (zenon_L2_ zenon_TT_bb zenon_TX_t); trivial.
% 1.91/2.08 apply zenon_H80. zenon_intro zenon_Hf.
% 1.91/2.08 apply (zenon_L1_ zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_Ha0. zenon_intro zenon_H9f.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_Ha0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H65 ].
% 1.91/2.08 apply (zenon_notand_s _ _ zenon_Ha1); [ zenon_intro zenon_H27 | zenon_intro zenon_Ha2 ].
% 1.91/2.08 apply (zenon_L4_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 generalize (definition_greater_or_equal (position zenon_TX_t zenon_TT0_s)). zenon_intro zenon_Ha3.
% 1.91/2.08 generalize (zenon_Ha3 (position zenon_TX_t zenon_TT_bb)). zenon_intro zenon_Ha4.
% 1.91/2.08 apply (zenon_equiv_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha2; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha5 ].
% 1.91/2.08 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_H50. zenon_intro zenon_Ha8.
% 1.91/2.08 generalize (zenon_H8f zenon_TT_bb). zenon_intro zenon_H4c.
% 1.91/2.08 generalize (zenon_H91 zenon_TT_bb). zenon_intro zenon_Ha9.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H19 | zenon_intro zenon_Haa ].
% 1.91/2.08 exact (zenon_H19 zenon_H11).
% 1.91/2.08 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Hac. zenon_intro zenon_Hab.
% 1.91/2.08 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_H41 | zenon_intro zenon_Had ].
% 1.91/2.08 apply (zenon_L6_ zenon_TT0_s zenon_TT_bb zenon_TX_t); trivial.
% 1.91/2.08 apply zenon_Ha8. apply sym_equal. exact zenon_Had.
% 1.91/2.08 exact (zenon_Ha2 zenon_Ha6).
% 1.91/2.08 apply (zenon_L7_ zenon_TT_bb zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 exact (zenon_H86 zenon_H96).
% 1.91/2.08 apply (zenon_L8_ zenon_TT0_s zenon_TX_t); trivial.
% 1.91/2.08 Qed.
% 1.91/2.08 % SZS output end Proof
% 1.91/2.08 (* END-PROOF *)
% 1.91/2.08 nodes searched: 111640
% 1.91/2.08 max branch formulas: 2448
% 1.91/2.08 proof nodes created: 1780
% 1.91/2.08 formulas created: 49490
% 1.91/2.08
%------------------------------------------------------------------------------