TSTP Solution File: MGT042+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT042+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 22:31:09 EDT 2022
% Result : Theorem 0.60s 0.82s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MGT042+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:22:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.82 (* PROOF-FOUND *)
% 0.60/0.82 % SZS status Theorem
% 0.60/0.82 (* BEGIN-PROOF *)
% 0.60/0.82 % SZS output start Proof
% 0.60/0.82 Theorem lemma_1 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_immunity X T0))/\(~(has_immunity X T))))->((((greater (stock_of_knowledge X T) (stock_of_knowledge X T0))/\((smaller_or_equal (internal_friction X T) (internal_friction X T0))/\(greater_or_equal (external_ties X T) (external_ties X T0))))->(smaller (hazard_of_mortality X T) (hazard_of_mortality X T0)))/\(((greater_or_equal (stock_of_knowledge X T) (stock_of_knowledge X T0))/\((smaller_or_equal (internal_friction X T) (internal_friction X T0))/\(greater (external_ties X T) (external_ties X T0))))->(smaller (hazard_of_mortality X T) (hazard_of_mortality X T0)))))))).
% 0.60/0.82 Proof.
% 0.60/0.82 assert (zenon_L1_ : forall (zenon_TT_m : zenon_U) (zenon_TT0_n : zenon_U) (zenon_TX_o : zenon_U), (greater (internal_friction zenon_TX_o zenon_TT0_n) (internal_friction zenon_TX_o zenon_TT_m)) -> (~(smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m) (internal_friction zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_Ha zenon_Hb.
% 0.60/0.82 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf.
% 0.60/0.82 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 0.60/0.82 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16.
% 0.60/0.82 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ].
% 0.60/0.82 exact (zenon_H19 zenon_Ha).
% 0.60/0.82 exact (zenon_H15 zenon_H18).
% 0.60/0.82 exact (zenon_Hb zenon_H12).
% 0.60/0.82 (* end of lemma zenon_L1_ *)
% 0.60/0.82 assert (zenon_L2_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (greater (stock_of_knowledge zenon_TX_o zenon_TT_m) (stock_of_knowledge zenon_TX_o zenon_TT0_n)) -> (greater (internal_friction zenon_TX_o zenon_TT0_n) (internal_friction zenon_TX_o zenon_TT_m)) -> (~(greater (capability zenon_TX_o zenon_TT_m) (capability zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H1b zenon_Ha zenon_H1c.
% 0.60/0.82 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d.
% 0.60/0.82 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e.
% 0.60/0.82 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_Hb ].
% 0.60/0.82 exact (zenon_H26 zenon_H1b).
% 0.60/0.82 apply (zenon_L1_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial.
% 0.60/0.82 exact (zenon_H1c zenon_H24).
% 0.60/0.82 (* end of lemma zenon_L2_ *)
% 0.60/0.82 assert (zenon_L3_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (greater (external_ties zenon_TX_o zenon_TT_m) (external_ties zenon_TX_o zenon_TT0_n)) -> (~(greater (position zenon_TX_o zenon_TT_m) (position zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H27 zenon_H28.
% 0.60/0.82 generalize (assumption_6 zenon_TX_o). zenon_intro zenon_H29.
% 0.60/0.82 generalize (zenon_H29 zenon_TT0_n). zenon_intro zenon_H2a.
% 0.60/0.82 generalize (zenon_H2a zenon_TT_m). zenon_intro zenon_H2b.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.60/0.82 exact (zenon_H30 zenon_H27).
% 0.60/0.82 exact (zenon_H28 zenon_H2f).
% 0.60/0.82 (* end of lemma zenon_L3_ *)
% 0.60/0.82 assert (zenon_L4_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (greater (external_ties zenon_TX_o zenon_TT_m) (external_ties zenon_TX_o zenon_TT0_n)) -> (~(greater_or_equal (position zenon_TX_o zenon_TT_m) (position zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H27 zenon_H31.
% 0.60/0.82 generalize (definition_greater_or_equal (position zenon_TX_o zenon_TT_m)). zenon_intro zenon_H32.
% 0.60/0.82 generalize (zenon_H32 (position zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H33.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H31; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H28. zenon_intro zenon_H37.
% 0.60/0.82 apply (zenon_L3_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 exact (zenon_H31 zenon_H35).
% 0.60/0.82 (* end of lemma zenon_L4_ *)
% 0.60/0.82 assert (zenon_L5_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (smaller (hazard_of_mortality zenon_TX_o zenon_TT_m) (hazard_of_mortality zenon_TX_o zenon_TT0_n)) -> (~(greater (hazard_of_mortality zenon_TX_o zenon_TT0_n) (hazard_of_mortality zenon_TX_o zenon_TT_m))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H38 zenon_H39.
% 0.60/0.82 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a.
% 0.60/0.82 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.82 exact (zenon_H3d zenon_H38).
% 0.60/0.82 exact (zenon_H39 zenon_H3c).
% 0.60/0.82 (* end of lemma zenon_L5_ *)
% 0.60/0.82 assert (zenon_L6_ : forall (zenon_TT_m : zenon_U) (zenon_TT0_n : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (~(has_immunity zenon_TX_o zenon_TT0_n)) -> (~(has_immunity zenon_TX_o zenon_TT_m)) -> (greater (stock_of_knowledge zenon_TX_o zenon_TT_m) (stock_of_knowledge zenon_TX_o zenon_TT0_n)) -> (greater (internal_friction zenon_TX_o zenon_TT0_n) (internal_friction zenon_TX_o zenon_TT_m)) -> (greater (external_ties zenon_TX_o zenon_TT_m) (external_ties zenon_TX_o zenon_TT0_n)) -> (~(greater (hazard_of_mortality zenon_TX_o zenon_TT0_n) (hazard_of_mortality zenon_TX_o zenon_TT_m))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H3e zenon_H3f zenon_H1b zenon_Ha zenon_H27 zenon_H39.
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.60/0.82 apply (zenon_L2_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 (* end of lemma zenon_L6_ *)
% 0.60/0.82 assert (zenon_L7_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), ((internal_friction zenon_TX_o zenon_TT_m) = (internal_friction zenon_TX_o zenon_TT0_n)) -> (~(smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m) (internal_friction zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H4b zenon_Hb.
% 0.60/0.82 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf.
% 0.60/0.82 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 0.60/0.82 exact (zenon_H14 zenon_H4b).
% 0.60/0.82 exact (zenon_Hb zenon_H12).
% 0.60/0.82 (* end of lemma zenon_L7_ *)
% 0.60/0.82 assert (zenon_L8_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (greater (stock_of_knowledge zenon_TX_o zenon_TT_m) (stock_of_knowledge zenon_TX_o zenon_TT0_n)) -> ((internal_friction zenon_TX_o zenon_TT_m) = (internal_friction zenon_TX_o zenon_TT0_n)) -> (~(greater (capability zenon_TX_o zenon_TT_m) (capability zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H1b zenon_H4b zenon_H1c.
% 0.60/0.82 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d.
% 0.60/0.82 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e.
% 0.60/0.82 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_Hb ].
% 0.60/0.82 exact (zenon_H26 zenon_H1b).
% 0.60/0.82 apply (zenon_L7_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 exact (zenon_H1c zenon_H24).
% 0.60/0.82 (* end of lemma zenon_L8_ *)
% 0.60/0.82 assert (zenon_L9_ : forall (zenon_TT_m : zenon_U) (zenon_TT0_n : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> (~(has_immunity zenon_TX_o zenon_TT0_n)) -> (~(has_immunity zenon_TX_o zenon_TT_m)) -> (greater (stock_of_knowledge zenon_TX_o zenon_TT_m) (stock_of_knowledge zenon_TX_o zenon_TT0_n)) -> ((internal_friction zenon_TX_o zenon_TT_m) = (internal_friction zenon_TX_o zenon_TT0_n)) -> (greater (external_ties zenon_TX_o zenon_TT_m) (external_ties zenon_TX_o zenon_TT0_n)) -> (~(greater (hazard_of_mortality zenon_TX_o zenon_TT0_n) (hazard_of_mortality zenon_TX_o zenon_TT_m))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H3e zenon_H3f zenon_H1b zenon_H4b zenon_H27 zenon_H39.
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.60/0.82 apply (zenon_L8_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 (* end of lemma zenon_L9_ *)
% 0.60/0.82 assert (zenon_L10_ : forall (zenon_TT0_n : zenon_U) (zenon_TT_m : zenon_U) (zenon_TX_o : zenon_U), (organization zenon_TX_o) -> ((external_ties zenon_TX_o zenon_TT_m) = (external_ties zenon_TX_o zenon_TT0_n)) -> (~(greater_or_equal (position zenon_TX_o zenon_TT_m) (position zenon_TX_o zenon_TT0_n))) -> False).
% 0.60/0.82 do 3 intro. intros zenon_H1a zenon_H4c zenon_H31.
% 0.60/0.82 generalize (definition_greater_or_equal (position zenon_TX_o zenon_TT_m)). zenon_intro zenon_H32.
% 0.60/0.82 generalize (zenon_H32 (position zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H33.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H31; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H28. zenon_intro zenon_H37.
% 0.60/0.82 generalize (assumption_6 zenon_TX_o). zenon_intro zenon_H29.
% 0.60/0.82 generalize (zenon_H29 zenon_TT0_n). zenon_intro zenon_H2a.
% 0.60/0.82 generalize (zenon_H2a zenon_TT_m). zenon_intro zenon_H2b.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.60/0.82 exact (zenon_H4e zenon_H4c).
% 0.60/0.82 exact (zenon_H37 zenon_H4d).
% 0.60/0.82 exact (zenon_H31 zenon_H35).
% 0.60/0.82 (* end of lemma zenon_L10_ *)
% 0.60/0.82 apply NNPP. intro zenon_G.
% 0.60/0.82 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_immunity X T0))/\(~(has_immunity X T))))->((((greater (stock_of_knowledge X T) (stock_of_knowledge X T0))/\((smaller_or_equal (internal_friction X T) (internal_friction X T0))/\(greater_or_equal (external_ties X T) (external_ties X T0))))->(smaller (hazard_of_mortality X T) (hazard_of_mortality X T0)))/\(((greater_or_equal (stock_of_knowledge X T) (stock_of_knowledge X T0))/\((smaller_or_equal (internal_friction X T) (internal_friction X T0))/\(greater (external_ties X T) (external_ties X T0))))->(smaller (hazard_of_mortality X T) (hazard_of_mortality X T0)))))))) zenon_G); [ zenon_intro zenon_H4f; idtac ].
% 0.60/0.82 elim zenon_H4f. zenon_intro zenon_TX_o. zenon_intro zenon_H50.
% 0.60/0.82 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_o)/\((~(has_immunity zenon_TX_o T0))/\(~(has_immunity zenon_TX_o T))))->((((greater (stock_of_knowledge zenon_TX_o T) (stock_of_knowledge zenon_TX_o T0))/\((smaller_or_equal (internal_friction zenon_TX_o T) (internal_friction zenon_TX_o T0))/\(greater_or_equal (external_ties zenon_TX_o T) (external_ties zenon_TX_o T0))))->(smaller (hazard_of_mortality zenon_TX_o T) (hazard_of_mortality zenon_TX_o T0)))/\(((greater_or_equal (stock_of_knowledge zenon_TX_o T) (stock_of_knowledge zenon_TX_o T0))/\((smaller_or_equal (internal_friction zenon_TX_o T) (internal_friction zenon_TX_o T0))/\(greater (external_ties zenon_TX_o T) (external_ties zenon_TX_o T0))))->(smaller (hazard_of_mortality zenon_TX_o T) (hazard_of_mortality zenon_TX_o T0))))))) zenon_H50); [ zenon_intro zenon_H51; idtac ].
% 0.60/0.82 elim zenon_H51. zenon_intro zenon_TT0_n. zenon_intro zenon_H52.
% 0.60/0.82 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_o)/\((~(has_immunity zenon_TX_o zenon_TT0_n))/\(~(has_immunity zenon_TX_o T))))->((((greater (stock_of_knowledge zenon_TX_o T) (stock_of_knowledge zenon_TX_o zenon_TT0_n))/\((smaller_or_equal (internal_friction zenon_TX_o T) (internal_friction zenon_TX_o zenon_TT0_n))/\(greater_or_equal (external_ties zenon_TX_o T) (external_ties zenon_TX_o zenon_TT0_n))))->(smaller (hazard_of_mortality zenon_TX_o T) (hazard_of_mortality zenon_TX_o zenon_TT0_n)))/\(((greater_or_equal (stock_of_knowledge zenon_TX_o T) (stock_of_knowledge zenon_TX_o zenon_TT0_n))/\((smaller_or_equal (internal_friction zenon_TX_o T) (internal_friction zenon_TX_o zenon_TT0_n))/\(greater (external_ties zenon_TX_o T) (external_ties zenon_TX_o zenon_TT0_n))))->(smaller (hazard_of_mortality zenon_TX_o T) (hazard_of_mortality zenon_TX_o zenon_TT0_n)))))) zenon_H52); [ zenon_intro zenon_H53; idtac ].
% 0.60/0.82 elim zenon_H53. zenon_intro zenon_TT_m. zenon_intro zenon_H54.
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H1a. zenon_intro zenon_H57.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H3e. zenon_intro zenon_H3f.
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_H59). zenon_intro zenon_H5a. zenon_intro zenon_H3d.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H1b. zenon_intro zenon_H5b.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H12. zenon_intro zenon_H5c.
% 0.60/0.82 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf.
% 0.60/0.82 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ].
% 0.60/0.82 exact (zenon_Hb zenon_H12).
% 0.60/0.82 generalize (definition_greater_or_equal (external_ties zenon_TX_o zenon_TT_m)). zenon_intro zenon_H5d.
% 0.60/0.82 generalize (zenon_H5d (external_ties zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H5e.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H5c; zenon_intro zenon_H5f ].
% 0.60/0.82 exact (zenon_H61 zenon_H5c).
% 0.60/0.82 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a.
% 0.60/0.82 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H27 | zenon_intro zenon_H4c ].
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ].
% 0.60/0.82 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16.
% 0.60/0.82 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ].
% 0.60/0.82 exact (zenon_H15 zenon_H18).
% 0.60/0.82 apply (zenon_L6_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L9_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ].
% 0.60/0.82 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16.
% 0.60/0.82 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ].
% 0.60/0.82 exact (zenon_H15 zenon_H18).
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.60/0.82 apply (zenon_L2_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L10_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.60/0.82 apply (zenon_L8_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L10_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 exact (zenon_H3d zenon_H38).
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_H58). zenon_intro zenon_H62. zenon_intro zenon_H3d.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H12. zenon_intro zenon_H27.
% 0.60/0.82 generalize (definition_greater_or_equal (stock_of_knowledge zenon_TX_o zenon_TT_m)). zenon_intro zenon_H65.
% 0.60/0.82 generalize (zenon_H65 (stock_of_knowledge zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H66.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H69; zenon_intro zenon_H68 | zenon_intro zenon_H64; zenon_intro zenon_H67 ].
% 0.60/0.82 exact (zenon_H69 zenon_H64).
% 0.60/0.82 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf.
% 0.60/0.82 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ].
% 0.60/0.82 exact (zenon_Hb zenon_H12).
% 0.60/0.82 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a.
% 0.60/0.82 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ].
% 0.60/0.82 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16.
% 0.60/0.82 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ].
% 0.60/0.82 exact (zenon_H15 zenon_H18).
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1b | zenon_intro zenon_H6a ].
% 0.60/0.82 apply (zenon_L6_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial.
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.60/0.82 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d.
% 0.60/0.82 generalize (zenon_H1d zenon_TT_m). zenon_intro zenon_H6b.
% 0.60/0.82 generalize (zenon_H6b zenon_TT0_n). zenon_intro zenon_H6c.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H21 | zenon_intro zenon_H6d ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H73); [ zenon_intro zenon_H74 | zenon_intro zenon_H19 ].
% 0.60/0.82 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H75.
% 0.60/0.82 generalize (zenon_H75 (stock_of_knowledge zenon_TX_o zenon_TT_m)). zenon_intro zenon_H76.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H74; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H77 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7b. zenon_intro zenon_H7a.
% 0.60/0.82 apply zenon_H7a. apply sym_equal. exact zenon_H6a.
% 0.60/0.82 exact (zenon_H74 zenon_H78).
% 0.60/0.82 exact (zenon_H19 zenon_Ha).
% 0.60/0.82 generalize (definition_smaller (capability zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H7c.
% 0.60/0.82 generalize (zenon_H7c (capability zenon_TX_o zenon_TT_m)). zenon_intro zenon_H7d.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H7e; zenon_intro zenon_H1c | zenon_intro zenon_H72; zenon_intro zenon_H24 ].
% 0.60/0.82 exact (zenon_H7e zenon_H72).
% 0.60/0.82 exact (zenon_H1c zenon_H24).
% 0.60/0.82 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1b | zenon_intro zenon_H6a ].
% 0.60/0.82 apply (zenon_L9_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial.
% 0.60/0.82 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41.
% 0.60/0.82 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.60/0.82 exact (zenon_H47 zenon_H3e).
% 0.60/0.82 exact (zenon_H46 zenon_H3f).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H38 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H82 | zenon_intro zenon_H28 ].
% 0.60/0.82 generalize (definition_greater_or_equal (capability zenon_TX_o zenon_TT_m)). zenon_intro zenon_H83.
% 0.60/0.82 generalize (zenon_H83 (capability zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H84.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H84); [ zenon_intro zenon_H82; zenon_intro zenon_H87 | zenon_intro zenon_H86; zenon_intro zenon_H85 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H1c. zenon_intro zenon_H88.
% 0.60/0.82 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d.
% 0.60/0.82 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e.
% 0.60/0.82 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.60/0.82 exact (zenon_H21 zenon_H1a).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H14 ].
% 0.60/0.82 exact (zenon_H8d zenon_H6a).
% 0.60/0.82 exact (zenon_H14 zenon_H4b).
% 0.60/0.82 exact (zenon_H88 zenon_H8b).
% 0.60/0.82 exact (zenon_H82 zenon_H86).
% 0.60/0.82 apply (zenon_L3_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial.
% 0.60/0.82 exact (zenon_H3d zenon_H38).
% 0.60/0.82 Qed.
% 0.60/0.82 % SZS output end Proof
% 0.60/0.82 (* END-PROOF *)
% 0.60/0.82 nodes searched: 22833
% 0.60/0.82 max branch formulas: 442
% 0.60/0.82 proof nodes created: 436
% 0.60/0.82 formulas created: 14820
% 0.60/0.82
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