%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT042+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:22 AM UTC 2026 % Result : Theorem 0.65s 1.03s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT042+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.36 % Computer : n005.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 13:03:50 UTC 2026 % 0.10/0.37 % CPUTime : % 0.65/1.03 (* PROOF-FOUND *) % 0.65/1.03 % SZS status Theorem % 0.65/1.03 (* BEGIN-PROOF *) % 0.65/1.03 % SZS output start Proof % 0.65/1.03 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)))))))). % 0.65/1.03 Proof. % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_Ha zenon_Hb. % 0.65/1.03 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf. % 0.65/1.03 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.65/1.03 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.65/1.03 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16. % 0.65/1.03 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ]. % 0.65/1.03 exact (zenon_H19 zenon_Ha). % 0.65/1.03 exact (zenon_H15 zenon_H18). % 0.65/1.03 exact (zenon_Hb zenon_H12). % 0.65/1.03 (* end of lemma zenon_L1_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H1b zenon_Ha zenon_H1c. % 0.65/1.03 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d. % 0.65/1.03 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e. % 0.65/1.03 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_Hb ]. % 0.65/1.03 exact (zenon_H26 zenon_H1b). % 0.65/1.03 apply (zenon_L1_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial. % 0.65/1.03 exact (zenon_H1c zenon_H24). % 0.65/1.03 (* end of lemma zenon_L2_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H27 zenon_H28. % 0.65/1.03 generalize (assumption_6 zenon_TX_o). zenon_intro zenon_H29. % 0.65/1.03 generalize (zenon_H29 zenon_TT0_n). zenon_intro zenon_H2a. % 0.65/1.03 generalize (zenon_H2a zenon_TT_m). zenon_intro zenon_H2b. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.65/1.03 exact (zenon_H30 zenon_H27). % 0.65/1.03 exact (zenon_H28 zenon_H2f). % 0.65/1.03 (* end of lemma zenon_L3_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H27 zenon_H31. % 0.65/1.03 generalize (definition_greater_or_equal (position zenon_TX_o zenon_TT_m)). zenon_intro zenon_H32. % 0.65/1.03 generalize (zenon_H32 (position zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H33. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H31; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.65/1.03 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H28. zenon_intro zenon_H37. % 0.65/1.03 apply (zenon_L3_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 exact (zenon_H31 zenon_H35). % 0.65/1.03 (* end of lemma zenon_L4_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H38 zenon_H39. % 0.65/1.03 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a. % 0.65/1.03 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ]. % 0.65/1.03 exact (zenon_H3d zenon_H38). % 0.65/1.03 exact (zenon_H39 zenon_H3c). % 0.65/1.03 (* end of lemma zenon_L5_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H3e zenon_H3f zenon_H1b zenon_Ha zenon_H27 zenon_H39. % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.65/1.03 exact (zenon_H47 zenon_H3e). % 0.65/1.03 exact (zenon_H46 zenon_H3f). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.65/1.03 apply (zenon_L2_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 (* end of lemma zenon_L6_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H4b zenon_Hb. % 0.65/1.03 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf. % 0.65/1.03 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.65/1.03 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.65/1.03 exact (zenon_H14 zenon_H4b). % 0.65/1.03 exact (zenon_Hb zenon_H12). % 0.65/1.03 (* end of lemma zenon_L7_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H1b zenon_H4b zenon_H1c. % 0.65/1.03 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d. % 0.65/1.03 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e. % 0.65/1.03 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_Hb ]. % 0.65/1.03 exact (zenon_H26 zenon_H1b). % 0.65/1.03 apply (zenon_L7_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 exact (zenon_H1c zenon_H24). % 0.65/1.03 (* end of lemma zenon_L8_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H3e zenon_H3f zenon_H1b zenon_H4b zenon_H27 zenon_H39. % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.65/1.03 exact (zenon_H47 zenon_H3e). % 0.65/1.03 exact (zenon_H46 zenon_H3f). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.65/1.03 apply (zenon_L8_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 (* end of lemma zenon_L9_ *) % 0.65/1.03 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). % 0.65/1.03 do 3 intro. intros zenon_H1a zenon_H4c zenon_H31. % 0.65/1.03 generalize (definition_greater_or_equal (position zenon_TX_o zenon_TT_m)). zenon_intro zenon_H32. % 0.65/1.03 generalize (zenon_H32 (position zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H33. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H31; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.65/1.03 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H28. zenon_intro zenon_H37. % 0.65/1.03 generalize (assumption_6 zenon_TX_o). zenon_intro zenon_H29. % 0.65/1.03 generalize (zenon_H29 zenon_TT0_n). zenon_intro zenon_H2a. % 0.65/1.03 generalize (zenon_H2a zenon_TT_m). zenon_intro zenon_H2b. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.65/1.03 exact (zenon_H4e zenon_H4c). % 0.65/1.03 exact (zenon_H37 zenon_H4d). % 0.65/1.03 exact (zenon_H31 zenon_H35). % 0.65/1.03 (* end of lemma zenon_L10_ *) % 0.65/1.03 apply NNPP. intro zenon_G. % 0.65/1.03 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 ]. % 0.65/1.03 elim zenon_H4f. zenon_intro zenon_TX_o. zenon_intro zenon_H50. % 0.65/1.03 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 ]. % 0.65/1.03 elim zenon_H51. zenon_intro zenon_TT0_n. zenon_intro zenon_H52. % 0.65/1.03 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 ]. % 0.65/1.03 elim zenon_H53. zenon_intro zenon_TT_m. zenon_intro zenon_H54. % 0.65/1.03 apply (zenon_notimply_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H1a. zenon_intro zenon_H57. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H3e. zenon_intro zenon_H3f. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.65/1.03 apply (zenon_notimply_s _ _ zenon_H59). zenon_intro zenon_H5a. zenon_intro zenon_H3d. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H1b. zenon_intro zenon_H5b. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H12. zenon_intro zenon_H5c. % 0.65/1.03 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf. % 0.65/1.03 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.65/1.03 exact (zenon_Hb zenon_H12). % 0.65/1.03 generalize (definition_greater_or_equal (external_ties zenon_TX_o zenon_TT_m)). zenon_intro zenon_H5d. % 0.65/1.03 generalize (zenon_H5d (external_ties zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H5e. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H5c; zenon_intro zenon_H5f ]. % 0.65/1.03 exact (zenon_H61 zenon_H5c). % 0.65/1.03 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a. % 0.65/1.03 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ]. % 0.65/1.03 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H27 | zenon_intro zenon_H4c ]. % 0.65/1.03 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ]. % 0.65/1.03 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16. % 0.65/1.03 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ]. % 0.65/1.03 exact (zenon_H15 zenon_H18). % 0.65/1.03 apply (zenon_L6_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L9_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ]. % 0.65/1.03 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16. % 0.65/1.03 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ]. % 0.65/1.03 exact (zenon_H15 zenon_H18). % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.65/1.03 exact (zenon_H47 zenon_H3e). % 0.65/1.03 exact (zenon_H46 zenon_H3f). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.65/1.03 apply (zenon_L2_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L10_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.65/1.03 exact (zenon_H47 zenon_H3e). % 0.65/1.03 exact (zenon_H46 zenon_H3f). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.65/1.03 apply (zenon_L8_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L10_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 exact (zenon_H3d zenon_H38). % 0.65/1.03 apply (zenon_notimply_s _ _ zenon_H58). zenon_intro zenon_H62. zenon_intro zenon_H3d. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H12. zenon_intro zenon_H27. % 0.65/1.03 generalize (definition_greater_or_equal (stock_of_knowledge zenon_TX_o zenon_TT_m)). zenon_intro zenon_H65. % 0.65/1.03 generalize (zenon_H65 (stock_of_knowledge zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H66. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H69; zenon_intro zenon_H68 | zenon_intro zenon_H64; zenon_intro zenon_H67 ]. % 0.65/1.03 exact (zenon_H69 zenon_H64). % 0.65/1.03 generalize (definition_smaller_or_equal (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_Hf. % 0.65/1.03 generalize (zenon_Hf (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H10. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hb; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.65/1.03 exact (zenon_Hb zenon_H12). % 0.65/1.03 generalize (definition_smaller (hazard_of_mortality zenon_TX_o zenon_TT_m)). zenon_intro zenon_H3a. % 0.65/1.03 generalize (zenon_H3a (hazard_of_mortality zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H3b. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H3c ]. % 0.65/1.03 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H4b ]. % 0.65/1.03 generalize (definition_smaller (internal_friction zenon_TX_o zenon_TT_m)). zenon_intro zenon_H16. % 0.65/1.03 generalize (zenon_H16 (internal_friction zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H17. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_Ha ]. % 0.65/1.03 exact (zenon_H15 zenon_H18). % 0.65/1.03 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1b | zenon_intro zenon_H6a ]. % 0.65/1.03 apply (zenon_L6_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial. % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.65/1.03 exact (zenon_H47 zenon_H3e). % 0.65/1.03 exact (zenon_H46 zenon_H3f). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H38 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ]. % 0.65/1.03 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d. % 0.65/1.03 generalize (zenon_H1d zenon_TT_m). zenon_intro zenon_H6b. % 0.65/1.03 generalize (zenon_H6b zenon_TT0_n). zenon_intro zenon_H6c. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H21 | zenon_intro zenon_H6d ]. % 0.65/1.03 exact (zenon_H21 zenon_H1a). % 0.65/1.03 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 0.65/1.03 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.65/1.03 apply (zenon_notand_s _ _ zenon_H73); [ zenon_intro zenon_H74 | zenon_intro zenon_H19 ]. % 0.65/1.03 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H75. % 0.65/1.03 generalize (zenon_H75 (stock_of_knowledge zenon_TX_o zenon_TT_m)). zenon_intro zenon_H76. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H74; zenon_intro zenon_H79 | zenon_intro zenon_H78; zenon_intro zenon_H77 ]. % 0.65/1.03 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 0.65/1.03 apply zenon_H7a. apply sym_equal. exact zenon_H6a. % 0.65/1.03 exact (zenon_H74 zenon_H78). % 0.65/1.03 exact (zenon_H19 zenon_Ha). % 0.65/1.03 generalize (definition_smaller (capability zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H7c. % 0.65/1.03 generalize (zenon_H7c (capability zenon_TX_o zenon_TT_m)). zenon_intro zenon_H7d. % 0.65/1.03 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H7e; zenon_intro zenon_H1c | zenon_intro zenon_H72; zenon_intro zenon_H24 ]. % 0.65/1.03 exact (zenon_H7e zenon_H72). % 0.65/1.03 exact (zenon_H1c zenon_H24). % 0.65/1.03 apply (zenon_L4_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.65/1.03 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1b | zenon_intro zenon_H6a ]. % 0.65/1.03 apply (zenon_L9_ zenon_TT_m zenon_TT0_n zenon_TX_o); trivial. % 0.65/1.03 generalize (assumption_4 zenon_TX_o). zenon_intro zenon_H40. % 0.65/1.03 generalize (zenon_H40 zenon_TT0_n). zenon_intro zenon_H41. % 0.65/1.03 generalize (zenon_H41 zenon_TT_m). zenon_intro zenon_H42. % 0.65/1.03 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.16/1.03 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 0.16/1.03 exact (zenon_H21 zenon_H1a). % 0.16/1.03 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.16/1.03 exact (zenon_H47 zenon_H3e). % 0.16/1.03 exact (zenon_H46 zenon_H3f). % 0.16/1.03 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.16/1.03 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.16/1.03 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H38 ]. % 0.16/1.03 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H82 | zenon_intro zenon_H28 ]. % 0.16/1.03 generalize (definition_greater_or_equal (capability zenon_TX_o zenon_TT_m)). zenon_intro zenon_H83. % 0.16/1.03 generalize (zenon_H83 (capability zenon_TX_o zenon_TT0_n)). zenon_intro zenon_H84. % 0.16/1.03 apply (zenon_equiv_s _ _ zenon_H84); [ zenon_intro zenon_H82; zenon_intro zenon_H87 | zenon_intro zenon_H86; zenon_intro zenon_H85 ]. % 0.16/1.03 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H1c. zenon_intro zenon_H88. % 0.16/1.03 generalize (assumption_5 zenon_TX_o). zenon_intro zenon_H1d. % 0.16/1.03 generalize (zenon_H1d zenon_TT0_n). zenon_intro zenon_H1e. % 0.16/1.03 generalize (zenon_H1e zenon_TT_m). zenon_intro zenon_H1f. % 0.16/1.03 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.16/1.03 exact (zenon_H21 zenon_H1a). % 0.16/1.03 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.16/1.03 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 0.16/1.03 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 0.16/1.03 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H8d | zenon_intro zenon_H14 ]. % 0.16/1.03 exact (zenon_H8d zenon_H6a). % 0.16/1.03 exact (zenon_H14 zenon_H4b). % 0.16/1.03 exact (zenon_H88 zenon_H8b). % 0.16/1.03 exact (zenon_H82 zenon_H86). % 0.16/1.03 apply (zenon_L3_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.16/1.03 apply (zenon_L5_ zenon_TT0_n zenon_TT_m zenon_TX_o); trivial. % 0.16/1.03 exact (zenon_H3d zenon_H38). % 0.16/1.03 Qed. % 0.16/1.03 % SZS output end Proof % 0.16/1.03 (* END-PROOF *) % 0.16/1.03 nodes searched: 22833 % 0.16/1.03 max branch formulas: 442 % 0.16/1.03 proof nodes created: 436 % 0.16/1.03 formulas created: 14684 % 0.16/1.03 %------------------------------------------------------------------------------