%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT043+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n031.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 0.37s 0.67s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT043+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.34 % Computer : n031.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Mon Sep 7 13:08:11 UTC 2026 % 0.08/0.35 % CPUTime : % 0.37/0.67 (* PROOF-FOUND *) % 0.37/0.67 % SZS status Theorem % 0.37/0.67 (* BEGIN-PROOF *) % 0.37/0.67 % SZS output start Proof % 0.37/0.67 Theorem lemma_2 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((~(has_immunity X T0))/\((~(has_immunity X T))/\(((stock_of_knowledge X T) = (stock_of_knowledge X T0))/\((greater (internal_friction X T) (internal_friction X T0))/\((external_ties X T0) = (external_ties X T)))))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))). % 0.37/0.67 Proof. % 0.37/0.67 assert (zenon_L1_ : forall (zenon_TT0_o : zenon_U) (zenon_TT_p : zenon_U) (zenon_TX_q : zenon_U), (forall T : zenon_U, ((organization zenon_TX_q)->(((greater (external_ties zenon_TX_q T) (external_ties zenon_TX_q zenon_TT_p))->(greater (position zenon_TX_q T) (position zenon_TX_q zenon_TT_p)))/\(((external_ties zenon_TX_q T) = (external_ties zenon_TX_q zenon_TT_p))->((position zenon_TX_q T) = (position zenon_TX_q zenon_TT_p)))))) -> (organization zenon_TX_q) -> ((external_ties zenon_TX_q zenon_TT0_o) = (external_ties zenon_TX_q zenon_TT_p)) -> (~((position zenon_TX_q zenon_TT0_o) = (position zenon_TX_q zenon_TT_p))) -> False). % 0.37/0.67 do 3 intro. intros zenon_Ha zenon_Hb zenon_Hc zenon_Hd. % 0.37/0.67 generalize (zenon_Ha zenon_TT0_o). zenon_intro zenon_H11. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.37/0.67 exact (zenon_H13 zenon_Hb). % 0.37/0.67 apply (zenon_and_s _ _ zenon_H12). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.37/0.67 exact (zenon_H17 zenon_Hc). % 0.37/0.67 exact (zenon_Hd zenon_H16). % 0.37/0.67 (* end of lemma zenon_L1_ *) % 0.37/0.67 assert (zenon_L2_ : forall (zenon_TT_p : zenon_U) (zenon_TT0_o : zenon_U) (zenon_TX_q : zenon_U), (smaller (hazard_of_mortality zenon_TX_q zenon_TT0_o) (hazard_of_mortality zenon_TX_q zenon_TT_p)) -> (~(greater (hazard_of_mortality zenon_TX_q zenon_TT_p) (hazard_of_mortality zenon_TX_q zenon_TT0_o))) -> False). % 0.37/0.67 do 3 intro. intros zenon_H18 zenon_H19. % 0.37/0.67 generalize (definition_smaller (hazard_of_mortality zenon_TX_q zenon_TT0_o)). zenon_intro zenon_H1a. % 0.37/0.67 generalize (zenon_H1a (hazard_of_mortality zenon_TX_q zenon_TT_p)). zenon_intro zenon_H1b. % 0.37/0.67 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_H1c ]. % 0.37/0.67 exact (zenon_H1d zenon_H18). % 0.37/0.67 exact (zenon_H19 zenon_H1c). % 0.37/0.67 (* end of lemma zenon_L2_ *) % 0.37/0.67 apply NNPP. intro zenon_G. % 0.37/0.67 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))/\(((stock_of_knowledge X T) = (stock_of_knowledge X T0))/\((greater (internal_friction X T) (internal_friction X T0))/\((external_ties X T0) = (external_ties X T)))))))->(greater (hazard_of_mortality X T) (hazard_of_mortality X T0)))))) zenon_G); [ zenon_intro zenon_H1e; idtac ]. % 0.37/0.67 elim zenon_H1e. zenon_intro zenon_TX_q. zenon_intro zenon_H1f. % 0.37/0.67 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_q)/\((~(has_immunity zenon_TX_q T0))/\((~(has_immunity zenon_TX_q T))/\(((stock_of_knowledge zenon_TX_q T) = (stock_of_knowledge zenon_TX_q T0))/\((greater (internal_friction zenon_TX_q T) (internal_friction zenon_TX_q T0))/\((external_ties zenon_TX_q T0) = (external_ties zenon_TX_q T)))))))->(greater (hazard_of_mortality zenon_TX_q T) (hazard_of_mortality zenon_TX_q T0))))) zenon_H1f); [ zenon_intro zenon_H20; idtac ]. % 0.37/0.67 elim zenon_H20. zenon_intro zenon_TT0_o. zenon_intro zenon_H21. % 0.37/0.67 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_q)/\((~(has_immunity zenon_TX_q zenon_TT0_o))/\((~(has_immunity zenon_TX_q T))/\(((stock_of_knowledge zenon_TX_q T) = (stock_of_knowledge zenon_TX_q zenon_TT0_o))/\((greater (internal_friction zenon_TX_q T) (internal_friction zenon_TX_q zenon_TT0_o))/\((external_ties zenon_TX_q zenon_TT0_o) = (external_ties zenon_TX_q T)))))))->(greater (hazard_of_mortality zenon_TX_q T) (hazard_of_mortality zenon_TX_q zenon_TT0_o)))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.37/0.67 elim zenon_H22. zenon_intro zenon_TT_p. zenon_intro zenon_H23. % 0.37/0.67 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H24. zenon_intro zenon_H19. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_Hb. zenon_intro zenon_H25. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_Hc. % 0.37/0.67 generalize (assumption_4 zenon_TX_q). zenon_intro zenon_H2d. % 0.37/0.67 generalize (zenon_H2d zenon_TT_p). zenon_intro zenon_H2e. % 0.37/0.67 generalize (zenon_H2e zenon_TT0_o). zenon_intro zenon_H2f. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.37/0.67 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H13 | zenon_intro zenon_H32 ]. % 0.37/0.67 exact (zenon_H13 zenon_Hb). % 0.37/0.67 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.37/0.67 exact (zenon_H34 zenon_H29). % 0.37/0.67 exact (zenon_H33 zenon_H27). % 0.37/0.67 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H37 | zenon_intro zenon_H18 ]. % 0.37/0.67 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.37/0.67 generalize (assumption_5 zenon_TX_q). zenon_intro zenon_H3a. % 0.37/0.67 generalize (zenon_H3a zenon_TT0_o). zenon_intro zenon_H3b. % 0.37/0.67 generalize (zenon_H3b zenon_TT_p). zenon_intro zenon_H3c. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H13 | zenon_intro zenon_H3d ]. % 0.37/0.67 exact (zenon_H13 zenon_Hb). % 0.37/0.67 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.37/0.67 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.37/0.67 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.37/0.67 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.37/0.67 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_q zenon_TT_p)). zenon_intro zenon_H46. % 0.37/0.67 generalize (zenon_H46 (stock_of_knowledge zenon_TX_q zenon_TT0_o)). zenon_intro zenon_H47. % 0.37/0.67 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H45; zenon_intro zenon_H4a | zenon_intro zenon_H49; zenon_intro zenon_H48 ]. % 0.37/0.67 apply (zenon_notor_s _ _ zenon_H4a). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.37/0.67 exact (zenon_H4b zenon_H2b). % 0.37/0.67 exact (zenon_H45 zenon_H49). % 0.37/0.67 exact (zenon_H44 zenon_H2c). % 0.37/0.67 generalize (definition_smaller (capability zenon_TX_q zenon_TT_p)). zenon_intro zenon_H4d. % 0.37/0.67 generalize (zenon_H4d (capability zenon_TX_q zenon_TT0_o)). zenon_intro zenon_H4e. % 0.37/0.67 apply (zenon_equiv_s _ _ zenon_H4e); [ zenon_intro zenon_H50; zenon_intro zenon_H39 | zenon_intro zenon_H42; zenon_intro zenon_H4f ]. % 0.37/0.67 exact (zenon_H50 zenon_H42). % 0.37/0.67 exact (zenon_H39 zenon_H4f). % 0.37/0.67 generalize (definition_greater_or_equal (position zenon_TX_q zenon_TT0_o)). zenon_intro zenon_H51. % 0.37/0.67 generalize (zenon_H51 (position zenon_TX_q zenon_TT_p)). zenon_intro zenon_H52. % 0.37/0.67 apply (zenon_equiv_s _ _ zenon_H52); [ zenon_intro zenon_H38; zenon_intro zenon_H55 | zenon_intro zenon_H54; zenon_intro zenon_H53 ]. % 0.37/0.67 apply (zenon_notor_s _ _ zenon_H55). zenon_intro zenon_H56. zenon_intro zenon_Hd. % 0.37/0.67 generalize (assumption_6 zenon_TX_q). zenon_intro zenon_H57. % 0.37/0.67 generalize (zenon_H57 zenon_TT_p). zenon_intro zenon_Ha. % 0.37/0.67 apply (zenon_L1_ zenon_TT0_o zenon_TT_p zenon_TX_q); trivial. % 0.37/0.67 exact (zenon_H38 zenon_H54). % 0.37/0.67 apply (zenon_L2_ zenon_TT_p zenon_TT0_o zenon_TX_q); trivial. % 0.37/0.67 Qed. % 0.37/0.67 % SZS output end Proof % 0.37/0.67 (* END-PROOF *) % 0.37/0.67 nodes searched: 9160 % 0.37/0.67 max branch formulas: 562 % 0.37/0.67 proof nodes created: 190 % 0.37/0.67 formulas created: 8242 % 0.37/0.67 %------------------------------------------------------------------------------