%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT039+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 06:24:21 AM UTC 2026 % Result : Theorem 0.21s 0.46s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT039+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.11/0.36 % Computer : n006.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Mon Sep 7 12:53:46 UTC 2026 % 0.11/0.36 % CPUTime : % 0.21/0.46 (* PROOF-FOUND *) % 0.21/0.46 % SZS status Theorem % 0.21/0.46 (* BEGIN-PROOF *) % 0.21/0.46 % SZS output start Proof % 0.21/0.46 Theorem prove_t8 : (forall P : zenon_U, (((observational_period P)/\(slow_change P))->(selection_favors (efficient_producers) (first_movers) P))). % 0.21/0.46 Proof. % 0.21/0.46 assert (zenon_L1_ : forall (zenon_TE_r : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (exists T : zenon_U, ((in_environment zenon_TE_r T)/\(greater T (critical_point zenon_TE_r)))) -> (~(greater (end_time zenon_TE_r) (critical_point zenon_TE_r))) -> (environment zenon_TE_r) -> (forall T : zenon_U, (((environment zenon_TE_r)/\(in_environment zenon_TE_r T))->(greater_or_equal (end_time zenon_TE_r) T))) -> False). % 0.21/0.46 do 1 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf zenon_H10. % 0.21/0.46 elim zenon_Hd. zenon_intro zenon_TT_s. zenon_intro zenon_H13. % 0.21/0.46 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.21/0.46 elim (classic ((~((end_time zenon_TE_r) = zenon_TT_s))/\(~(greater (end_time zenon_TE_r) zenon_TT_s)))); [ zenon_intro zenon_H16 | zenon_intro zenon_H17 ]. % 0.21/0.46 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.21/0.46 generalize (zenon_H10 zenon_TT_s). zenon_intro zenon_H1a. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.21/0.46 exact (zenon_H1e zenon_Hf). % 0.21/0.46 exact (zenon_H1d zenon_H15). % 0.21/0.46 generalize (mp_greater_or_equal (end_time zenon_TE_r)). zenon_intro zenon_H1f. % 0.21/0.46 generalize (zenon_H1f zenon_TT_s). zenon_intro zenon_H20. % 0.21/0.46 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H23; zenon_intro zenon_H22 | zenon_intro zenon_H1b; zenon_intro zenon_H21 ]. % 0.21/0.46 exact (zenon_H23 zenon_H1b). % 0.21/0.46 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.21/0.46 exact (zenon_H18 zenon_H25). % 0.21/0.46 exact (zenon_H19 zenon_H24). % 0.21/0.46 cut ((greater zenon_TT_s (critical_point zenon_TE_r)) = (greater (end_time zenon_TE_r) (critical_point zenon_TE_r))). % 0.21/0.46 intro zenon_D_pnotp. % 0.21/0.46 apply zenon_He. % 0.21/0.46 rewrite <- zenon_D_pnotp. % 0.21/0.46 exact zenon_H14. % 0.21/0.46 cut (((critical_point zenon_TE_r) = (critical_point zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.21/0.46 cut ((zenon_TT_s = (end_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 0.21/0.46 congruence. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.21/0.46 apply zenon_H29. zenon_intro zenon_H24. % 0.21/0.46 elim (classic ((end_time zenon_TE_r) = (end_time zenon_TE_r))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 0.21/0.46 cut (((end_time zenon_TE_r) = (end_time zenon_TE_r)) = (zenon_TT_s = (end_time zenon_TE_r))). % 0.21/0.46 intro zenon_D_pnotp. % 0.21/0.46 apply zenon_H27. % 0.21/0.46 rewrite <- zenon_D_pnotp. % 0.21/0.46 exact zenon_H2a. % 0.21/0.46 cut (((end_time zenon_TE_r) = (end_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.21/0.46 cut (((end_time zenon_TE_r) = zenon_TT_s)); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.21/0.46 congruence. % 0.21/0.46 exact (zenon_H19 zenon_H24). % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 apply zenon_H28. zenon_intro zenon_H25. % 0.21/0.46 generalize (zenon_Hc (end_time zenon_TE_r)). zenon_intro zenon_H2c. % 0.21/0.46 generalize (zenon_H2c zenon_TT_s). zenon_intro zenon_H2d. % 0.21/0.46 generalize (zenon_H2d (critical_point zenon_TE_r)). zenon_intro zenon_H2e. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H18 | zenon_intro zenon_H2f ]. % 0.21/0.46 exact (zenon_H18 zenon_H25). % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.21/0.46 exact (zenon_H31 zenon_H14). % 0.21/0.46 exact (zenon_He zenon_H30). % 0.21/0.46 apply zenon_H26. apply refl_equal. % 0.21/0.46 (* end of lemma zenon_L1_ *) % 0.21/0.46 assert (zenon_L2_ : forall (zenon_TE_r : zenon_U) (zenon_TP_cb : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (observational_period zenon_TP_cb) -> (slow_change zenon_TP_cb) -> (environment zenon_TE_r) -> (in_environment zenon_TP_cb zenon_TE_r) -> (~(greater (end_time zenon_TE_r) (critical_point zenon_TE_r))) -> (forall T : zenon_U, (((environment zenon_TE_r)/\(in_environment zenon_TE_r T))->(greater_or_equal (end_time zenon_TE_r) T))) -> False). % 0.21/0.46 do 2 intro. intros zenon_Hc zenon_H32 zenon_H33 zenon_Hf zenon_H34 zenon_He zenon_H10. % 0.21/0.46 generalize (mp4_critical_point zenon_TP_cb). zenon_intro zenon_H36. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.21/0.46 exact (zenon_H3a zenon_H32). % 0.21/0.46 exact (zenon_H39 zenon_H33). % 0.21/0.46 generalize (zenon_H37 zenon_TE_r). zenon_intro zenon_H3b. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_Hd ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H1e | zenon_intro zenon_H3d ]. % 0.21/0.46 exact (zenon_H1e zenon_Hf). % 0.21/0.46 exact (zenon_H3d zenon_H34). % 0.21/0.46 apply (zenon_L1_ zenon_TE_r); trivial. % 0.21/0.46 (* end of lemma zenon_L2_ *) % 0.21/0.46 apply NNPP. intro zenon_G. % 0.21/0.46 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z))))))); [ zenon_intro zenon_Hc | zenon_intro zenon_H3e ]. % 0.21/0.46 apply (zenon_notallex_s (fun P : zenon_U => (((observational_period P)/\(slow_change P))->(selection_favors (efficient_producers) (first_movers) P))) zenon_G); [ zenon_intro zenon_H3f; idtac ]. % 0.21/0.46 elim zenon_H3f. zenon_intro zenon_TP_cb. zenon_intro zenon_H40. % 0.21/0.46 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.21/0.46 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H32. zenon_intro zenon_H33. % 0.21/0.46 generalize (mp3_favoured_trategy zenon_TP_cb). zenon_intro zenon_H43. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H3a | zenon_intro zenon_H46 ]. % 0.21/0.46 exact (zenon_H3a zenon_H32). % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 0.21/0.46 exact (zenon_H48 mp_organizational_sets1). % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.21/0.46 exact (zenon_H4a mp_organizational_sets2). % 0.21/0.46 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(in_environment zenon_TP_cb E))->(selection_favors (efficient_producers) (first_movers) (end_time E)))) zenon_H49); [ zenon_intro zenon_H4b; idtac ]. % 0.21/0.46 elim zenon_H4b. zenon_intro zenon_TE_r. zenon_intro zenon_H4c. % 0.21/0.46 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.21/0.46 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_Hf. zenon_intro zenon_H34. % 0.21/0.46 generalize (mp_time_in_environment zenon_TE_r). zenon_intro zenon_H4f. % 0.21/0.46 generalize (mp_environment_end_point zenon_TE_r). zenon_intro zenon_H10. % 0.21/0.46 generalize (l8 zenon_TE_r). zenon_intro zenon_H50. % 0.21/0.46 generalize (zenon_H4f (end_time zenon_TE_r)). zenon_intro zenon_H51. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H1e | zenon_intro zenon_H54 ]. % 0.21/0.46 exact (zenon_H1e zenon_Hf). % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.21/0.46 generalize (mp_greater_or_equal (end_time zenon_TE_r)). zenon_intro zenon_H1f. % 0.21/0.46 generalize (zenon_H1f (start_time zenon_TE_r)). zenon_intro zenon_H57. % 0.21/0.46 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H56; zenon_intro zenon_H5a | zenon_intro zenon_H59; zenon_intro zenon_H58 ]. % 0.21/0.46 apply (zenon_notor_s _ _ zenon_H5a). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 0.21/0.46 generalize (mp_time_of_critical_point zenon_TE_r). zenon_intro zenon_H5d. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H1e | zenon_intro zenon_H5e ]. % 0.21/0.46 exact (zenon_H1e zenon_Hf). % 0.21/0.46 generalize (mp_greater_or_equal (critical_point zenon_TE_r)). zenon_intro zenon_H5f. % 0.21/0.46 generalize (zenon_H5f (start_time zenon_TE_r)). zenon_intro zenon_H60. % 0.21/0.46 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H63; zenon_intro zenon_H62 | zenon_intro zenon_H5e; zenon_intro zenon_H61 ]. % 0.21/0.46 exact (zenon_H63 zenon_H5e). % 0.21/0.46 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.21/0.46 elim (classic ((~((end_time zenon_TE_r) = (critical_point zenon_TE_r)))/\(~(greater (end_time zenon_TE_r) (critical_point zenon_TE_r))))); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ]. % 0.21/0.46 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H68. zenon_intro zenon_He. % 0.21/0.46 apply (zenon_L2_ zenon_TE_r zenon_TP_cb); trivial. % 0.21/0.46 cut ((greater (critical_point zenon_TE_r) (start_time zenon_TE_r)) = (greater (end_time zenon_TE_r) (start_time zenon_TE_r))). % 0.21/0.46 intro zenon_D_pnotp. % 0.21/0.46 apply zenon_H5c. % 0.21/0.46 rewrite <- zenon_D_pnotp. % 0.21/0.46 exact zenon_H65. % 0.21/0.46 cut (((start_time zenon_TE_r) = (start_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 0.21/0.46 cut (((critical_point zenon_TE_r) = (end_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 0.21/0.46 congruence. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.21/0.46 apply zenon_H6c. zenon_intro zenon_H6d. % 0.21/0.46 elim (classic ((end_time zenon_TE_r) = (end_time zenon_TE_r))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 0.21/0.46 cut (((end_time zenon_TE_r) = (end_time zenon_TE_r)) = ((critical_point zenon_TE_r) = (end_time zenon_TE_r))). % 0.21/0.46 intro zenon_D_pnotp. % 0.21/0.46 apply zenon_H6a. % 0.21/0.46 rewrite <- zenon_D_pnotp. % 0.21/0.46 exact zenon_H2a. % 0.21/0.46 cut (((end_time zenon_TE_r) = (end_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.21/0.46 cut (((end_time zenon_TE_r) = (critical_point zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 0.21/0.46 congruence. % 0.21/0.46 exact (zenon_H68 zenon_H6d). % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 apply zenon_H6b. zenon_intro zenon_H30. % 0.21/0.46 generalize (zenon_Hc (end_time zenon_TE_r)). zenon_intro zenon_H2c. % 0.21/0.46 generalize (zenon_H2c (critical_point zenon_TE_r)). zenon_intro zenon_H6e. % 0.21/0.46 generalize (zenon_H6e (start_time zenon_TE_r)). zenon_intro zenon_H6f. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_He | zenon_intro zenon_H70 ]. % 0.21/0.46 exact (zenon_He zenon_H30). % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ]. % 0.21/0.46 exact (zenon_H72 zenon_H65). % 0.21/0.46 exact (zenon_H5c zenon_H71). % 0.21/0.46 apply zenon_H69. apply refl_equal. % 0.21/0.46 elim (classic (greater (end_time zenon_TE_r) (critical_point zenon_TE_r))); [ zenon_intro zenon_H30 | zenon_intro zenon_He ]. % 0.21/0.46 cut ((greater (end_time zenon_TE_r) (critical_point zenon_TE_r)) = (greater (end_time zenon_TE_r) (start_time zenon_TE_r))). % 0.21/0.46 intro zenon_D_pnotp. % 0.21/0.46 apply zenon_H5c. % 0.21/0.46 rewrite <- zenon_D_pnotp. % 0.21/0.46 exact zenon_H30. % 0.21/0.46 cut (((critical_point zenon_TE_r) = (start_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 0.21/0.46 cut (((end_time zenon_TE_r) = (end_time zenon_TE_r))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.21/0.46 congruence. % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 exact (zenon_H73 zenon_H64). % 0.21/0.46 apply (zenon_L2_ zenon_TE_r zenon_TP_cb); trivial. % 0.21/0.46 exact (zenon_H56 zenon_H59). % 0.21/0.46 generalize (mp_greater_or_equal (end_time zenon_TE_r)). zenon_intro zenon_H1f. % 0.21/0.46 generalize (zenon_H1f (end_time zenon_TE_r)). zenon_intro zenon_H74. % 0.21/0.46 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H55; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ]. % 0.21/0.46 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H78. zenon_intro zenon_H2b. % 0.21/0.46 apply zenon_H2b. apply refl_equal. % 0.21/0.46 exact (zenon_H55 zenon_H76). % 0.21/0.46 generalize (zenon_H50 (end_time zenon_TE_r)). zenon_intro zenon_H79. % 0.21/0.46 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ]. % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H1e | zenon_intro zenon_H7c ]. % 0.21/0.46 exact (zenon_H1e zenon_Hf). % 0.21/0.46 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H7d | zenon_intro zenon_He ]. % 0.21/0.46 exact (zenon_H7d zenon_H52). % 0.21/0.46 apply (zenon_L2_ zenon_TE_r zenon_TP_cb); trivial. % 0.21/0.46 exact (zenon_H4d zenon_H7a). % 0.21/0.46 exact (zenon_H41 zenon_H44). % 0.21/0.46 apply zenon_H3e. zenon_intro zenon_Tx_ew. apply NNPP. zenon_intro zenon_H7f. % 0.21/0.46 apply zenon_H7f. zenon_intro zenon_Ty_ey. apply NNPP. zenon_intro zenon_H81. % 0.21/0.46 apply zenon_H81. zenon_intro zenon_Tz_fa. apply NNPP. zenon_intro zenon_H83. % 0.21/0.46 apply (zenon_notimply_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84. % 0.21/0.46 apply (zenon_notimply_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86. % 0.21/0.46 generalize (mp_greater_transitivity zenon_Tx_ew). zenon_intro zenon_H88. % 0.21/0.46 generalize (zenon_H88 zenon_Ty_ey). zenon_intro zenon_H89. % 0.21/0.46 generalize (zenon_H89 zenon_Tz_fa). zenon_intro zenon_H8a. % 0.21/0.47 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 0.21/0.47 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ]. % 0.21/0.47 exact (zenon_H8e zenon_H85). % 0.21/0.47 exact (zenon_H8d zenon_H87). % 0.21/0.47 exact (zenon_H86 zenon_H8b). % 0.21/0.47 Qed. % 0.21/0.47 % SZS output end Proof % 0.21/0.47 (* END-PROOF *) % 0.21/0.47 nodes searched: 317 % 0.21/0.47 max branch formulas: 130 % 0.21/0.47 proof nodes created: 78 % 0.21/0.47 formulas created: 1203 % 0.21/0.47 %------------------------------------------------------------------------------