%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 06:24:18 AM UTC 2026 % Result : Theorem 0.22s 0.56s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.06 % Command : run_zenon %s %d % 0.18/0.43 % Computer : n019.cluster.edu % 0.18/0.43 % Model : x86_64 x86_64 % 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.43 % Memory : 8046.5625MB % 0.18/0.43 % OS : Linux 6.8.0-71-generic % 0.18/0.44 % CPULimit : 300 % 0.18/0.44 % WCLimit : 300 % 0.18/0.44 % DateTime : Mon Sep 7 12:07:37 UTC 2026 % 0.18/0.44 % CPUTime : % 0.22/0.56 (* PROOF-FOUND *) % 0.22/0.56 % SZS status Theorem % 0.22/0.56 (* BEGIN-PROOF *) % 0.22/0.56 % SZS output start Proof % 0.22/0.56 Theorem prove_l5 : (forall E : zenon_U, (((environment E)/\(stable E))->(in_environment E (critical_point E)))). % 0.22/0.56 Proof. % 0.22/0.56 apply NNPP. intro zenon_G. % 0.22/0.56 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(stable E))->(in_environment E (critical_point E)))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.22/0.56 elim zenon_H4. zenon_intro zenon_TE_f. zenon_intro zenon_H6. % 0.22/0.56 apply (zenon_notimply_s _ _ zenon_H6). zenon_intro zenon_H8. zenon_intro zenon_H7. % 0.22/0.56 apply (zenon_and_s _ _ zenon_H8). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.22/0.56 generalize (d1 zenon_TE_f). zenon_intro zenon_Hb. % 0.22/0.56 generalize (mp_earliest_time_growth_rate_exceeds zenon_TE_f). zenon_intro zenon_Hc. % 0.22/0.56 apply (zenon_imply_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.22/0.56 apply (zenon_notand_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.22/0.56 exact (zenon_H10 zenon_Ha). % 0.22/0.56 generalize (l1 zenon_TE_f). zenon_intro zenon_H11. % 0.22/0.56 apply (zenon_imply_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.22/0.56 apply (zenon_notand_s _ _ zenon_H13); [ zenon_intro zenon_H10 | zenon_intro zenon_H14 ]. % 0.22/0.56 exact (zenon_H10 zenon_Ha). % 0.22/0.56 exact (zenon_H14 zenon_H9). % 0.22/0.56 exact (zenon_Hf zenon_H12). % 0.22/0.56 elim zenon_Hd. zenon_intro zenon_TTo_v. zenon_intro zenon_H16. % 0.22/0.56 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.22/0.56 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.22/0.56 generalize (zenon_Hb zenon_TTo_v). zenon_intro zenon_H1b. % 0.22/0.56 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.22/0.56 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H10 | zenon_intro zenon_H1e ]. % 0.22/0.56 exact (zenon_H10 zenon_Ha). % 0.22/0.56 apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.22/0.56 exact (zenon_H20 zenon_H1a). % 0.22/0.56 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.22/0.56 exact (zenon_H22 zenon_H18). % 0.22/0.56 exact (zenon_H21 zenon_H19). % 0.22/0.56 cut ((in_environment zenon_TE_f zenon_TTo_v) = (in_environment zenon_TE_f (critical_point zenon_TE_f))). % 0.22/0.56 intro zenon_D_pnotp. % 0.22/0.56 apply zenon_H7. % 0.22/0.56 rewrite <- zenon_D_pnotp. % 0.22/0.56 exact zenon_H18. % 0.22/0.56 cut ((zenon_TTo_v = (critical_point zenon_TE_f))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 0.22/0.56 cut ((zenon_TE_f = zenon_TE_f)); [idtac | apply NNPP; zenon_intro zenon_H24]. % 0.22/0.56 congruence. % 0.22/0.56 apply zenon_H24. apply refl_equal. % 0.22/0.56 exact (zenon_H23 zenon_H1c). % 0.22/0.56 Qed. % 0.22/0.56 % SZS output end Proof % 0.22/0.56 (* END-PROOF *) % 0.22/0.56 nodes searched: 304 % 0.22/0.56 max branch formulas: 141 % 0.22/0.56 proof nodes created: 80 % 0.22/0.56 formulas created: 1473 % 0.22/0.56 %------------------------------------------------------------------------------