%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 06:24:19 AM UTC 2026 % Result : Theorem 0.12s 0.44s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n013.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 12:14:20 UTC 2026 % 0.09/0.36 % CPUTime : % 0.12/0.44 (* PROOF-FOUND *) % 0.12/0.44 % SZS status Theorem % 0.12/0.44 (* BEGIN-PROOF *) % 0.12/0.44 % SZS output start Proof % 0.12/0.44 Theorem prove_l10 : (forall E : zenon_U, (((environment E)/\(stable E))->(exists T2 : zenon_U, ((greater T2 (appear (efficient_producers) E))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T T2))->(greater (zero) (growth_rate (first_movers) T)))))))). % 0.12/0.44 Proof. % 0.12/0.44 assert (zenon_L1_ : forall (zenon_TT_f : zenon_U), ((greater (growth_rate (efficient_producers) zenon_TT_f) (zero))/\(greater (zero) (growth_rate (first_movers) zenon_TT_f))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_f))) -> False). % 0.12/0.44 do 1 intro. intros zenon_H3 zenon_H4. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H3). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.12/0.44 exact (zenon_H4 zenon_H6). % 0.12/0.44 (* end of lemma zenon_L1_ *) % 0.12/0.44 apply NNPP. intro zenon_G. % 0.12/0.44 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(stable E))->(exists T2 : zenon_U, ((greater T2 (appear (efficient_producers) E))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T T2))->(greater (zero) (growth_rate (first_movers) T)))))))) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.12/0.44 elim zenon_H8. zenon_intro zenon_TE_j. zenon_intro zenon_Ha. % 0.12/0.44 apply (zenon_notimply_s _ _ zenon_Ha). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.12/0.44 apply (zenon_and_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.12/0.44 generalize (l11 zenon_TE_j). zenon_intro zenon_Hf. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.12/0.44 exact (zenon_H13 zenon_He). % 0.12/0.44 exact (zenon_H12 zenon_Hd). % 0.12/0.44 elim zenon_H10. zenon_intro zenon_TTo_u. zenon_intro zenon_H15. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.12/0.44 generalize (mp_first_movers_negative_growth zenon_TE_j). zenon_intro zenon_H18. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H13 | zenon_intro zenon_H1b ]. % 0.12/0.44 exact (zenon_H13 zenon_He). % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H12 | zenon_intro zenon_H1c ]. % 0.12/0.44 exact (zenon_H12 zenon_Hd). % 0.12/0.44 apply zenon_H1c. exists zenon_TTo_u. apply NNPP. zenon_intro zenon_H1d. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.12/0.44 exact (zenon_H1f zenon_H17). % 0.12/0.44 apply (zenon_notallex_s (fun T : zenon_U => (((subpopulations (first_movers) (efficient_producers) zenon_TE_j T)/\(greater_or_equal T zenon_TTo_u))->(greater (zero) (growth_rate (first_movers) T)))) zenon_H1e); [ zenon_intro zenon_H20; idtac ]. % 0.12/0.44 elim zenon_H20. zenon_intro zenon_TT_f. zenon_intro zenon_H21. % 0.12/0.44 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H22. zenon_intro zenon_H4. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.12/0.44 generalize (zenon_H16 zenon_TT_f). zenon_intro zenon_H25. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_H3 ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.12/0.44 exact (zenon_H28 zenon_H24). % 0.12/0.44 exact (zenon_H27 zenon_H23). % 0.12/0.44 apply (zenon_L1_ zenon_TT_f); trivial. % 0.12/0.44 exact (zenon_Hb zenon_H19). % 0.12/0.44 Qed. % 0.12/0.44 % SZS output end Proof % 0.12/0.44 (* END-PROOF *) % 0.12/0.44 nodes searched: 144 % 0.12/0.44 max branch formulas: 134 % 0.12/0.44 proof nodes created: 42 % 0.12/0.44 formulas created: 892 % 0.12/0.44 %------------------------------------------------------------------------------