%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 06:24:20 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 % 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.34 % Computer : n026.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Mon Sep 7 12:24:57 UTC 2026 % 0.09/0.35 % 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_t1 : (forall E : zenon_U, (((environment E)/\(stable E))->(exists To : zenon_U, ((in_environment E To)/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T To))->(selection_favors (efficient_producers) (first_movers) T))))))). % 0.12/0.44 Proof. % 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 To : zenon_U, ((in_environment E To)/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T To))->(selection_favors (efficient_producers) (first_movers) T))))))) zenon_G); [ zenon_intro zenon_H3; idtac ]. % 0.12/0.44 elim zenon_H3. zenon_intro zenon_TE_e. zenon_intro zenon_H5. % 0.12/0.44 apply (zenon_notimply_s _ _ zenon_H5). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.12/0.44 generalize (mp1_high_growth_rates zenon_TE_e). zenon_intro zenon_Ha. % 0.12/0.44 generalize (zenon_Ha (first_movers)). zenon_intro zenon_Hb. % 0.12/0.44 generalize (zenon_Hb (efficient_producers)). zenon_intro zenon_Hc. % 0.12/0.44 generalize (l1 zenon_TE_e). zenon_intro zenon_Hd. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_Hd); [ zenon_intro zenon_Hf | zenon_intro zenon_He ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.12/0.44 exact (zenon_H11 zenon_H9). % 0.12/0.44 exact (zenon_H10 zenon_H8). % 0.12/0.44 elim zenon_He. zenon_intro zenon_TTo_s. zenon_intro zenon_H13. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.12/0.44 apply zenon_H6. exists zenon_TTo_s. apply NNPP. zenon_intro zenon_H16. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.12/0.44 exact (zenon_H18 zenon_H15). % 0.12/0.44 apply (zenon_notallex_s (fun T : zenon_U => (((subpopulations (first_movers) (efficient_producers) zenon_TE_e T)/\(greater_or_equal T zenon_TTo_s))->(selection_favors (efficient_producers) (first_movers) T))) zenon_H17); [ zenon_intro zenon_H19; idtac ]. % 0.12/0.44 elim zenon_H19. zenon_intro zenon_TT_ba. zenon_intro zenon_H1b. % 0.12/0.44 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.12/0.44 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.12/0.44 generalize (zenon_Hc zenon_TT_ba). zenon_intro zenon_H20. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H11 | zenon_intro zenon_H23 ]. % 0.12/0.44 exact (zenon_H11 zenon_H9). % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.12/0.44 exact (zenon_H25 zenon_H1f). % 0.12/0.44 generalize (zenon_H14 zenon_TT_ba). zenon_intro zenon_H26. % 0.12/0.44 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H25 | zenon_intro zenon_H29 ]. % 0.12/0.44 exact (zenon_H25 zenon_H1f). % 0.12/0.44 exact (zenon_H29 zenon_H1e). % 0.12/0.44 exact (zenon_H24 zenon_H27). % 0.12/0.44 exact (zenon_H1c zenon_H21). % 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: 175 % 0.12/0.44 max branch formulas: 141 % 0.12/0.44 proof nodes created: 48 % 0.12/0.44 formulas created: 943 % 0.12/0.44 %------------------------------------------------------------------------------