%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT030+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 0.14s 0.41s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n013.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 12:17:05 UTC 2026 % 0.08/0.35 % CPUTime : % 0.14/0.41 (* PROOF-FOUND *) % 0.14/0.41 % SZS status Theorem % 0.14/0.41 (* BEGIN-PROOF *) % 0.14/0.41 % SZS output start Proof % 0.14/0.41 Theorem prove_l12 : (forall E : zenon_U, (((environment E)/\(stable E))->(exists To : zenon_U, ((in_environment E To)/\((~(greater (growth_rate (efficient_producers) To) (growth_rate (first_movers) To)))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater T To))->(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))))). % 0.14/0.41 Proof. % 0.14/0.41 apply NNPP. intro zenon_G. % 0.14/0.41 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(stable E))->(exists To : zenon_U, ((in_environment E To)/\((~(greater (growth_rate (efficient_producers) To) (growth_rate (first_movers) To)))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater T To))->(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))))) zenon_G); [ zenon_intro zenon_H3; idtac ]. % 0.14/0.41 elim zenon_H3. zenon_intro zenon_TE_e. zenon_intro zenon_H5. % 0.14/0.41 apply (zenon_notimply_s _ _ zenon_H5). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.14/0.41 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.14/0.41 generalize (mp_earliest_time_growth_rate_exceeds zenon_TE_e). zenon_intro zenon_Ha. % 0.14/0.41 apply (zenon_imply_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.14/0.41 apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.14/0.41 exact (zenon_He zenon_H9). % 0.14/0.41 generalize (l1 zenon_TE_e). zenon_intro zenon_Hf. % 0.14/0.41 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.14/0.41 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_He | zenon_intro zenon_H12 ]. % 0.14/0.41 exact (zenon_He zenon_H9). % 0.14/0.41 exact (zenon_H12 zenon_H8). % 0.14/0.41 exact (zenon_Hd zenon_H10). % 0.14/0.41 exact (zenon_H6 zenon_Hb). % 0.14/0.41 Qed. % 0.14/0.41 % SZS output end Proof % 0.14/0.41 (* END-PROOF *) % 0.14/0.41 nodes searched: 102 % 0.14/0.41 max branch formulas: 98 % 0.14/0.41 proof nodes created: 25 % 0.14/0.41 formulas created: 800 % 0.14/0.41 %------------------------------------------------------------------------------