%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT036+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 0.25s 0.59s % Output : Proof 0.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT036+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n016.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 12:43:32 UTC 2026 % 0.09/0.36 % CPUTime : % 0.25/0.59 (* PROOF-FOUND *) % 0.25/0.59 % SZS status Theorem % 0.25/0.59 (* BEGIN-PROOF *) % 0.25/0.59 % SZS output start Proof % 0.25/0.59 Theorem prove_t5 : (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(outcompetes (first_movers) (efficient_producers) T))))). % 0.25/0.59 Proof. % 0.25/0.59 assert (zenon_L1_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (~(subpopulations (efficient_producers) (first_movers) zenon_TE_n zenon_TT_m)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_n zenon_TT_m) -> (environment zenon_TE_n) -> False). % 0.25/0.59 do 2 intro. intros zenon_H9 zenon_Ha zenon_Hb. % 0.25/0.59 generalize (mp_symmetry_of_FM_and_EP zenon_TE_n). zenon_intro zenon_He. % 0.25/0.59 generalize (zenon_He zenon_TT_m). zenon_intro zenon_Hf. % 0.25/0.59 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.25/0.59 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.25/0.59 exact (zenon_H13 zenon_Hb). % 0.25/0.59 exact (zenon_H12 zenon_Ha). % 0.25/0.59 exact (zenon_H9 zenon_H10). % 0.25/0.59 (* end of lemma zenon_L1_ *) % 0.25/0.59 assert (zenon_L2_ : forall (zenon_TT_m : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_m)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_m)) -> (~(greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False). % 0.25/0.59 do 1 intro. intros zenon_H14 zenon_H15 zenon_H16. % 0.25/0.59 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.25/0.59 exact (zenon_H18 zenon_H16). % 0.25/0.59 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.25/0.59 exact (zenon_H15 zenon_H1b). % 0.25/0.59 (* end of lemma zenon_L2_ *) % 0.25/0.59 assert (zenon_L3_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_n)/\((in_environment zenon_TE_n T)/\((~(greater (zero) (growth_rate S1 T)))/\(greater (resilience S2) (resilience S1)))))->(~(greater (zero) (growth_rate S2 T))))))) -> (environment zenon_TE_n) -> (in_environment zenon_TE_n zenon_TT_m) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_m))) -> (greater (zero) (growth_rate (efficient_producers) zenon_TT_m)) -> False). % 0.25/0.59 do 2 intro. intros zenon_H1c zenon_Hb zenon_H1d zenon_H1e zenon_H1a. % 0.25/0.59 generalize (zenon_H1c (first_movers)). zenon_intro zenon_H1f. % 0.25/0.59 generalize (zenon_H1f (efficient_producers)). zenon_intro zenon_H20. % 0.25/0.59 generalize (zenon_H20 zenon_TT_m). zenon_intro zenon_H21. % 0.25/0.59 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.25/0.59 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H13 | zenon_intro zenon_H24 ]. % 0.25/0.59 exact (zenon_H13 zenon_Hb). % 0.25/0.59 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.25/0.59 exact (zenon_H26 zenon_H1d). % 0.25/0.59 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.25/0.59 exact (zenon_H28 zenon_H1e). % 0.25/0.59 exact (zenon_H27 a2). % 0.25/0.59 exact (zenon_H22 zenon_H1a). % 0.25/0.59 (* end of lemma zenon_L3_ *) % 0.25/0.59 assert (zenon_L4_ : forall (zenon_TT_m : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_m)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_m)) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_m))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False). % 0.25/0.59 do 1 intro. intros zenon_H14 zenon_H22 zenon_H16. % 0.25/0.59 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.25/0.59 exact (zenon_H18 zenon_H16). % 0.25/0.59 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.25/0.59 exact (zenon_H22 zenon_H1a). % 0.25/0.59 (* end of lemma zenon_L4_ *) % 0.25/0.59 assert (zenon_L5_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_n)/\(subpopulations S1 S2 zenon_TE_n T))->(((greater_or_equal (growth_rate S2 T) (zero))/\(greater (zero) (growth_rate S1 T)))<->(outcompetes S2 S1 T)))))) -> (environment zenon_TE_n) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_n zenon_TT_m) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_m))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False). % 0.25/0.60 do 2 intro. intros zenon_H29 zenon_Hb zenon_Ha zenon_H22 zenon_H16. % 0.25/0.60 generalize (zenon_H29 (efficient_producers)). zenon_intro zenon_H2a. % 0.25/0.60 generalize (zenon_H2a (first_movers)). zenon_intro zenon_H2b. % 0.25/0.60 generalize (zenon_H2b zenon_TT_m). zenon_intro zenon_H2c. % 0.25/0.60 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H14 ]. % 0.25/0.60 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H13 | zenon_intro zenon_H9 ]. % 0.25/0.60 exact (zenon_H13 zenon_Hb). % 0.25/0.60 apply (zenon_L1_ zenon_TT_m zenon_TE_n); trivial. % 0.25/0.60 apply (zenon_L4_ zenon_TT_m); trivial. % 0.25/0.60 (* end of lemma zenon_L5_ *) % 0.25/0.60 apply NNPP. intro zenon_G. % 0.25/0.60 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(outcompetes (first_movers) (efficient_producers) T))))) zenon_G); [ zenon_intro zenon_H2e; idtac ]. % 0.25/0.60 elim zenon_H2e. zenon_intro zenon_TE_n. zenon_intro zenon_H2f. % 0.25/0.60 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_n)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_n T))->(~(outcompetes (first_movers) (efficient_producers) T)))) zenon_H2f); [ zenon_intro zenon_H30; idtac ]. % 0.25/0.60 elim zenon_H30. zenon_intro zenon_TT_m. zenon_intro zenon_H31. % 0.25/0.60 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.25/0.60 apply zenon_H32. zenon_intro zenon_H16. % 0.25/0.60 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.25/0.60 generalize (mp_growth_rate_relationships zenon_E). zenon_intro zenon_H34. % 0.25/0.60 generalize (mp_time_point_occur zenon_TE_n). zenon_intro zenon_H35. % 0.25/0.60 generalize (zenon_H35 zenon_TT_m). zenon_intro zenon_H36. % 0.25/0.60 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H11 | zenon_intro zenon_H1d ]. % 0.25/0.60 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.25/0.60 exact (zenon_H13 zenon_Hb). % 0.25/0.60 exact (zenon_H12 zenon_Ha). % 0.25/0.60 generalize (a12 zenon_TE_n). zenon_intro zenon_H1c. % 0.25/0.60 generalize (zenon_H34 (first_movers)). zenon_intro zenon_H37. % 0.25/0.60 generalize (zenon_H37 zenon_E). zenon_intro zenon_H38. % 0.25/0.60 generalize (zenon_H38 zenon_TT_m). zenon_intro zenon_H39. % 0.25/0.60 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3b; zenon_intro zenon_H28 | zenon_intro zenon_H3a; zenon_intro zenon_H1e ]. % 0.25/0.60 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3c. zenon_intro zenon_H15. % 0.25/0.60 generalize (d2 zenon_TE_n). zenon_intro zenon_H29. % 0.25/0.60 generalize (zenon_H29 (efficient_producers)). zenon_intro zenon_H2a. % 0.25/0.60 generalize (zenon_H2a (first_movers)). zenon_intro zenon_H2b. % 0.25/0.60 generalize (zenon_H2b zenon_TT_m). zenon_intro zenon_H2c. % 0.25/0.60 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H14 ]. % 0.25/0.60 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H13 | zenon_intro zenon_H9 ]. % 0.25/0.60 exact (zenon_H13 zenon_Hb). % 0.25/0.60 apply (zenon_L1_ zenon_TT_m zenon_TE_n); trivial. % 0.25/0.60 apply (zenon_L2_ zenon_TT_m); trivial. % 0.25/0.60 generalize (d2 zenon_TE_n). zenon_intro zenon_H29. % 0.25/0.60 generalize (zenon_H34 (efficient_producers)). zenon_intro zenon_H3d. % 0.25/0.60 generalize (zenon_H3d zenon_E). zenon_intro zenon_H3e. % 0.25/0.60 generalize (zenon_H3e zenon_TT_m). zenon_intro zenon_H3f. % 0.25/0.60 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H22 ]. % 0.25/0.60 apply zenon_H41. zenon_intro zenon_H1a. % 0.25/0.60 apply (zenon_L3_ zenon_TT_m zenon_TE_n); trivial. % 0.25/0.60 apply (zenon_L5_ zenon_TT_m zenon_TE_n); trivial. % 0.25/0.60 Qed. % 0.25/0.60 % SZS output end Proof % 0.25/0.60 (* END-PROOF *) % 0.25/0.60 nodes searched: 7647 % 0.25/0.60 max branch formulas: 1753 % 0.25/0.60 proof nodes created: 270 % 0.25/0.60 formulas created: 28406 % 0.25/0.60 %------------------------------------------------------------------------------