%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT021+1 : 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 0.13s 0.44s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n019.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 12:02:22 UTC 2026 % 0.08/0.36 % CPUTime : % 0.13/0.44 (* PROOF-FOUND *) % 0.13/0.44 % SZS status Theorem % 0.13/0.44 (* BEGIN-PROOF *) % 0.13/0.44 % SZS output start Proof % 0.13/0.44 Theorem prove_l3 : (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))). % 0.13/0.44 Proof. % 0.13/0.44 assert (zenon_L1_ : forall (zenon_TE_l : zenon_U) (zenon_TT_m : zenon_U), (decreases (difference (disbanding_rate (first_movers) zenon_TT_m) (disbanding_rate (efficient_producers) zenon_TT_m))) -> (constant (resources zenon_TE_l zenon_TT_m)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_l zenon_TT_m) -> (environment zenon_TE_l) -> False). % 0.13/0.44 do 2 intro. intros zenon_H7 zenon_H8 zenon_H9 zenon_Ha. % 0.13/0.44 generalize (l4 zenon_TE_l). zenon_intro zenon_Hd. % 0.13/0.44 generalize (zenon_Hd zenon_TT_m). zenon_intro zenon_He. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.13/0.44 exact (zenon_H12 zenon_Ha). % 0.13/0.44 exact (zenon_H11 zenon_H9). % 0.13/0.44 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.13/0.44 exact (zenon_H16 zenon_H8). % 0.13/0.44 exact (zenon_H15 zenon_H7). % 0.13/0.44 (* end of lemma zenon_L1_ *) % 0.13/0.44 assert (zenon_L2_ : forall (zenon_TT_m : zenon_U), (increases (difference (disbanding_rate (first_movers) zenon_TT_m) (disbanding_rate (efficient_producers) zenon_TT_m))) -> (decreases (difference (disbanding_rate (first_movers) zenon_TT_m) (disbanding_rate (efficient_producers) zenon_TT_m))) -> False). % 0.13/0.44 do 1 intro. intros zenon_H17 zenon_H7. % 0.13/0.44 generalize (mp_increase_not_decrease (difference (disbanding_rate (first_movers) zenon_TT_m) (disbanding_rate (efficient_producers) zenon_TT_m))). zenon_intro zenon_H18. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H19 | zenon_intro zenon_H15 ]. % 0.13/0.44 exact (zenon_H19 zenon_H17). % 0.13/0.44 exact (zenon_H15 zenon_H7). % 0.13/0.44 (* end of lemma zenon_L2_ *) % 0.13/0.44 apply NNPP. intro zenon_G. % 0.13/0.44 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) zenon_G); [ zenon_intro zenon_H1a; idtac ]. % 0.13/0.44 elim zenon_H1a. zenon_intro zenon_TE_l. zenon_intro zenon_H1b. % 0.13/0.44 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_l)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_l T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T)))))) zenon_H1b); [ zenon_intro zenon_H1c; idtac ]. % 0.13/0.44 elim zenon_H1c. zenon_intro zenon_TT_m. zenon_intro zenon_H1d. % 0.13/0.44 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.13/0.44 apply zenon_H1e. zenon_intro zenon_H7. % 0.13/0.44 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.13/0.44 generalize (mp_time_point_in_environment zenon_TE_l). zenon_intro zenon_H20. % 0.13/0.44 generalize (zenon_H20 zenon_TT_m). zenon_intro zenon_H21. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H10 | zenon_intro zenon_H22 ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.13/0.44 exact (zenon_H12 zenon_Ha). % 0.13/0.44 exact (zenon_H11 zenon_H9). % 0.13/0.44 generalize (a3 zenon_TE_l). zenon_intro zenon_H23. % 0.13/0.44 generalize (zenon_H23 zenon_TT_m). zenon_intro zenon_H24. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H12 | zenon_intro zenon_H27 ]. % 0.13/0.44 exact (zenon_H12 zenon_Ha). % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.13/0.44 exact (zenon_H29 zenon_H22). % 0.13/0.44 generalize (mp_environment_not_empty zenon_TE_l). zenon_intro zenon_H2a. % 0.13/0.44 generalize (zenon_H2a zenon_TT_m). zenon_intro zenon_H2b. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H10 | zenon_intro zenon_H2c ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.13/0.44 exact (zenon_H12 zenon_Ha). % 0.13/0.44 exact (zenon_H11 zenon_H9). % 0.13/0.44 exact (zenon_H28 zenon_H2c). % 0.13/0.44 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H31 | zenon_intro zenon_H8 ]. % 0.13/0.44 exact (zenon_H31 zenon_H30). % 0.13/0.44 apply (zenon_L1_ zenon_TE_l zenon_TT_m); trivial. % 0.13/0.44 generalize (l4 zenon_TE_l). zenon_intro zenon_Hd. % 0.13/0.44 generalize (zenon_Hd zenon_TT_m). zenon_intro zenon_He. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.13/0.44 exact (zenon_H12 zenon_Ha). % 0.13/0.44 exact (zenon_H11 zenon_H9). % 0.13/0.44 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H32 | zenon_intro zenon_H17 ]. % 0.13/0.44 exact (zenon_H32 zenon_H2f). % 0.13/0.44 apply (zenon_L2_ zenon_TT_m); trivial. % 0.13/0.44 Qed. % 0.13/0.44 % SZS output end Proof % 0.13/0.44 (* END-PROOF *) % 0.13/0.44 nodes searched: 226 % 0.13/0.44 max branch formulas: 121 % 0.13/0.44 proof nodes created: 59 % 0.13/0.44 formulas created: 874 % 0.13/0.44 %------------------------------------------------------------------------------