%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT022+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 0.42s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT022+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n010.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 12:04:10 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.42 (* PROOF-FOUND *) % 0.13/0.42 % SZS status Theorem % 0.13/0.42 (* BEGIN-PROOF *) % 0.13/0.42 % SZS output start Proof % 0.13/0.42 Theorem prove_l4 : (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(((decreases (resources E T))->(increases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))/\((constant (resources E T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))))). % 0.13/0.42 Proof. % 0.13/0.42 apply NNPP. intro zenon_G. % 0.13/0.42 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(((decreases (resources E T))->(increases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))/\((constant (resources E T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.13/0.42 elim zenon_H4. zenon_intro zenon_TE_f. zenon_intro zenon_H6. % 0.13/0.42 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_f)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_f T))->(((decreases (resources zenon_TE_f T))->(increases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))/\((constant (resources zenon_TE_f T))->(~(decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T)))))))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.13/0.42 elim zenon_H7. zenon_intro zenon_TT_i. zenon_intro zenon_H9. % 0.13/0.42 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.13/0.42 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.13/0.42 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_Hf | zenon_intro zenon_He ]. % 0.13/0.42 generalize (a5 zenon_TE_f). zenon_intro zenon_H10. % 0.13/0.42 generalize (zenon_H10 (first_movers)). zenon_intro zenon_H11. % 0.13/0.42 generalize (zenon_H11 (efficient_producers)). zenon_intro zenon_H12. % 0.13/0.42 generalize (zenon_H12 zenon_TT_i). zenon_intro zenon_H13. % 0.13/0.42 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.13/0.42 apply (zenon_notand_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.13/0.42 exact (zenon_H17 zenon_Hd). % 0.13/0.42 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.13/0.42 exact (zenon_H19 zenon_Hc). % 0.13/0.42 exact (zenon_H18 a2). % 0.13/0.42 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.13/0.42 exact (zenon_Hf zenon_H1b). % 0.13/0.42 apply (zenon_notimply_s _ _ zenon_He). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.13/0.42 apply zenon_H1c. zenon_intro zenon_H1e. % 0.13/0.42 generalize (mp_constant_not_decrease (difference (disbanding_rate (first_movers) zenon_TT_i) (disbanding_rate (efficient_producers) zenon_TT_i))). zenon_intro zenon_H1f. % 0.13/0.42 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.13/0.42 generalize (a5 zenon_TE_f). zenon_intro zenon_H10. % 0.13/0.42 generalize (zenon_H10 (first_movers)). zenon_intro zenon_H11. % 0.13/0.42 generalize (zenon_H11 (efficient_producers)). zenon_intro zenon_H12. % 0.13/0.42 generalize (zenon_H12 zenon_TT_i). zenon_intro zenon_H13. % 0.13/0.42 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.13/0.42 apply (zenon_notand_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.13/0.42 exact (zenon_H17 zenon_Hd). % 0.13/0.42 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.13/0.42 exact (zenon_H19 zenon_Hc). % 0.13/0.42 exact (zenon_H18 a2). % 0.13/0.42 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.13/0.42 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.13/0.42 exact (zenon_H23 zenon_H1d). % 0.13/0.42 exact (zenon_H21 zenon_H22). % 0.13/0.42 exact (zenon_H20 zenon_H1e). % 0.13/0.42 Qed. % 0.13/0.42 % SZS output end Proof % 0.13/0.42 (* END-PROOF *) % 0.13/0.42 nodes searched: 321 % 0.13/0.42 max branch formulas: 173 % 0.13/0.42 proof nodes created: 51 % 0.13/0.42 formulas created: 1053 % 0.13/0.42 %------------------------------------------------------------------------------