%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 0.43s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.34 % Computer : n004.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 12:05:45 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.43 (* PROOF-FOUND *) % 0.13/0.43 % SZS status Theorem % 0.13/0.43 (* BEGIN-PROOF *) % 0.13/0.43 % SZS output start Proof % 0.13/0.43 Theorem prove_l5 : (forall E : zenon_U, (((environment E)/\(stable E))->(in_environment E (critical_point E)))). % 0.13/0.43 Proof. % 0.13/0.43 apply NNPP. intro zenon_G. % 0.13/0.43 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(stable E))->(in_environment E (critical_point E)))) zenon_G); [ zenon_intro zenon_H3; idtac ]. % 0.13/0.43 elim zenon_H3. zenon_intro zenon_TE_e. zenon_intro zenon_H5. % 0.13/0.43 apply (zenon_notimply_s _ _ zenon_H5). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.13/0.43 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.13/0.43 generalize (d1 zenon_TE_e). zenon_intro zenon_Ha. % 0.13/0.43 generalize (l12 zenon_TE_e). zenon_intro zenon_Hb. % 0.13/0.43 apply (zenon_imply_s _ _ zenon_Hb); [ zenon_intro zenon_Hd | zenon_intro zenon_Hc ]. % 0.13/0.43 apply (zenon_notand_s _ _ zenon_Hd); [ zenon_intro zenon_Hf | zenon_intro zenon_He ]. % 0.13/0.43 exact (zenon_Hf zenon_H9). % 0.13/0.43 exact (zenon_He zenon_H8). % 0.13/0.43 elim zenon_Hc. zenon_intro zenon_TTo_q. zenon_intro zenon_H11. % 0.13/0.43 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H13. zenon_intro zenon_H12. % 0.13/0.43 apply (zenon_and_s _ _ zenon_H12). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.13/0.43 generalize (zenon_Ha zenon_TTo_q). zenon_intro zenon_H16. % 0.13/0.43 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.13/0.43 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_Hf | zenon_intro zenon_H19 ]. % 0.13/0.43 exact (zenon_Hf zenon_H9). % 0.13/0.43 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.13/0.43 exact (zenon_H1b zenon_H15). % 0.13/0.43 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.13/0.43 exact (zenon_H1d zenon_H13). % 0.13/0.43 exact (zenon_H1c zenon_H14). % 0.13/0.43 cut ((in_environment zenon_TE_e zenon_TTo_q) = (in_environment zenon_TE_e (critical_point zenon_TE_e))). % 0.13/0.43 intro zenon_D_pnotp. % 0.13/0.43 apply zenon_H6. % 0.13/0.43 rewrite <- zenon_D_pnotp. % 0.13/0.43 exact zenon_H13. % 0.13/0.43 cut ((zenon_TTo_q = (critical_point zenon_TE_e))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.13/0.43 cut ((zenon_TE_e = zenon_TE_e)); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.13/0.43 congruence. % 0.13/0.43 apply zenon_H1f. apply refl_equal. % 0.13/0.43 exact (zenon_H1e zenon_H17). % 0.13/0.43 Qed. % 0.13/0.43 % SZS output end Proof % 0.13/0.43 (* END-PROOF *) % 0.13/0.43 nodes searched: 100 % 0.13/0.43 max branch formulas: 66 % 0.13/0.43 proof nodes created: 31 % 0.13/0.43 formulas created: 591 % 0.13/0.43 %------------------------------------------------------------------------------