%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 06:24:26 AM UTC 2026 % Result : Theorem 0.35s 0.60s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.06 % Command : run_zenon %s %d % 0.16/0.42 % Computer : n020.cluster.edu % 0.16/0.42 % Model : x86_64 x86_64 % 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.42 % Memory : 8046.5625MB % 0.16/0.42 % OS : Linux 6.8.0-71-generic % 0.16/0.42 % CPULimit : 300 % 0.16/0.42 % WCLimit : 300 % 0.16/0.42 % DateTime : Mon Sep 7 14:11:43 UTC 2026 % 0.16/0.42 % CPUTime : % 0.35/0.60 (* PROOF-FOUND *) % 0.35/0.60 % SZS status Theorem % 0.35/0.60 (* BEGIN-PROOF *) % 0.35/0.60 % SZS output start Proof % 0.35/0.60 Theorem odrl302 : (~(exists X : zenon_U, ((in_open X (v0) (v600))/\(leq (v600) X)))). % 0.35/0.60 Proof. % 0.35/0.60 assert (zenon_L1_ : forall (zenon_TX_bj : zenon_U), (~(less zenon_TX_bj zenon_TX_bj)) -> (less zenon_TX_bj (v600)) -> ((v600) = zenon_TX_bj) -> False). % 0.35/0.60 do 1 intro. intros zenon_H20 zenon_H21 zenon_H22. % 0.35/0.60 cut ((less zenon_TX_bj (v600)) = (less zenon_TX_bj zenon_TX_bj)). % 0.35/0.60 intro zenon_D_pnotp. % 0.35/0.60 apply zenon_H20. % 0.35/0.60 rewrite <- zenon_D_pnotp. % 0.35/0.60 exact zenon_H21. % 0.35/0.60 cut (((v600) = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H24]. % 0.35/0.60 cut ((zenon_TX_bj = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.35/0.60 congruence. % 0.35/0.60 apply zenon_H25. apply refl_equal. % 0.35/0.60 exact (zenon_H24 zenon_H22). % 0.35/0.60 (* end of lemma zenon_L1_ *) % 0.35/0.60 apply NNPP. intro zenon_G. % 0.35/0.60 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less x y)->((less y z)->(less x z))))))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 0.35/0.60 apply zenon_G. zenon_intro zenon_H28. % 0.35/0.60 elim zenon_H28. zenon_intro zenon_TX_bj. zenon_intro zenon_H29. % 0.35/0.60 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.35/0.60 generalize (in_open zenon_TX_bj). zenon_intro zenon_H2c. % 0.35/0.60 generalize (zenon_H2c (v0)). zenon_intro zenon_H2d. % 0.35/0.60 generalize (zenon_H2d (v600)). zenon_intro zenon_H2e. % 0.35/0.60 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H31; zenon_intro zenon_H30 | zenon_intro zenon_H2b; zenon_intro zenon_H2f ]. % 0.35/0.60 exact (zenon_H31 zenon_H2b). % 0.35/0.60 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H21. % 0.35/0.60 generalize (leq_def (v600)). zenon_intro zenon_H33. % 0.35/0.60 generalize (zenon_H33 zenon_TX_bj). zenon_intro zenon_H34. % 0.35/0.60 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H2a; zenon_intro zenon_H35 ]. % 0.35/0.60 exact (zenon_H37 zenon_H2a). % 0.35/0.60 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H22 ]. % 0.35/0.60 generalize (irreflexive zenon_TX_bj). zenon_intro zenon_H20. % 0.35/0.60 elim (classic ((~(zenon_TX_bj = (v600)))/\(~(less zenon_TX_bj (v600))))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 0.35/0.60 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 0.35/0.60 exact (zenon_H3b zenon_H21). % 0.35/0.60 cut ((less (v600) zenon_TX_bj) = (less zenon_TX_bj zenon_TX_bj)). % 0.35/0.60 intro zenon_D_pnotp. % 0.35/0.60 apply zenon_H20. % 0.35/0.60 rewrite <- zenon_D_pnotp. % 0.35/0.60 exact zenon_H38. % 0.35/0.60 cut ((zenon_TX_bj = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.35/0.60 cut (((v600) = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H24]. % 0.35/0.60 congruence. % 0.35/0.60 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.35/0.60 apply zenon_H3e. zenon_intro zenon_H3f. % 0.35/0.60 elim (classic (zenon_TX_bj = zenon_TX_bj)); [ zenon_intro zenon_H40 | zenon_intro zenon_H25 ]. % 0.35/0.60 cut ((zenon_TX_bj = zenon_TX_bj) = ((v600) = zenon_TX_bj)). % 0.35/0.60 intro zenon_D_pnotp. % 0.35/0.60 apply zenon_H24. % 0.35/0.60 rewrite <- zenon_D_pnotp. % 0.35/0.60 exact zenon_H40. % 0.35/0.60 cut ((zenon_TX_bj = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.35/0.60 cut ((zenon_TX_bj = (v600))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 0.35/0.60 congruence. % 0.35/0.60 exact (zenon_H3c zenon_H3f). % 0.35/0.60 apply zenon_H25. apply refl_equal. % 0.35/0.60 apply zenon_H25. apply refl_equal. % 0.35/0.60 apply zenon_H3d. zenon_intro zenon_H21. % 0.35/0.60 generalize (zenon_H26 zenon_TX_bj). zenon_intro zenon_H41. % 0.35/0.60 generalize (zenon_H41 (v600)). zenon_intro zenon_H42. % 0.35/0.60 generalize (zenon_H42 zenon_TX_bj). zenon_intro zenon_H43. % 0.35/0.60 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H3b | zenon_intro zenon_H44 ]. % 0.35/0.60 exact (zenon_H3b zenon_H21). % 0.35/0.60 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.35/0.60 exact (zenon_H46 zenon_H38). % 0.35/0.60 exact (zenon_H20 zenon_H45). % 0.35/0.60 apply zenon_H25. apply refl_equal. % 0.35/0.60 generalize (irreflexive zenon_TX_bj). zenon_intro zenon_H20. % 0.35/0.60 apply (zenon_L1_ zenon_TX_bj); trivial. % 0.35/0.60 apply zenon_H27. zenon_intro zenon_Tx_ct. apply NNPP. zenon_intro zenon_H48. % 0.35/0.60 apply zenon_H48. zenon_intro zenon_Ty_cv. apply NNPP. zenon_intro zenon_H4a. % 0.35/0.60 apply zenon_H4a. zenon_intro zenon_Tz_cx. apply NNPP. zenon_intro zenon_H4c. % 0.35/0.60 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.35/0.61 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.35/0.61 generalize (transitive zenon_Tx_ct). zenon_intro zenon_H51. % 0.35/0.61 generalize (zenon_H51 zenon_Ty_cv). zenon_intro zenon_H52. % 0.35/0.61 generalize (zenon_H52 zenon_Tz_cx). zenon_intro zenon_H53. % 0.35/0.61 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.35/0.61 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.35/0.61 exact (zenon_H57 zenon_H4e). % 0.35/0.61 exact (zenon_H56 zenon_H50). % 0.35/0.61 exact (zenon_H4f zenon_H54). % 0.35/0.61 Qed. % 0.35/0.61 % SZS output end Proof % 0.35/0.61 (* END-PROOF *) % 0.35/0.61 nodes searched: 666 % 0.35/0.61 max branch formulas: 181 % 0.35/0.61 proof nodes created: 69 % 0.35/0.61 formulas created: 1799 % 0.35/0.61 %------------------------------------------------------------------------------