%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET809+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 06:38:43 EDT 2022 % Result : Theorem 0.83s 1.04s % Output : Proof 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET809+4 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 22:33:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.83/1.04 (* PROOF-FOUND *) % 0.83/1.04 % SZS status Theorem % 0.83/1.04 (* BEGIN-PROOF *) % 0.83/1.04 % SZS output start Proof % 0.83/1.04 Theorem thV2 : (forall A : zenon_U, ((member A (on))->(~(member A A)))). % 0.83/1.04 Proof. % 0.83/1.04 assert (zenon_L1_ : forall (zenon_TA_x : zenon_U), (forall Y : zenon_U, (((member zenon_TA_x zenon_TA_x)/\(member Y zenon_TA_x))->(~((apply (member_predicate) zenon_TA_x Y)/\(apply (member_predicate) Y zenon_TA_x))))) -> (member zenon_TA_x zenon_TA_x) -> (apply (member_predicate) zenon_TA_x zenon_TA_x) -> False). % 0.83/1.04 do 1 intro. intros zenon_H14 zenon_H15 zenon_H16. % 0.83/1.04 generalize (zenon_H14 zenon_TA_x). zenon_intro zenon_H18. % 0.83/1.04 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.83/1.04 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1b | zenon_intro zenon_H1b ]. % 0.83/1.04 exact (zenon_H1b zenon_H15). % 0.83/1.04 exact (zenon_H1b zenon_H15). % 0.83/1.04 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1c | zenon_intro zenon_H1c ]. % 0.83/1.04 exact (zenon_H1c zenon_H16). % 0.83/1.04 exact (zenon_H1c zenon_H16). % 0.83/1.04 (* end of lemma zenon_L1_ *) % 0.83/1.04 apply NNPP. intro zenon_G. % 0.83/1.04 apply (zenon_notallex_s (fun A : zenon_U => ((member A (on))->(~(member A A)))) zenon_G); [ zenon_intro zenon_H1d; idtac ]. % 0.83/1.04 elim zenon_H1d. zenon_intro zenon_TA_x. zenon_intro zenon_H1e. % 0.83/1.04 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.83/1.04 apply zenon_H1f. zenon_intro zenon_H15. % 0.83/1.04 generalize (ordinal_number zenon_TA_x). zenon_intro zenon_H21. % 0.83/1.04 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H24; zenon_intro zenon_H23 | zenon_intro zenon_H20; zenon_intro zenon_H22 ]. % 0.83/1.04 exact (zenon_H24 zenon_H20). % 0.83/1.04 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.83/1.04 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.83/1.04 generalize (strict_well_order (member_predicate)). zenon_intro zenon_H29. % 0.83/1.04 generalize (zenon_H29 zenon_TA_x). zenon_intro zenon_H2a. % 0.83/1.04 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2d; zenon_intro zenon_H2c | zenon_intro zenon_H28; zenon_intro zenon_H2b ]. % 0.83/1.04 exact (zenon_H2d zenon_H28). % 0.83/1.04 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.83/1.04 generalize (strict_order (member_predicate)). zenon_intro zenon_H30. % 0.83/1.04 generalize (zenon_H30 zenon_TA_x). zenon_intro zenon_H31. % 0.83/1.04 apply (zenon_equiv_s _ _ zenon_H31); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H2f; zenon_intro zenon_H32 ]. % 0.83/1.04 exact (zenon_H34 zenon_H2f). % 0.83/1.04 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.83/1.04 generalize (zenon_H36 zenon_TA_x). zenon_intro zenon_H14. % 0.83/1.04 generalize (rel_member zenon_TA_x). zenon_intro zenon_H37. % 0.83/1.04 generalize (zenon_H37 zenon_TA_x). zenon_intro zenon_H38. % 0.83/1.04 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H16; zenon_intro zenon_H15 ]. % 0.83/1.04 exact (zenon_H1b zenon_H15). % 0.83/1.04 apply (zenon_L1_ zenon_TA_x); trivial. % 0.83/1.04 Qed. % 0.83/1.04 % SZS output end Proof % 0.83/1.04 (* END-PROOF *) % 0.83/1.04 nodes searched: 25720 % 0.83/1.04 max branch formulas: 6956 % 0.83/1.04 proof nodes created: 785 % 0.83/1.04 formulas created: 157851 % 0.83/1.04 %------------------------------------------------------------------------------