%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 : Mon Jul 18 15:56:37 EDT 2022 % Result : Theorem 0.18s 0.56s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n012.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 : Wed Jul 6 00:22:15 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.56 (* PROOF-FOUND *) % 0.18/0.56 % SZS status Theorem % 0.18/0.56 (* BEGIN-PROOF *) % 0.18/0.56 % SZS output start Proof % 0.18/0.56 Theorem m__ : ((((aSet0 (sdtpldt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))\/(W0 = (xx)))))))->(((aSet0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtpldt0 (xS) (xx)))/\(~(W0 = (xx))))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))))\/(aSubsetOf0 (xS) (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx))))))/\(((aSet0 (sdtpldt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))\/(W0 = (xx)))))))->(((aSet0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtpldt0 (xS) (xx)))/\(~(W0 = (xx))))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS))))\/(aSubsetOf0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)) (xS)))))). % 0.18/0.56 Proof. % 0.18/0.56 assert (zenon_L1_ : forall (zenon_TW0_x : zenon_U), (aSet0 (xS)) -> (aElementOf0 zenon_TW0_x (xS)) -> (~(aElement0 zenon_TW0_x)) -> False). % 0.18/0.56 do 1 intro. intros zenon_H14 zenon_H15 zenon_H16. % 0.18/0.56 generalize (mEOfElem (xS)). zenon_intro zenon_H18. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.18/0.56 exact (zenon_H1a zenon_H14). % 0.18/0.56 generalize (zenon_H19 zenon_TW0_x). zenon_intro zenon_H1b. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.18/0.56 exact (zenon_H1d zenon_H15). % 0.18/0.56 exact (zenon_H16 zenon_H1c). % 0.18/0.56 (* end of lemma zenon_L1_ *) % 0.18/0.56 assert (zenon_L2_ : (~((xS) = (xS))) -> False). % 0.18/0.56 do 0 intro. intros zenon_H1e. % 0.18/0.56 apply zenon_H1e. apply refl_equal. % 0.18/0.56 (* end of lemma zenon_L2_ *) % 0.18/0.56 apply NNPP. intro zenon_G. % 0.18/0.56 apply (zenon_and_s _ _ m__679). zenon_intro zenon_H1f. zenon_intro zenon_H14. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.18/0.56 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.18/0.56 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.18/0.56 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.18/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx))))) zenon_H27); [ zenon_intro zenon_H2c; idtac ]. % 0.18/0.56 elim zenon_H2c. zenon_intro zenon_TW0_x. zenon_intro zenon_H2d. % 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H2d). zenon_intro zenon_H15. zenon_intro zenon_H2e. % 0.18/0.56 generalize (zenon_H28 zenon_TW0_x). zenon_intro zenon_H2f. % 0.18/0.56 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2e; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ]. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H16 | zenon_intro zenon_H33 ]. % 0.18/0.56 apply (zenon_L1_ zenon_TW0_x); trivial. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.18/0.56 generalize (zenon_H2a zenon_TW0_x). zenon_intro zenon_H36. % 0.18/0.56 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H35; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H37 ]. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H16 | zenon_intro zenon_H3a ]. % 0.18/0.56 apply (zenon_L1_ zenon_TW0_x); trivial. % 0.18/0.56 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H1d. zenon_intro zenon_H3b. % 0.18/0.56 exact (zenon_H1d zenon_H15). % 0.18/0.56 exact (zenon_H35 zenon_H38). % 0.18/0.56 apply zenon_H34. zenon_intro zenon_H3c. % 0.18/0.56 cut ((aElementOf0 zenon_TW0_x (xS)) = (aElementOf0 (xx) (xS))). % 0.18/0.56 intro zenon_D_pnotp. % 0.18/0.56 apply m__679_02. % 0.18/0.56 rewrite <- zenon_D_pnotp. % 0.18/0.56 exact zenon_H15. % 0.18/0.56 cut (((xS) = (xS))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.18/0.56 cut ((zenon_TW0_x = (xx))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 0.18/0.56 congruence. % 0.18/0.56 exact (zenon_H3b zenon_H3c). % 0.18/0.56 apply zenon_H1e. apply refl_equal. % 0.18/0.56 exact (zenon_H2e zenon_H31). % 0.18/0.57 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H3d. % 0.18/0.57 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H25. zenon_intro zenon_H3e. % 0.18/0.57 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.18/0.57 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.18/0.57 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.18/0.57 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtmndt0 (sdtpldt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS)))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.18/0.57 elim zenon_H41. zenon_intro zenon_TW0_co. zenon_intro zenon_H43. % 0.18/0.57 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 0.18/0.57 generalize (zenon_H2a zenon_TW0_co). zenon_intro zenon_H46. % 0.18/0.57 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H4a; zenon_intro zenon_H49 | zenon_intro zenon_H48; zenon_intro zenon_H47 ]. % 0.18/0.57 generalize (zenon_H28 zenon_TW0_co). zenon_intro zenon_H4b. % 0.18/0.57 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4e; zenon_intro zenon_H4d | zenon_intro zenon_H45; zenon_intro zenon_H4c ]. % 0.18/0.57 exact (zenon_H4e zenon_H45). % 0.18/0.57 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.18/0.57 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H48. zenon_intro zenon_H51. % 0.18/0.57 exact (zenon_H4a zenon_H48). % 0.18/0.57 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H50. zenon_intro zenon_H52. % 0.18/0.57 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.18/0.57 exact (zenon_H44 zenon_H54). % 0.18/0.57 generalize (zenon_H28 zenon_TW0_co). zenon_intro zenon_H4b. % 0.18/0.57 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4e; zenon_intro zenon_H4d | zenon_intro zenon_H45; zenon_intro zenon_H4c ]. % 0.18/0.57 exact (zenon_H4e zenon_H45). % 0.18/0.57 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.18/0.57 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H48. zenon_intro zenon_H51. % 0.18/0.57 exact (zenon_H51 zenon_H53). % 0.18/0.57 Qed. % 0.18/0.57 % SZS output end Proof % 0.18/0.57 (* END-PROOF *) % 0.18/0.57 nodes searched: 1597 % 0.18/0.57 max branch formulas: 430 % 0.18/0.57 proof nodes created: 81 % 0.18/0.57 formulas created: 6798 % 0.18/0.57 %------------------------------------------------------------------------------