%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 15:56:36 EDT 2022 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jul 6 19:53:52 EDT 2022 % 0.13/0.34 % CPUTime : % 0.37/0.56 (* PROOF-FOUND *) % 0.37/0.56 % SZS status Theorem % 0.37/0.56 (* BEGIN-PROOF *) % 0.37/0.56 % SZS output start Proof % 0.37/0.56 Theorem m__ : ((((aSet0 (sdtmndt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))/\(~(W0 = (xx))))))))->(((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtmndt0 (xS) (xx)))\/(W0 = (xx)))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))))\/(aSubsetOf0 (xS) (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))))/\(((aSet0 (sdtmndt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))/\(~(W0 = (xx))))))))->(((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtmndt0 (xS) (xx)))\/(W0 = (xx)))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS))))\/(aSubsetOf0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)) (xS)))))). % 0.37/0.56 Proof. % 0.37/0.56 assert (zenon_L1_ : forall (zenon_TW0_v : zenon_U), (aElementOf0 zenon_TW0_v (xS)) -> (~(aElement0 zenon_TW0_v)) -> False). % 0.37/0.56 do 1 intro. intros zenon_H13 zenon_H14. % 0.37/0.56 generalize (mEOfElem (xS)). zenon_intro zenon_H16. % 0.37/0.56 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.37/0.56 exact (zenon_H18 m__617). % 0.37/0.56 generalize (zenon_H17 zenon_TW0_v). zenon_intro zenon_H19. % 0.37/0.56 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.37/0.56 exact (zenon_H1b zenon_H13). % 0.37/0.56 exact (zenon_H14 zenon_H1a). % 0.37/0.56 (* end of lemma zenon_L1_ *) % 0.37/0.56 assert (zenon_L2_ : (~((xS) = (xS))) -> False). % 0.37/0.56 do 0 intro. intros zenon_H1c. % 0.37/0.56 apply zenon_H1c. apply refl_equal. % 0.37/0.56 (* end of lemma zenon_L2_ *) % 0.37/0.56 assert (zenon_L3_ : forall (zenon_TW0_bf : zenon_U), ((aElement0 zenon_TW0_bf)/\((aElementOf0 zenon_TW0_bf (xS))/\(~(zenon_TW0_bf = (xx))))) -> (~(aElementOf0 zenon_TW0_bf (xS))) -> False). % 0.37/0.56 do 1 intro. intros zenon_H1d zenon_H1e. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.37/0.56 exact (zenon_H1e zenon_H23). % 0.37/0.56 (* end of lemma zenon_L3_ *) % 0.37/0.56 apply NNPP. intro zenon_G. % 0.37/0.56 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.37/0.56 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.37/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))) zenon_H2b); [ zenon_intro zenon_H30; idtac ]. % 0.37/0.56 elim zenon_H30. zenon_intro zenon_TW0_v. zenon_intro zenon_H31. % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H13. zenon_intro zenon_H32. % 0.37/0.56 generalize (zenon_H2c zenon_TW0_v). zenon_intro zenon_H33. % 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.37/0.56 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H14 | zenon_intro zenon_H37 ]. % 0.37/0.56 apply (zenon_L1_ zenon_TW0_v); trivial. % 0.37/0.56 apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.37/0.56 generalize (zenon_H2e zenon_TW0_v). zenon_intro zenon_H3a. % 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H39; zenon_intro zenon_H3d | zenon_intro zenon_H3c; zenon_intro zenon_H3b ]. % 0.37/0.56 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H14 | zenon_intro zenon_H3e ]. % 0.37/0.56 apply (zenon_L1_ zenon_TW0_v); trivial. % 0.37/0.56 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H1b | zenon_intro zenon_H3f ]. % 0.37/0.56 exact (zenon_H1b zenon_H13). % 0.37/0.56 exact (zenon_H3f zenon_H38). % 0.37/0.56 exact (zenon_H39 zenon_H3c). % 0.37/0.56 exact (zenon_H32 zenon_H35). % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H40. % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H29. zenon_intro zenon_H41. % 0.37/0.56 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.37/0.56 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.37/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS)))) zenon_H43); [ zenon_intro zenon_H44; idtac ]. % 0.37/0.56 elim zenon_H44. zenon_intro zenon_TW0_bf. zenon_intro zenon_H45. % 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H45). zenon_intro zenon_H46. zenon_intro zenon_H1e. % 0.37/0.56 generalize (zenon_H2e zenon_TW0_bf). zenon_intro zenon_H47. % 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H4a; zenon_intro zenon_H49 | zenon_intro zenon_H48; zenon_intro zenon_H1d ]. % 0.37/0.56 cut ((aElementOf0 (xx) (xS)) = (aElementOf0 zenon_TW0_bf (xS))). % 0.37/0.56 intro zenon_D_pnotp. % 0.37/0.56 apply zenon_H1e. % 0.37/0.56 rewrite <- zenon_D_pnotp. % 0.37/0.56 exact m__617_02. % 0.37/0.56 cut (((xS) = (xS))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 0.37/0.56 cut (((xx) = zenon_TW0_bf)); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 0.37/0.56 congruence. % 0.37/0.56 generalize (zenon_H2c zenon_TW0_bf). zenon_intro zenon_H4c. % 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H46; zenon_intro zenon_H4d ]. % 0.37/0.56 exact (zenon_H4f zenon_H46). % 0.37/0.56 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H21. zenon_intro zenon_H50. % 0.37/0.56 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H48 | zenon_intro zenon_H51 ]. % 0.37/0.56 exact (zenon_H4a zenon_H48). % 0.37/0.56 apply zenon_H4b. apply sym_equal. exact zenon_H51. % 0.37/0.56 apply zenon_H1c. apply refl_equal. % 0.37/0.56 apply (zenon_L3_ zenon_TW0_bf); trivial. % 0.37/0.56 Qed. % 0.37/0.56 % SZS output end Proof % 0.37/0.56 (* END-PROOF *) % 0.37/0.56 nodes searched: 1480 % 0.37/0.56 max branch formulas: 433 % 0.37/0.56 proof nodes created: 81 % 0.37/0.56 formulas created: 6368 % 0.37/0.56 %------------------------------------------------------------------------------