%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : RNG093+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 20:48:26 EDT 2022 % Result : Theorem 0.50s 0.66s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : RNG093+2 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % 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 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon May 30 04:45:49 EDT 2022 % 0.13/0.33 % CPUTime : % 0.50/0.66 (* PROOF-FOUND *) % 0.50/0.66 % SZS status Theorem % 0.50/0.66 (* BEGIN-PROOF *) % 0.50/0.66 % SZS output start Proof % 0.50/0.66 Theorem m__ : (((aSet0 (sdtasasdt0 (xI) (xJ)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ))))))))\/(aIdeal0 (sdtasasdt0 (xI) (xJ))))). % 0.50/0.66 Proof. % 0.50/0.66 assert (zenon_L1_ : forall (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW0_be (xI))) -> False). % 0.50/0.66 do 1 intro. intros zenon_H1b zenon_H1c zenon_H1d. % 0.50/0.66 generalize (zenon_H1b zenon_TW0_be). zenon_intro zenon_H1f. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1c; zenon_intro zenon_H20 ]. % 0.50/0.66 exact (zenon_H22 zenon_H1c). % 0.50/0.66 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.50/0.66 exact (zenon_H1d zenon_H24). % 0.50/0.66 (* end of lemma zenon_L1_ *) % 0.50/0.66 assert (zenon_L2_ : forall (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW0_be (xJ))) -> False). % 0.50/0.66 do 1 intro. intros zenon_H1b zenon_H1c zenon_H25. % 0.50/0.66 generalize (zenon_H1b zenon_TW0_be). zenon_intro zenon_H1f. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1c; zenon_intro zenon_H20 ]. % 0.50/0.66 exact (zenon_H22 zenon_H1c). % 0.50/0.66 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.50/0.66 exact (zenon_H25 zenon_H23). % 0.50/0.66 (* end of lemma zenon_L2_ *) % 0.50/0.66 assert (zenon_L3_ : forall (zenon_TW1_bp : zenon_U) (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (xI))->((forall W1 : zenon_U, ((aElementOf0 W1 (xI))->(aElementOf0 (sdtpldt0 W0 W1) (xI))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (xI))))))) -> (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 (sdtasdt0 zenon_TW1_bp zenon_TW0_be) (xI))) -> (aElement0 zenon_TW1_bp) -> False). % 0.50/0.66 do 2 intro. intros zenon_H26 zenon_H1b zenon_H1c zenon_H27 zenon_H28. % 0.50/0.66 generalize (zenon_H26 zenon_TW0_be). zenon_intro zenon_H2a. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2b ]. % 0.50/0.66 apply (zenon_L1_ zenon_TW0_be); trivial. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.50/0.66 generalize (zenon_H2c zenon_TW1_bp). zenon_intro zenon_H2e. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.50/0.66 exact (zenon_H30 zenon_H28). % 0.50/0.66 exact (zenon_H27 zenon_H2f). % 0.50/0.66 (* end of lemma zenon_L3_ *) % 0.50/0.66 assert (zenon_L4_ : forall (zenon_TW1_bp : zenon_U) (zenon_TW0_be : zenon_U), ((forall W1 : zenon_U, ((aElementOf0 W1 (xJ))->(aElementOf0 (sdtpldt0 zenon_TW0_be W1) (xJ))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 zenon_TW0_be) (xJ))))) -> (~(aElementOf0 (sdtasdt0 zenon_TW1_bp zenon_TW0_be) (xJ))) -> (aElement0 zenon_TW1_bp) -> False). % 0.50/0.66 do 2 intro. intros zenon_H31 zenon_H32 zenon_H28. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.50/0.66 generalize (zenon_H33 zenon_TW1_bp). zenon_intro zenon_H35. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H30 | zenon_intro zenon_H36 ]. % 0.50/0.66 exact (zenon_H30 zenon_H28). % 0.50/0.66 exact (zenon_H32 zenon_H36). % 0.50/0.66 (* end of lemma zenon_L4_ *) % 0.50/0.66 apply NNPP. intro zenon_G. % 0.50/0.66 apply (zenon_and_s _ _ m__1150). zenon_intro zenon_H38. zenon_intro zenon_H37. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H26. zenon_intro zenon_H39. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.50/0.66 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.50/0.66 apply (zenon_notor_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H1b. % 0.50/0.66 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ)))))))) zenon_H43); [ zenon_intro zenon_H45; idtac ]. % 0.50/0.66 elim zenon_H45. zenon_intro zenon_TW0_be. zenon_intro zenon_H46. % 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H1c. zenon_intro zenon_H47. % 0.50/0.66 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.50/0.66 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 zenon_TW0_be W1) (sdtasasdt0 (xI) (xJ))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ]. % 0.50/0.66 elim zenon_H4a. zenon_intro zenon_TW1_cx. zenon_intro zenon_H4c. % 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.50/0.66 generalize (zenon_H1b (sdtpldt0 zenon_TW0_be zenon_TW1_cx)). zenon_intro zenon_H4f. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H4d; zenon_intro zenon_H52 | zenon_intro zenon_H51; zenon_intro zenon_H50 ]. % 0.50/0.66 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.50/0.66 generalize (zenon_H26 zenon_TW0_be). zenon_intro zenon_H2a. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2b ]. % 0.50/0.66 apply (zenon_L1_ zenon_TW0_be); trivial. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.50/0.66 generalize (zenon_H2d zenon_TW1_cx). zenon_intro zenon_H55. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.50/0.66 generalize (zenon_H1b zenon_TW1_cx). zenon_intro zenon_H58. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H4e; zenon_intro zenon_H59 ]. % 0.50/0.66 exact (zenon_H5b zenon_H4e). % 0.50/0.66 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.50/0.66 exact (zenon_H57 zenon_H5d). % 0.50/0.66 exact (zenon_H54 zenon_H56). % 0.50/0.66 generalize (zenon_H3f zenon_TW0_be). zenon_intro zenon_H5e. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H25 | zenon_intro zenon_H31 ]. % 0.50/0.66 apply (zenon_L2_ zenon_TW0_be); trivial. % 0.50/0.66 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.50/0.66 generalize (zenon_H34 zenon_TW1_cx). zenon_intro zenon_H5f. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.50/0.66 generalize (zenon_H1b zenon_TW1_cx). zenon_intro zenon_H58. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H4e; zenon_intro zenon_H59 ]. % 0.50/0.66 exact (zenon_H5b zenon_H4e). % 0.50/0.66 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.50/0.66 exact (zenon_H61 zenon_H5c). % 0.50/0.66 exact (zenon_H53 zenon_H60). % 0.50/0.66 exact (zenon_H4d zenon_H51). % 0.50/0.66 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 zenon_TW0_be) (sdtasasdt0 (xI) (xJ))))) zenon_H48); [ zenon_intro zenon_H62; idtac ]. % 0.50/0.66 elim zenon_H62. zenon_intro zenon_TW1_bp. zenon_intro zenon_H63. % 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H28. zenon_intro zenon_H64. % 0.50/0.66 generalize (zenon_H1b (sdtasdt0 zenon_TW1_bp zenon_TW0_be)). zenon_intro zenon_H65. % 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H64; zenon_intro zenon_H68 | zenon_intro zenon_H67; zenon_intro zenon_H66 ]. % 0.50/0.66 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H27 | zenon_intro zenon_H32 ]. % 0.50/0.66 apply (zenon_L3_ zenon_TW1_bp zenon_TW0_be); trivial. % 0.50/0.66 generalize (zenon_H3f zenon_TW0_be). zenon_intro zenon_H5e. % 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H25 | zenon_intro zenon_H31 ]. % 0.50/0.66 apply (zenon_L2_ zenon_TW0_be); trivial. % 0.50/0.66 apply (zenon_L4_ zenon_TW1_bp zenon_TW0_be); trivial. % 0.50/0.66 exact (zenon_H64 zenon_H67). % 0.50/0.66 Qed. % 0.50/0.66 % SZS output end Proof % 0.50/0.66 (* END-PROOF *) % 0.50/0.66 nodes searched: 3605 % 0.50/0.66 max branch formulas: 693 % 0.50/0.66 proof nodes created: 191 % 0.50/0.66 formulas created: 17535 % 0.50/0.66 %------------------------------------------------------------------------------