%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM443+4 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 15:55:43 EDT 2022 % Result : Theorem 2.23s 2.42s % Output : Proof 2.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM443+4 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.13 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n007.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 : Fri Jul 8 02:09:45 EDT 2022 % 0.12/0.34 % CPUTime : % 2.23/2.42 (* PROOF-FOUND *) % 2.23/2.42 % SZS status Theorem % 2.23/2.42 (* BEGIN-PROOF *) % 2.23/2.42 % SZS output start Proof % 2.23/2.42 Theorem m__ : (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))/\((forall W0 : zenon_U, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))->((aInteger0 W0)/\((exists W1 : zenon_U, ((aInteger0 W1)/\((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa))))))/\((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa))))/\(sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))))/\(((aInteger0 W0)/\((exists W1 : zenon_U, ((aInteger0 W1)/\((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa))))))\/((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa))))\/(sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))->(aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))))/\((~(aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))/\((aElementOf0 (xb) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))/\((exists W0 : zenon_U, ((aInteger0 W0)/\((sdtasdt0 (xq) W0) = (sdtpldt0 (xc) (smndt0 (xb))))))/\((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xb))))/\(sdteqdtlpzmzozddtrp0 (xc) (xb) (xq))))))))->(((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))/\(forall W0 : zenon_U, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))->((aInteger0 W0)/\((exists W1 : zenon_U, ((aInteger0 W1)/\((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa))))))/\((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa))))/\(sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))))/\(((aInteger0 W0)/\((exists W1 : zenon_U, ((aInteger0 W1)/\((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa))))))\/((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa))))\/(sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))->(aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))))->((~(aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))\/(aElementOf0 (xc) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))))). % 2.23/2.42 Proof. % 2.23/2.42 assert (zenon_L1_ : (aInteger0 (xc)) -> (aInteger0 (xb)) -> (aInteger0 (xq)) -> (~((xq) = (sz00))) -> (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) -> (~(sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) -> False). % 2.23/2.42 do 0 intro. intros zenon_H2b zenon_H2c zenon_H2d zenon_H2e zenon_H2f zenon_H30. % 2.23/2.42 generalize (mEquModSym (xc)). zenon_intro zenon_H31. % 2.23/2.42 generalize (zenon_H31 (xb)). zenon_intro zenon_H32. % 2.23/2.42 generalize (zenon_H32 (xq)). zenon_intro zenon_H33. % 2.23/2.42 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 2.23/2.42 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 2.23/2.42 exact (zenon_H37 zenon_H2b). % 2.23/2.42 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 2.23/2.42 exact (zenon_H39 zenon_H2c). % 2.23/2.42 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 2.23/2.42 exact (zenon_H3b zenon_H2d). % 2.23/2.42 exact (zenon_H3a zenon_H2e). % 2.23/2.42 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 2.23/2.42 exact (zenon_H3d zenon_H2f). % 2.23/2.42 exact (zenon_H30 zenon_H3c). % 2.23/2.42 (* end of lemma zenon_L1_ *) % 2.23/2.42 apply NNPP. intro zenon_G. % 2.23/2.42 apply (zenon_and_s _ _ m__1962). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H2e. % 2.23/2.42 apply (zenon_and_s _ _ m__2010). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 2.23/2.42 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H41. zenon_intro zenon_H40. % 2.23/2.42 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42. % 2.23/2.42 apply (zenon_notor_s _ _ zenon_H42). zenon_intro zenon_H45. zenon_intro zenon_H44. % 2.23/2.42 apply zenon_H45. zenon_intro zenon_H46. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H48. zenon_intro zenon_H47. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H2f. % 2.23/2.42 generalize (zenon_H4a (xb)). zenon_intro zenon_H52. % 2.23/2.42 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 2.23/2.42 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 2.23/2.42 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H39 | zenon_intro zenon_H57 ]. % 2.27/2.42 exact (zenon_H39 zenon_H2c). % 2.27/2.42 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H58. % 2.27/2.42 apply (zenon_notor_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 2.27/2.42 generalize (mEquModTrn (xb)). zenon_intro zenon_H5c. % 2.27/2.42 generalize (zenon_H5c (xc)). zenon_intro zenon_H5d. % 2.27/2.42 generalize (zenon_H5d (xq)). zenon_intro zenon_H5e. % 2.27/2.42 generalize (zenon_H5e (xa)). zenon_intro zenon_H5f. % 2.27/2.42 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 2.27/2.42 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H39 | zenon_intro zenon_H62 ]. % 2.27/2.42 exact (zenon_H39 zenon_H2c). % 2.27/2.42 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H37 | zenon_intro zenon_H63 ]. % 2.27/2.42 exact (zenon_H37 zenon_H2b). % 2.27/2.42 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H3b | zenon_intro zenon_H64 ]. % 2.27/2.42 exact (zenon_H3b zenon_H2d). % 2.27/2.42 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H3a | zenon_intro zenon_H65 ]. % 2.27/2.42 exact (zenon_H3a zenon_H2e). % 2.27/2.42 exact (zenon_H65 zenon_H3f). % 2.27/2.42 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H67 | zenon_intro zenon_H66 ]. % 2.27/2.42 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H30 | zenon_intro zenon_H68 ]. % 2.27/2.42 apply (zenon_L1_); trivial. % 2.27/2.42 generalize (zenon_H4a (xc)). zenon_intro zenon_H69. % 2.27/2.42 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 2.27/2.42 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 2.27/2.42 exact (zenon_H6d zenon_H46). % 2.27/2.42 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H2b. zenon_intro zenon_H6e. % 2.27/2.42 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 2.27/2.42 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 2.27/2.42 exact (zenon_H68 zenon_H71). % 2.27/2.42 exact (zenon_H5a zenon_H66). % 2.27/2.42 exact (zenon_H4c zenon_H55). % 2.27/2.42 Qed. % 2.27/2.42 % SZS output end Proof % 2.27/2.42 (* END-PROOF *) % 2.27/2.42 nodes searched: 22407 % 2.27/2.42 max branch formulas: 5160 % 2.27/2.42 proof nodes created: 1157 % 2.27/2.42 formulas created: 150721 % 2.27/2.42 %------------------------------------------------------------------------------