%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM482+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 15:56:05 EDT 2022 % Result : Theorem 1.01s 1.19s % Output : Proof 1.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM482+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jul 7 05:43:07 EDT 2022 % 0.12/0.35 % CPUTime : % 1.01/1.19 (* PROOF-FOUND *) % 1.01/1.19 % SZS status Theorem % 1.01/1.19 (* BEGIN-PROOF *) % 1.01/1.19 % SZS output start Proof % 1.01/1.19 Theorem m__ : ((isPrime0 (xk))->(exists W0 : zenon_U, ((aNaturalNumber0 W0)/\((doDivides0 W0 (xk))/\(isPrime0 W0))))). % 1.01/1.19 Proof. % 1.01/1.19 apply NNPP. intro zenon_G. % 1.01/1.19 apply (zenon_and_s _ _ mSortsC_01). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 1.01/1.19 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 1.01/1.19 apply zenon_H2b. exists (xk). apply NNPP. zenon_intro zenon_H2d. % 1.01/1.19 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 1.01/1.19 exact (zenon_H2f m__1716). % 1.01/1.19 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 1.01/1.19 generalize (mDefDiv (xk)). zenon_intro zenon_H32. % 1.01/1.19 generalize (zenon_H32 (xk)). zenon_intro zenon_H33. % 1.01/1.19 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 1.01/1.19 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H2f | zenon_intro zenon_H2f ]. % 1.01/1.19 exact (zenon_H2f m__1716). % 1.01/1.19 exact (zenon_H2f m__1716). % 1.01/1.19 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H31; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 1.01/1.19 generalize (m_MulUnit (xk)). zenon_intro zenon_H39. % 1.01/1.19 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H2f | zenon_intro zenon_H3a ]. % 1.01/1.19 exact (zenon_H2f m__1716). % 1.01/1.19 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 1.01/1.19 apply zenon_H38. exists (sz10). apply NNPP. zenon_intro zenon_H3d. % 1.01/1.19 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 1.01/1.19 exact (zenon_H3f zenon_H2a). % 1.01/1.19 apply zenon_H3e. apply sym_equal. exact zenon_H3c. % 1.01/1.19 exact (zenon_H31 zenon_H37). % 1.01/1.19 exact (zenon_H30 zenon_H2c). % 1.01/1.19 Qed. % 1.01/1.19 % SZS output end Proof % 1.01/1.19 (* END-PROOF *) % 1.01/1.19 nodes searched: 6188 % 1.01/1.19 max branch formulas: 3542 % 1.01/1.19 proof nodes created: 324 % 1.01/1.19 formulas created: 70255 % 1.01/1.19 %------------------------------------------------------------------------------