%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM434+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 15:55:37 EDT 2022 % Result : Theorem 256.26s 256.55s % Output : Proof 256.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : NUM434+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 08:12:08 EDT 2022 % 0.12/0.33 % CPUTime : % 256.26/256.55 (* PROOF-FOUND *) % 256.26/256.55 % SZS status Theorem % 256.26/256.55 (* BEGIN-PROOF *) % 256.26/256.55 % SZS output start Proof % 256.26/256.55 Theorem m__ : (exists W0 : zenon_U, ((aInteger0 W0)/\((sdtasdt0 (sdtasdt0 (xp) (xq)) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))). % 256.26/256.55 Proof. % 256.26/256.55 assert (zenon_L1_ : (~(aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) -> (aInteger0 (xb)) -> (aInteger0 (xa)) -> False). % 256.26/256.55 do 0 intro. intros zenon_H19 zenon_H1a zenon_H1b. % 256.26/256.55 generalize (mIntPlus (xa)). zenon_intro zenon_H1c. % 256.26/256.55 generalize (zenon_H1c (smndt0 (xb))). zenon_intro zenon_H1d. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 256.26/256.55 exact (zenon_H21 zenon_H1b). % 256.26/256.55 generalize (mIntNeg (xb)). zenon_intro zenon_H22. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 256.26/256.55 exact (zenon_H24 zenon_H1a). % 256.26/256.55 exact (zenon_H20 zenon_H23). % 256.26/256.55 exact (zenon_H19 zenon_H1e). % 256.26/256.55 (* end of lemma zenon_L1_ *) % 256.26/256.55 assert (zenon_L2_ : (~(aInteger0 (sdtasdt0 (xp) (xq)))) -> (aInteger0 (xq)) -> (aInteger0 (xp)) -> False). % 256.26/256.55 do 0 intro. intros zenon_H25 zenon_H26 zenon_H27. % 256.26/256.55 generalize (mIntMult (xp)). zenon_intro zenon_H28. % 256.26/256.55 generalize (zenon_H28 (xq)). zenon_intro zenon_H29. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 256.26/256.55 exact (zenon_H2d zenon_H27). % 256.26/256.55 exact (zenon_H2c zenon_H26). % 256.26/256.55 exact (zenon_H25 zenon_H2a). % 256.26/256.55 (* end of lemma zenon_L2_ *) % 256.26/256.55 apply NNPP. intro zenon_G. % 256.26/256.55 apply (zenon_and_s _ _ m__979). zenon_intro zenon_H1b. zenon_intro zenon_H2e. % 256.26/256.55 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H1a. zenon_intro zenon_H2f. % 256.26/256.55 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H27. zenon_intro zenon_H30. % 256.26/256.55 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 256.26/256.55 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H33. % 256.26/256.55 generalize (mDivisor (sdtpldt0 (xa) (smndt0 (xb)))). zenon_intro zenon_H34. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H35 ]. % 256.26/256.55 apply (zenon_L1_); trivial. % 256.26/256.55 generalize (mEquMod (xa)). zenon_intro zenon_H36. % 256.26/256.55 generalize (zenon_H36 (xb)). zenon_intro zenon_H37. % 256.26/256.55 generalize (mZeroDiv (xp)). zenon_intro zenon_H38. % 256.26/256.55 generalize (zenon_H38 (xq)). zenon_intro zenon_H39. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H2b | zenon_intro zenon_H3a ]. % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 256.26/256.55 exact (zenon_H2d zenon_H27). % 256.26/256.55 exact (zenon_H2c zenon_H26). % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 256.26/256.55 generalize (zenon_H35 (sdtasdt0 (xp) (xq))). zenon_intro zenon_H3d. % 256.26/256.55 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H41; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ]. % 256.26/256.55 generalize (zenon_H37 (sdtasdt0 (xp) (xq))). zenon_intro zenon_H42. % 256.26/256.55 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H21 | zenon_intro zenon_H45 ]. % 256.26/256.55 exact (zenon_H21 zenon_H1b). % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H24 | zenon_intro zenon_H46 ]. % 256.26/256.55 exact (zenon_H24 zenon_H1a). % 256.26/256.55 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H25 | zenon_intro zenon_H47 ]. % 256.26/256.55 apply (zenon_L2_); trivial. % 256.26/256.55 exact (zenon_H47 zenon_H3c). % 256.26/256.55 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H48; zenon_intro zenon_H41 | zenon_intro m__1003; zenon_intro zenon_H3f ]. % 256.26/256.55 exact (zenon_H48 m__1003). % 256.26/256.55 exact (zenon_H41 zenon_H3f). % 256.26/256.55 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2a. zenon_intro zenon_H49. % 256.26/256.55 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H3c. zenon_intro zenon_H4a. % 256.26/256.55 exact (zenon_G zenon_H4a). % 256.26/256.55 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 256.26/256.55 exact (zenon_H32 zenon_H4c). % 256.26/256.55 exact (zenon_H33 zenon_H4b). % 256.26/256.55 Qed. % 256.26/256.55 % SZS output end Proof % 256.26/256.55 (* END-PROOF *) % 256.26/256.55 nodes searched: 312946 % 256.26/256.55 max branch formulas: 44019 % 256.26/256.55 proof nodes created: 9358 % 256.26/256.55 formulas created: 5662405 % 256.26/256.55 %------------------------------------------------------------------------------