%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM425+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 15:55:32 EDT 2022 % Result : Theorem 5.77s 5.95s % Output : Proof 5.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM425+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n013.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 20:28:59 EDT 2022 % 0.13/0.34 % CPUTime : % 5.77/5.95 (* PROOF-FOUND *) % 5.77/5.95 % SZS status Theorem % 5.77/5.95 (* BEGIN-PROOF *) % 5.77/5.95 % SZS output start Proof % 5.77/5.95 Theorem m__ : (exists W0 : zenon_U, ((aInteger0 W0)/\((sdtasdt0 (xq) W0) = (sdtpldt0 (xa) (smndt0 (xb)))))). % 5.77/5.95 Proof. % 5.77/5.95 assert (zenon_L1_ : (~(aInteger0 (sdtpldt0 (xa) (smndt0 (xb))))) -> (aInteger0 (xb)) -> (aInteger0 (xa)) -> False). % 5.77/5.95 do 0 intro. intros zenon_H17 zenon_H18 zenon_H19. % 5.77/5.95 generalize (mIntPlus (xa)). zenon_intro zenon_H1a. % 5.77/5.95 generalize (zenon_H1a (smndt0 (xb))). zenon_intro zenon_H1b. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 5.77/5.95 exact (zenon_H1f zenon_H19). % 5.77/5.95 generalize (mIntNeg (xb)). zenon_intro zenon_H20. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 5.77/5.95 exact (zenon_H22 zenon_H18). % 5.77/5.95 exact (zenon_H1e zenon_H21). % 5.77/5.95 exact (zenon_H17 zenon_H1c). % 5.77/5.95 (* end of lemma zenon_L1_ *) % 5.77/5.95 assert (zenon_L2_ : (~((xq) = (xq))) -> False). % 5.77/5.95 do 0 intro. intros zenon_H23. % 5.77/5.95 apply zenon_H23. apply refl_equal. % 5.77/5.95 (* end of lemma zenon_L2_ *) % 5.77/5.95 assert (zenon_L3_ : (~((sdtpldt0 (xa) (smndt0 (xb))) = (sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb))))) -> ((xa) = (sdtpldt0 (sz00) (xa))) -> False). % 5.77/5.95 do 0 intro. intros zenon_H24 zenon_H25. % 5.77/5.95 cut (((smndt0 (xb)) = (smndt0 (xb)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 5.77/5.95 cut (((xa) = (sdtpldt0 (sz00) (xa)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 5.77/5.95 congruence. % 5.77/5.95 exact (zenon_H27 zenon_H25). % 5.77/5.95 apply zenon_H26. apply refl_equal. % 5.77/5.95 (* end of lemma zenon_L3_ *) % 5.77/5.95 assert (zenon_L4_ : (~((sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb))) = (sdtpldt0 (xa) (smndt0 (xb))))) -> ((xa) = (sdtpldt0 (sz00) (xa))) -> False). % 5.77/5.95 do 0 intro. intros zenon_H28 zenon_H25. % 5.77/5.95 cut (((smndt0 (xb)) = (smndt0 (xb)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 5.77/5.95 cut (((sdtpldt0 (sz00) (xa)) = (xa))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 5.77/5.95 congruence. % 5.77/5.95 apply zenon_H29. apply sym_equal. exact zenon_H25. % 5.77/5.95 apply zenon_H26. apply refl_equal. % 5.77/5.95 (* end of lemma zenon_L4_ *) % 5.77/5.95 apply NNPP. intro zenon_G. % 5.77/5.95 apply (zenon_and_s _ _ m__704). zenon_intro zenon_H19. zenon_intro zenon_H2a. % 5.77/5.95 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H18. zenon_intro zenon_H2b. % 5.77/5.95 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 5.77/5.95 generalize (mAddZero (xa)). zenon_intro zenon_H2e. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H1f | zenon_intro zenon_H2f ]. % 5.77/5.95 exact (zenon_H1f zenon_H19). % 5.77/5.95 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H30. zenon_intro zenon_H25. % 5.77/5.95 generalize (mDivisor (sdtpldt0 (xa) (smndt0 (xb)))). zenon_intro zenon_H31. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H17 | zenon_intro zenon_H32 ]. % 5.77/5.95 apply (zenon_L1_); trivial. % 5.77/5.95 generalize (mEquMod (xa)). zenon_intro zenon_H33. % 5.77/5.95 generalize (zenon_H33 (xb)). zenon_intro zenon_H34. % 5.77/5.95 generalize (mEquMod (sdtpldt0 (sz00) (xa))). zenon_intro zenon_H35. % 5.77/5.95 generalize (zenon_H35 (xb)). zenon_intro zenon_H36. % 5.77/5.95 generalize (zenon_H36 (xq)). zenon_intro zenon_H37. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 5.77/5.95 generalize (mIntPlus (sz00)). zenon_intro zenon_H3c. % 5.77/5.95 generalize (zenon_H3c (xa)). zenon_intro zenon_H3d. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H40 | zenon_intro zenon_H1f ]. % 5.77/5.95 exact (zenon_H40 mIntZero). % 5.77/5.95 exact (zenon_H1f zenon_H19). % 5.77/5.95 exact (zenon_H3b zenon_H3e). % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H22 | zenon_intro zenon_H41 ]. % 5.77/5.95 exact (zenon_H22 zenon_H18). % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 5.77/5.95 exact (zenon_H43 zenon_H2d). % 5.77/5.95 exact (zenon_H42 zenon_H2c). % 5.77/5.95 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 5.77/5.95 generalize (zenon_H34 (xq)). zenon_intro zenon_H48. % 5.77/5.95 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H1f | zenon_intro zenon_H3a ]. % 5.77/5.95 exact (zenon_H1f zenon_H19). % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H22 | zenon_intro zenon_H41 ]. % 5.77/5.95 exact (zenon_H22 zenon_H18). % 5.77/5.95 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 5.77/5.95 exact (zenon_H43 zenon_H2d). % 5.77/5.95 exact (zenon_H42 zenon_H2c). % 5.77/5.95 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro m__724; zenon_intro zenon_H4b ]. % 5.77/5.95 exact (zenon_H4d m__724). % 5.77/5.95 cut ((aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb)))) = (aDivisorOf0 (xq) (sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb))))). % 5.77/5.95 intro zenon_D_pnotp. % 5.77/5.95 apply zenon_H46. % 5.77/5.95 rewrite <- zenon_D_pnotp. % 5.77/5.95 exact zenon_H4b. % 5.77/5.95 cut (((sdtpldt0 (xa) (smndt0 (xb))) = (sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb))))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 5.77/5.95 cut (((xq) = (xq))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 5.77/5.95 congruence. % 5.77/5.95 apply zenon_H23. apply refl_equal. % 5.77/5.95 apply (zenon_L3_); trivial. % 5.77/5.95 generalize (zenon_H32 (xq)). zenon_intro zenon_H4e. % 5.77/5.95 apply (zenon_equiv_s _ _ zenon_H4e); [ zenon_intro zenon_H4c; zenon_intro zenon_H50 | zenon_intro zenon_H4b; zenon_intro zenon_H4f ]. % 5.77/5.95 cut ((aDivisorOf0 (xq) (sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb)))) = (aDivisorOf0 (xq) (sdtpldt0 (xa) (smndt0 (xb))))). % 5.77/5.95 intro zenon_D_pnotp. % 5.77/5.95 apply zenon_H4c. % 5.77/5.95 rewrite <- zenon_D_pnotp. % 5.77/5.95 exact zenon_H44. % 5.77/5.95 cut (((sdtpldt0 (sdtpldt0 (sz00) (xa)) (smndt0 (xb))) = (sdtpldt0 (xa) (smndt0 (xb))))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 5.77/5.95 cut (((xq) = (xq))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 5.77/5.95 congruence. % 5.77/5.95 apply zenon_H23. apply refl_equal. % 5.77/5.95 apply (zenon_L4_); trivial. % 5.77/5.95 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H2d. zenon_intro zenon_H51. % 5.77/5.95 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H2c. zenon_intro zenon_H52. % 5.77/5.95 exact (zenon_G zenon_H52). % 5.77/5.95 Qed. % 5.77/5.95 % SZS output end Proof % 5.77/5.95 (* END-PROOF *) % 5.77/5.95 nodes searched: 20251 % 5.77/5.95 max branch formulas: 3983 % 5.77/5.95 proof nodes created: 839 % 5.77/5.95 formulas created: 263713 % 5.77/5.95 %------------------------------------------------------------------------------