%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : RNG118+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n023.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 20:48:30 EDT 2022 % Result : Theorem 161.27s 161.49s % Output : Proof 161.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : RNG118+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n023.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 : Mon May 30 16:49:12 EDT 2022 % 0.12/0.33 % CPUTime : % 161.27/161.49 (* PROOF-FOUND *) % 161.27/161.49 % SZS status Theorem % 161.27/161.49 (* BEGIN-PROOF *) % 161.27/161.49 % SZS output start Proof % 161.27/161.49 Theorem m__ : (exists W0 : zenon_U, (exists W1 : zenon_U, ((aElement0 W0)/\((aElement0 W1)/\(((xb) = (sdtpldt0 (sdtasdt0 W0 (xu)) W1))/\((W1 = (sz00))\/(iLess0 (sbrdtbr0 W1) (sbrdtbr0 (xu))))))))). % 161.27/161.49 Proof. % 161.27/161.49 assert (zenon_L1_ : (forall W1 : zenon_U, ((aElementOf0 W1 (xI))->(aElement0 W1))) -> (aElementOf0 (xu) (xI)) -> (~(aElement0 (xu))) -> False). % 161.27/161.49 do 0 intro. intros zenon_H32 zenon_H33 zenon_H34. % 161.27/161.49 generalize (zenon_H32 (xu)). zenon_intro zenon_H35. % 161.27/161.49 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 161.27/161.49 exact (zenon_H37 zenon_H33). % 161.27/161.49 exact (zenon_H34 zenon_H36). % 161.27/161.49 (* end of lemma zenon_L1_ *) % 161.27/161.49 assert (zenon_L2_ : (~((xb) = (xb))) -> False). % 161.27/161.49 do 0 intro. intros zenon_H38. % 161.27/161.49 apply zenon_H38. apply refl_equal. % 161.27/161.49 (* end of lemma zenon_L2_ *) % 161.27/161.49 assert (zenon_L3_ : (~((sz00) = (sz00))) -> False). % 161.27/161.49 do 0 intro. intros zenon_H39. % 161.27/161.49 apply zenon_H39. apply refl_equal. % 161.27/161.49 (* end of lemma zenon_L3_ *) % 161.27/161.49 assert (zenon_L4_ : (~(((sz00) = (sz00))\/(iLess0 (sbrdtbr0 (sz00)) (sbrdtbr0 (xu))))) -> False). % 161.27/161.49 do 0 intro. intros zenon_H3a. % 161.27/161.49 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H39. zenon_intro zenon_H3b. % 161.27/161.49 apply zenon_H39. apply refl_equal. % 161.27/161.49 (* end of lemma zenon_L4_ *) % 161.27/161.49 assert (zenon_L5_ : forall (zenon_TW3_ck : zenon_U), (~((zenon_TW3_ck = (sz00))\/(iLess0 (sbrdtbr0 zenon_TW3_ck) (sbrdtbr0 (xu))))) -> (iLess0 (sbrdtbr0 zenon_TW3_ck) (sbrdtbr0 (xu))) -> False). % 161.27/161.49 do 1 intro. intros zenon_H3c zenon_H3d. % 161.27/161.49 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 161.27/161.49 exact (zenon_H3f zenon_H3d). % 161.27/161.49 (* end of lemma zenon_L5_ *) % 161.27/161.49 assert (zenon_L6_ : forall (zenon_TW2_cq : zenon_U) (zenon_TW3_ck : zenon_U), (~(exists W0 : zenon_U, (exists W1 : zenon_U, ((aElement0 W0)/\((aElement0 W1)/\(((xb) = (sdtpldt0 (sdtasdt0 W0 (xu)) W1))/\((W1 = (sz00))\/(iLess0 (sbrdtbr0 W1) (sbrdtbr0 (xu)))))))))) -> (iLess0 (sbrdtbr0 zenon_TW3_ck) (sbrdtbr0 (xu))) -> ((xb) = (sdtpldt0 (sdtasdt0 zenon_TW2_cq (xu)) zenon_TW3_ck)) -> (aElement0 zenon_TW3_ck) -> (aElement0 zenon_TW2_cq) -> False). % 161.27/161.49 do 2 intro. intros zenon_G zenon_H3d zenon_H41 zenon_H42 zenon_H43. % 161.27/161.49 apply zenon_G. exists zenon_TW2_cq. apply NNPP. zenon_intro zenon_H45. % 161.27/161.49 apply zenon_H45. exists zenon_TW3_ck. apply NNPP. zenon_intro zenon_H46. % 161.27/161.49 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 161.27/161.49 exact (zenon_H48 zenon_H43). % 161.27/161.49 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 161.27/161.49 exact (zenon_H4a zenon_H42). % 161.27/161.49 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H3c ]. % 161.27/161.49 exact (zenon_H4b zenon_H41). % 161.27/161.49 apply (zenon_L5_ zenon_TW3_ck); trivial. % 161.27/161.49 (* end of lemma zenon_L6_ *) % 161.27/161.49 apply NNPP. intro zenon_G. % 161.27/161.49 apply (zenon_and_s _ _ m__2091). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 161.27/161.49 apply (zenon_and_s _ _ m__2174). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 161.27/161.49 generalize (mDefIdeal (xI)). zenon_intro zenon_H50. % 161.27/161.49 apply (zenon_equiv_s _ _ zenon_H50); [ zenon_intro zenon_H53; zenon_intro zenon_H52 | zenon_intro zenon_H4f; zenon_intro zenon_H51 ]. % 161.27/161.49 exact (zenon_H53 zenon_H4f). % 161.27/161.49 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H55. zenon_intro zenon_H54. % 161.27/161.49 apply (zenon_and_s _ _ m__2273). zenon_intro zenon_H33. zenon_intro zenon_H56. % 161.27/161.49 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 161.27/161.49 generalize (mEOfElem (xI)). zenon_intro zenon_H59. % 161.27/161.49 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H32 ]. % 161.27/161.49 exact (zenon_H5a zenon_H55). % 161.27/161.49 generalize (mDivision (xb)). zenon_intro zenon_H5b. % 161.27/161.49 generalize (zenon_H5b (xu)). zenon_intro zenon_H5c. % 161.27/161.49 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ]. % 161.27/161.49 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 161.27/161.49 exact (zenon_H60 zenon_H4c). % 161.27/161.49 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H34 | zenon_intro zenon_H61 ]. % 161.27/161.49 apply (zenon_L1_); trivial. % 161.27/161.49 exact (zenon_H61 zenon_H58). % 161.27/161.49 elim zenon_H5d. zenon_intro zenon_TW2_cq. zenon_intro zenon_H62. % 161.27/161.49 elim zenon_H62. zenon_intro zenon_TW3_ck. zenon_intro zenon_H63. % 161.27/161.51 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H43. zenon_intro zenon_H64. % 161.27/161.51 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H42. zenon_intro zenon_H65. % 161.27/161.51 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H41. zenon_intro zenon_H66. % 161.27/161.51 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H3d ]. % 161.27/161.51 apply zenon_H67. zenon_intro zenon_H68. % 161.27/161.51 apply zenon_G. exists zenon_TW2_cq. apply NNPP. zenon_intro zenon_H45. % 161.27/161.51 apply zenon_H45. exists (sz00). apply NNPP. zenon_intro zenon_H69. % 161.27/161.51 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H48 | zenon_intro zenon_H6a ]. % 161.27/161.51 exact (zenon_H48 zenon_H43). % 161.27/161.51 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 161.27/161.51 exact (zenon_H6c mSortsC). % 161.27/161.51 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H3a ]. % 161.27/161.51 cut (((xb) = (sdtpldt0 (sdtasdt0 zenon_TW2_cq (xu)) zenon_TW3_ck)) = ((xb) = (sdtpldt0 (sdtasdt0 zenon_TW2_cq (xu)) (sz00)))). % 161.27/161.51 intro zenon_D_pnotp. % 161.27/161.51 apply zenon_H6d. % 161.27/161.51 rewrite <- zenon_D_pnotp. % 161.27/161.51 exact zenon_H41. % 161.27/161.51 cut (((sdtpldt0 (sdtasdt0 zenon_TW2_cq (xu)) zenon_TW3_ck) = (sdtpldt0 (sdtasdt0 zenon_TW2_cq (xu)) (sz00)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 161.27/161.51 cut (((xb) = (xb))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 161.27/161.51 congruence. % 161.27/161.51 apply zenon_H38. apply refl_equal. % 161.27/161.51 cut ((zenon_TW3_ck = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 161.27/161.51 cut (((sdtasdt0 zenon_TW2_cq (xu)) = (sdtasdt0 zenon_TW2_cq (xu)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 161.27/161.51 congruence. % 161.27/161.51 apply zenon_H6f. apply refl_equal. % 161.27/161.51 exact (zenon_H40 zenon_H68). % 161.27/161.51 apply (zenon_L4_); trivial. % 161.27/161.51 apply (zenon_L6_ zenon_TW2_cq zenon_TW3_ck); trivial. % 161.27/161.51 Qed. % 161.27/161.51 % SZS output end Proof % 161.27/161.51 (* END-PROOF *) % 161.27/161.51 nodes searched: 1156308 % 161.27/161.51 max branch formulas: 29493 % 161.27/161.51 proof nodes created: 46049 % 161.27/161.51 formulas created: 5643414 % 161.27/161.51 %------------------------------------------------------------------------------