%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : RNG092+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 20:48:26 EDT 2022 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : RNG092+1 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.11/0.33 % Computer : n027.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Mon May 30 07:04:01 EDT 2022 % 0.11/0.33 % CPUTime : % 0.38/0.58 (* PROOF-FOUND *) % 0.38/0.58 % SZS status Theorem % 0.38/0.58 (* BEGIN-PROOF *) % 0.38/0.58 % SZS output start Proof % 0.38/0.58 Theorem m__ : ((forall W0 : zenon_U, (forall W1 : zenon_U, (forall W2 : zenon_U, (((aElementOf0 W0 (sdtpldt1 (xI) (xJ)))/\((aElementOf0 W1 (sdtpldt1 (xI) (xJ)))/\(aElement0 W2)))->(exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((W0 = (sdtpldt0 W3 W4))/\(exists W5 : zenon_U, (exists W6 : zenon_U, ((aElementOf0 W5 (xI))/\((aElementOf0 W6 (xJ))/\((W1 = (sdtpldt0 W5 W6))/\((aElementOf0 (sdtpldt0 W3 W5) (xI))/\((aElementOf0 (sdtpldt0 W4 W6) (xJ))/\((aElementOf0 (sdtasdt0 W2 W3) (xI))/\((aElementOf0 (sdtasdt0 W2 W4) (xJ))/\(((sdtpldt0 W0 W1) = (sdtpldt0 (sdtpldt0 W3 W5) (sdtpldt0 W4 W6)))/\((aElementOf0 (sdtpldt0 W0 W1) (sdtpldt1 (xI) (xJ)))/\(aElementOf0 (sdtasdt0 W2 W0) (sdtpldt1 (xI) (xJ)))))))))))))))))))))))->(aIdeal0 (sdtpldt1 (xI) (xJ)))). % 0.38/0.58 Proof. % 0.38/0.58 apply NNPP. intro zenon_G. % 0.38/0.58 apply (zenon_and_s _ _ m__870). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.38/0.58 generalize (mDefIdeal (xI)). zenon_intro zenon_H1c. % 0.38/0.58 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1b; zenon_intro zenon_H1d ]. % 0.38/0.58 exact (zenon_H1f zenon_H1b). % 0.38/0.58 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.38/0.58 generalize (mDefIdeal (xJ)). zenon_intro zenon_H22. % 0.38/0.58 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H25; zenon_intro zenon_H24 | zenon_intro zenon_H1a; zenon_intro zenon_H23 ]. % 0.38/0.58 exact (zenon_H25 zenon_H1a). % 0.38/0.58 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.38/0.58 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.38/0.58 generalize (mDefIdeal (sdtpldt1 (xI) (xJ))). zenon_intro zenon_H2a. % 0.38/0.58 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H28; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ]. % 0.38/0.58 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.38/0.58 generalize (mDefSSum (xI)). zenon_intro zenon_H30. % 0.38/0.58 generalize (zenon_H30 (xJ)). zenon_intro zenon_H31. % 0.38/0.58 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.38/0.58 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.38/0.58 exact (zenon_H35 zenon_H21). % 0.38/0.58 exact (zenon_H34 zenon_H27). % 0.38/0.58 generalize (zenon_H32 (sdtpldt1 (xI) (xJ))). zenon_intro zenon_H36. % 0.38/0.58 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H38; zenon_intro zenon_H37 ]. % 0.38/0.58 apply zenon_H3a. apply refl_equal. % 0.38/0.58 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 0.38/0.58 exact (zenon_H2f zenon_H3c). % 0.38/0.58 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElementOf0 W1 (sdtpldt1 (xI) (xJ)))->((forall W2 : zenon_U, ((aElementOf0 W2 (sdtpldt1 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W1 W2) (sdtpldt1 (xI) (xJ)))))/\(forall W2 : zenon_U, ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 W1) (sdtpldt1 (xI) (xJ)))))))) zenon_H2e); [ zenon_intro zenon_H3d; idtac ]. % 0.38/0.58 elim zenon_H3d. zenon_intro zenon_TW1_ck. zenon_intro zenon_H3f. % 0.38/0.58 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.38/0.58 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.38/0.58 apply (zenon_notallex_s (fun W2 : zenon_U => ((aElementOf0 W2 (sdtpldt1 (xI) (xJ)))->(aElementOf0 (sdtpldt0 zenon_TW1_ck W2) (sdtpldt1 (xI) (xJ))))) zenon_H43); [ zenon_intro zenon_H44; idtac ]. % 0.38/0.58 elim zenon_H44. zenon_intro zenon_TW2_cr. zenon_intro zenon_H46. % 0.38/0.58 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.38/0.58 generalize (zenon_H29 zenon_TW1_ck). zenon_intro zenon_H49. % 0.38/0.58 generalize (zenon_H49 zenon_TW2_cr). zenon_intro zenon_H4a. % 0.38/0.58 generalize (zenon_H4a (sz10)). zenon_intro zenon_H4b. % 0.38/0.58 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 0.38/0.58 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.38/0.58 exact (zenon_H4f zenon_H41). % 0.38/0.58 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.38/0.58 exact (zenon_H51 zenon_H48). % 0.38/0.58 exact (zenon_H50 mSortsC_01). % 0.38/0.59 elim zenon_H4c. zenon_intro zenon_TW3_de. zenon_intro zenon_H53. % 0.38/0.59 elim zenon_H53. zenon_intro zenon_TW4_dg. zenon_intro zenon_H55. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H59. zenon_intro zenon_H58. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 0.38/0.59 elim zenon_H5a. zenon_intro zenon_TW5_do. zenon_intro zenon_H5d. % 0.38/0.59 elim zenon_H5d. zenon_intro zenon_TW6_dq. zenon_intro zenon_H5f. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H61. zenon_intro zenon_H60. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 0.38/0.59 exact (zenon_H47 zenon_H71). % 0.38/0.59 apply (zenon_notallex_s (fun W2 : zenon_U => ((aElement0 W2)->(aElementOf0 (sdtasdt0 W2 zenon_TW1_ck) (sdtpldt1 (xI) (xJ))))) zenon_H42); [ zenon_intro zenon_H72; idtac ]. % 0.38/0.59 elim zenon_H72. zenon_intro zenon_TW2_el. zenon_intro zenon_H74. % 0.38/0.59 apply (zenon_notimply_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75. % 0.38/0.59 generalize (zenon_H29 zenon_TW1_ck). zenon_intro zenon_H49. % 0.38/0.59 generalize (zenon_H49 zenon_TW1_ck). zenon_intro zenon_H77. % 0.38/0.59 generalize (zenon_H77 zenon_TW2_el). zenon_intro zenon_H78. % 0.38/0.59 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 0.38/0.59 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H4f | zenon_intro zenon_H7b ]. % 0.38/0.59 exact (zenon_H4f zenon_H41). % 0.38/0.59 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H4f | zenon_intro zenon_H7c ]. % 0.38/0.59 exact (zenon_H4f zenon_H41). % 0.38/0.59 exact (zenon_H7c zenon_H76). % 0.38/0.59 elim zenon_H79. zenon_intro zenon_TW3_ev. zenon_intro zenon_H7e. % 0.38/0.59 elim zenon_H7e. zenon_intro zenon_TW4_ex. zenon_intro zenon_H80. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H82. zenon_intro zenon_H81. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 0.38/0.59 elim zenon_H85. zenon_intro zenon_TW5_ff. zenon_intro zenon_H88. % 0.38/0.59 elim zenon_H88. zenon_intro zenon_TW6_fh. zenon_intro zenon_H8a. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H98. zenon_intro zenon_H97. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.38/0.59 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 0.38/0.59 exact (zenon_H75 zenon_H9b). % 0.38/0.59 exact (zenon_H28 zenon_H2c). % 0.38/0.59 Qed. % 0.38/0.59 % SZS output end Proof % 0.38/0.59 (* END-PROOF *) % 0.38/0.59 nodes searched: 1922 % 0.38/0.59 max branch formulas: 505 % 0.38/0.59 proof nodes created: 121 % 0.38/0.59 formulas created: 14244 % 0.38/0.59 %------------------------------------------------------------------------------