%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:23 PM UTC 2026 % Result : Theorem 0.11s 0.45s % Output : Proof 0.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.11/0.36 % Computer : n026.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sun Sep 6 00:39:41 UTC 2026 % 0.11/0.36 % CPUTime : % 0.11/0.45 (* PROOF-FOUND *) % 0.11/0.45 % SZS status Theorem % 0.11/0.45 (* BEGIN-PROOF *) % 0.11/0.45 % SZS output start Proof % 0.11/0.45 Theorem s1_0_adjunction : (adjunction). % 0.11/0.45 Proof. % 0.11/0.45 apply NNPP. intro zenon_G. % 0.11/0.45 apply (zenon_equiv_s _ _ modus_ponens); [ zenon_intro zenon_H57; zenon_intro zenon_H56 | zenon_intro hilbert_modus_ponens; zenon_intro zenon_H55 ]. % 0.11/0.45 exact (zenon_H57 hilbert_modus_ponens). % 0.11/0.45 apply (zenon_equiv_s _ _ and_3); [ zenon_intro zenon_H5a; zenon_intro zenon_H59 | zenon_intro hilbert_and_3; zenon_intro zenon_H58 ]. % 0.11/0.45 exact (zenon_H5a hilbert_and_3). % 0.11/0.45 apply (zenon_equiv_s _ _ adjunction); [ zenon_intro zenon_G; zenon_intro zenon_H5d | zenon_intro zenon_H5c; zenon_intro zenon_H5b ]. % 0.11/0.45 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((is_a_theorem X)/\(is_a_theorem Y))->(is_a_theorem (and X Y))))) zenon_H5d); [ zenon_intro zenon_H5e; idtac ]. % 0.11/0.45 elim zenon_H5e. zenon_intro zenon_TX_dr. zenon_intro zenon_H60. % 0.11/0.45 apply (zenon_notallex_s (fun Y : zenon_U => (((is_a_theorem zenon_TX_dr)/\(is_a_theorem Y))->(is_a_theorem (and zenon_TX_dr Y)))) zenon_H60); [ zenon_intro zenon_H61; idtac ]. % 0.11/0.45 elim zenon_H61. zenon_intro zenon_TY_du. zenon_intro zenon_H63. % 0.11/0.45 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.11/0.45 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.11/0.45 generalize (zenon_H55 zenon_TY_du). zenon_intro zenon_H68. % 0.11/0.45 generalize (zenon_H55 zenon_TX_dr). zenon_intro zenon_H69. % 0.11/0.45 generalize (zenon_H68 (and zenon_TX_dr zenon_TY_du)). zenon_intro zenon_H6a. % 0.11/0.45 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.11/0.45 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 0.11/0.45 exact (zenon_H6e zenon_H66). % 0.11/0.45 generalize (zenon_H58 zenon_TX_dr). zenon_intro zenon_H6f. % 0.11/0.45 generalize (zenon_H6f zenon_TY_du). zenon_intro zenon_H70. % 0.11/0.45 generalize (zenon_H69 (implies zenon_TY_du (and zenon_TX_dr zenon_TY_du))). zenon_intro zenon_H71. % 0.11/0.45 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.11/0.45 apply (zenon_notand_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.11/0.45 exact (zenon_H75 zenon_H67). % 0.11/0.45 exact (zenon_H74 zenon_H70). % 0.11/0.45 exact (zenon_H6d zenon_H72). % 0.11/0.45 exact (zenon_H64 zenon_H6b). % 0.11/0.45 exact (zenon_G zenon_H5c). % 0.11/0.45 Qed. % 0.11/0.45 % SZS output end Proof % 0.11/0.45 (* END-PROOF *) % 0.11/0.45 nodes searched: 1317 % 0.11/0.45 max branch formulas: 839 % 0.11/0.45 proof nodes created: 97 % 0.11/0.45 formulas created: 8884 % 0.11/0.45 %------------------------------------------------------------------------------