%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 : Tue Jul 19 15:59:45 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 20 02:53:45 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.50 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.19/0.50 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem l23_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((in A B)->((set_union2 (singleton A) B) = B)))). % 0.19/0.50 Proof. % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((in A B)->((set_union2 (singleton A) B) = B)))) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.19/0.50 elim zenon_H8. zenon_intro zenon_TA_j. zenon_intro zenon_Ha. % 0.19/0.50 apply (zenon_notallex_s (fun B : zenon_U => ((in zenon_TA_j B)->((set_union2 (singleton zenon_TA_j) B) = B))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ]. % 0.19/0.50 elim zenon_Hb. zenon_intro zenon_TB_m. zenon_intro zenon_Hd. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_Hd). zenon_intro zenon_Hf. zenon_intro zenon_He. % 0.19/0.50 generalize (t12_xboole_1 (singleton zenon_TA_j)). zenon_intro zenon_H10. % 0.19/0.50 generalize (zenon_H10 zenon_TB_m). zenon_intro zenon_H11. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ]. % 0.19/0.50 generalize (l2_zfmisc_1 zenon_TA_j). zenon_intro zenon_H14. % 0.19/0.50 generalize (zenon_H14 zenon_TB_m). zenon_intro zenon_H15. % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H13; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_Hf ]. % 0.19/0.50 exact (zenon_H17 zenon_Hf). % 0.19/0.50 exact (zenon_H13 zenon_H16). % 0.19/0.50 exact (zenon_He zenon_H12). % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 308 % 0.19/0.50 max branch formulas: 124 % 0.19/0.50 proof nodes created: 61 % 0.19/0.50 formulas created: 1148 % 0.19/0.50 %------------------------------------------------------------------------------