%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 06:35:48 EDT 2022 % Result : Theorem 0.20s 0.51s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n024.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 : Mon Jul 11 02:15:58 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.51 (* PROOF-FOUND *) % 0.20/0.51 % SZS status Theorem % 0.20/0.51 (* BEGIN-PROOF *) % 0.20/0.51 % SZS output start Proof % 0.20/0.51 Theorem thI47 : (forall A : zenon_U, (member (empty_set) (power_set A))). % 0.20/0.51 Proof. % 0.20/0.51 apply NNPP. intro zenon_G. % 0.20/0.51 apply (zenon_notallex_s (fun A : zenon_U => (member (empty_set) (power_set A))) zenon_G); [ zenon_intro zenon_Hc; idtac ]. % 0.20/0.51 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He. % 0.20/0.51 generalize (power_set (empty_set)). zenon_intro zenon_Hf. % 0.20/0.51 generalize (zenon_Hf zenon_TA_n). zenon_intro zenon_H10. % 0.20/0.51 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_He; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.20/0.51 generalize (subset (empty_set)). zenon_intro zenon_H14. % 0.20/0.51 generalize (zenon_H14 zenon_TA_n). zenon_intro zenon_H15. % 0.20/0.51 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H13; zenon_intro zenon_H17 | zenon_intro zenon_H11; zenon_intro zenon_H16 ]. % 0.20/0.51 apply (zenon_notallex_s (fun X : zenon_U => ((member X (empty_set))->(member X zenon_TA_n))) zenon_H17); [ zenon_intro zenon_H18; idtac ]. % 0.20/0.51 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a. % 0.20/0.51 apply (zenon_notimply_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.20/0.51 generalize (empty_set zenon_TX_z). zenon_intro zenon_H1d. % 0.20/0.51 exact (zenon_H1d zenon_H1c). % 0.20/0.51 exact (zenon_H13 zenon_H11). % 0.20/0.51 exact (zenon_He zenon_H12). % 0.20/0.51 Qed. % 0.20/0.51 % SZS output end Proof % 0.20/0.51 (* END-PROOF *) % 0.20/0.51 nodes searched: 339 % 0.20/0.51 max branch formulas: 294 % 0.20/0.51 proof nodes created: 30 % 0.20/0.51 formulas created: 2597 % 0.20/0.51 %------------------------------------------------------------------------------