%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0. % 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 06:33:18 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 % 0.11/0.13 % Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n029.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 : Sun Jul 10 12:26:16 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 prove_empty_set_subset : (forall B : zenon_U, (subset (empty_set) B)). % 0.20/0.51 Proof. % 0.20/0.51 apply NNPP. intro zenon_G. % 0.20/0.51 apply (zenon_notallex_s (fun B : zenon_U => (subset (empty_set) B)) zenon_G); [ zenon_intro zenon_H5; idtac ]. % 0.20/0.51 elim zenon_H5. zenon_intro zenon_TB_g. zenon_intro zenon_H7. % 0.20/0.51 generalize (subset_defn (empty_set)). zenon_intro zenon_H8. % 0.20/0.51 generalize (zenon_H8 zenon_TB_g). zenon_intro zenon_H9. % 0.20/0.51 apply (zenon_equiv_s _ _ zenon_H9); [ zenon_intro zenon_H7; zenon_intro zenon_Hc | zenon_intro zenon_Hb; zenon_intro zenon_Ha ]. % 0.20/0.51 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_g))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 0.20/0.51 elim zenon_Hd. zenon_intro zenon_TD_o. zenon_intro zenon_Hf. % 0.20/0.51 apply (zenon_notimply_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10. % 0.20/0.51 generalize (empty_set_defn zenon_TD_o). zenon_intro zenon_H12. % 0.20/0.51 exact (zenon_H12 zenon_H11). % 0.20/0.51 exact (zenon_H7 zenon_Hb). % 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: 11 % 0.20/0.51 max branch formulas: 12 % 0.20/0.51 proof nodes created: 7 % 0.20/0.51 formulas created: 126 % 0.20/0.51 %------------------------------------------------------------------------------