%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 06:33:21 EDT 2022 % Result : Theorem 0.19s 0.49s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 21:48:23 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.49 (* PROOF-FOUND *) % 0.19/0.49 % SZS status Theorem % 0.19/0.49 (* BEGIN-PROOF *) % 0.19/0.49 % SZS output start Proof % 0.19/0.49 Theorem prove_subset_of_empty_set_is_empty_set : (forall B : zenon_U, ((subset B (empty_set))->(B = (empty_set)))). % 0.19/0.49 Proof. % 0.19/0.49 apply NNPP. intro zenon_G. % 0.19/0.49 apply (zenon_notallex_s (fun B : zenon_U => ((subset B (empty_set))->(B = (empty_set)))) zenon_G); [ zenon_intro zenon_H7; idtac ]. % 0.19/0.49 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9. % 0.19/0.49 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.19/0.49 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hc. % 0.19/0.49 generalize (zenon_Hc (empty_set)). zenon_intro zenon_Hd. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_Hb; zenon_intro zenon_He ]. % 0.19/0.49 exact (zenon_H10 zenon_Hb). % 0.19/0.49 generalize (equal_defn (empty_set)). zenon_intro zenon_H11. % 0.19/0.49 generalize (zenon_H11 zenon_TB_i). zenon_intro zenon_H12. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 0.19/0.49 apply (zenon_notand_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H10 ]. % 0.19/0.49 generalize (subset_defn (empty_set)). zenon_intro zenon_H18. % 0.19/0.49 generalize (zenon_H18 zenon_TB_i). zenon_intro zenon_H19. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H17; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 0.19/0.49 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_i))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.19/0.49 elim zenon_H1d. zenon_intro zenon_TD_be. zenon_intro zenon_H1f. % 0.19/0.49 apply (zenon_notimply_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.19/0.49 generalize (empty_set_defn zenon_TD_be). zenon_intro zenon_H22. % 0.19/0.49 exact (zenon_H22 zenon_H21). % 0.19/0.49 exact (zenon_H17 zenon_H1b). % 0.19/0.49 generalize (subset_defn zenon_TB_i). zenon_intro zenon_Hc. % 0.19/0.49 generalize (zenon_Hc (empty_set)). zenon_intro zenon_Hd. % 0.19/0.49 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_Hb; zenon_intro zenon_He ]. % 0.19/0.49 exact (zenon_Hf zenon_He). % 0.19/0.49 exact (zenon_H10 zenon_Hb). % 0.19/0.49 apply zenon_Ha. apply sym_equal. exact zenon_H14. % 0.19/0.49 Qed. % 0.19/0.49 % SZS output end Proof % 0.19/0.49 (* END-PROOF *) % 0.19/0.49 nodes searched: 67 % 0.19/0.49 max branch formulas: 60 % 0.19/0.49 proof nodes created: 17 % 0.19/0.49 formulas created: 462 % 0.19/0.49 %------------------------------------------------------------------------------