%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET583+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 06:37:00 EDT 2022 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET583+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n008.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 : Sat Jul 9 16:37:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.52 (* PROOF-FOUND *) % 0.20/0.52 % SZS status Theorem % 0.20/0.52 (* BEGIN-PROOF *) % 0.20/0.52 % SZS output start Proof % 0.20/0.52 Theorem prove_extensionality : (forall B : zenon_U, (forall C : zenon_U, (((subset B C)/\(subset C B))->(B = C)))). % 0.20/0.52 Proof. % 0.20/0.52 apply NNPP. intro zenon_G. % 0.20/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((subset B C)/\(subset C B))->(B = C)))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.20/0.52 elim zenon_H4. zenon_intro zenon_TB_f. zenon_intro zenon_H6. % 0.20/0.52 apply (zenon_notallex_s (fun C : zenon_U => (((subset zenon_TB_f C)/\(subset C zenon_TB_f))->(zenon_TB_f = C))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.20/0.52 elim zenon_H7. zenon_intro zenon_TC_i. zenon_intro zenon_H9. % 0.20/0.52 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.20/0.52 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.20/0.52 generalize (subset_defn zenon_TB_f). zenon_intro zenon_He. % 0.20/0.52 generalize (zenon_He zenon_TC_i). zenon_intro zenon_Hf. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_Hd; zenon_intro zenon_H10 ]. % 0.20/0.52 exact (zenon_H12 zenon_Hd). % 0.20/0.52 generalize (subset_defn zenon_TC_i). zenon_intro zenon_H13. % 0.20/0.52 generalize (zenon_H13 zenon_TB_f). zenon_intro zenon_H14. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_Hc; zenon_intro zenon_H15 ]. % 0.20/0.52 exact (zenon_H17 zenon_Hc). % 0.20/0.52 generalize (equal_defn zenon_TB_f). zenon_intro zenon_H18. % 0.20/0.52 generalize (zenon_H18 zenon_TC_i). zenon_intro zenon_H19. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_Ha; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_Hb ]. % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H12 | zenon_intro zenon_H17 ]. % 0.20/0.52 generalize (subset_defn zenon_TB_f). zenon_intro zenon_He. % 0.20/0.52 generalize (zenon_He zenon_TC_i). zenon_intro zenon_Hf. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_Hd; zenon_intro zenon_H10 ]. % 0.20/0.52 exact (zenon_H11 zenon_H10). % 0.20/0.52 exact (zenon_H12 zenon_Hd). % 0.20/0.52 generalize (subset_defn zenon_TC_i). zenon_intro zenon_H13. % 0.20/0.52 generalize (zenon_H13 zenon_TB_f). zenon_intro zenon_H14. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_Hc; zenon_intro zenon_H15 ]. % 0.20/0.52 exact (zenon_H16 zenon_H15). % 0.20/0.52 exact (zenon_H17 zenon_Hc). % 0.20/0.52 exact (zenon_Ha zenon_H1a). % 0.20/0.52 Qed. % 0.20/0.52 % SZS output end Proof % 0.20/0.52 (* END-PROOF *) % 0.20/0.52 nodes searched: 68 % 0.20/0.52 max branch formulas: 64 % 0.20/0.52 proof nodes created: 14 % 0.20/0.52 formulas created: 445 % 0.20/0.52 %------------------------------------------------------------------------------