%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 06:37:03 EDT 2022 % Result : Theorem 0.20s 0.54s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n021.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jul 9 20:55:36 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.54 (* PROOF-FOUND *) % 0.20/0.54 % SZS status Theorem % 0.20/0.54 (* BEGIN-PROOF *) % 0.20/0.54 % SZS output start Proof % 0.20/0.54 Theorem prove_difference_subset1 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (difference B D) (difference C D)))))). % 0.20/0.54 Proof. % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (difference B D) (difference C D)))))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.20/0.54 elim zenon_H4. zenon_intro zenon_TB_f. zenon_intro zenon_H6. % 0.20/0.54 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((subset zenon_TB_f C)->(subset (difference zenon_TB_f D) (difference C D))))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.20/0.54 elim zenon_H7. zenon_intro zenon_TC_i. zenon_intro zenon_H9. % 0.20/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((subset zenon_TB_f zenon_TC_i)->(subset (difference zenon_TB_f D) (difference zenon_TC_i D)))) zenon_H9); [ zenon_intro zenon_Ha; idtac ]. % 0.20/0.54 elim zenon_Ha. zenon_intro zenon_TD_l. zenon_intro zenon_Hc. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.20/0.54 generalize (subset_defn zenon_TB_f). zenon_intro zenon_Hf. % 0.20/0.54 generalize (zenon_Hf zenon_TC_i). zenon_intro zenon_H10. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_He; zenon_intro zenon_H11 ]. % 0.20/0.54 exact (zenon_H13 zenon_He). % 0.20/0.54 generalize (subset_defn (difference zenon_TB_f zenon_TD_l)). zenon_intro zenon_H14. % 0.20/0.54 generalize (zenon_H14 (difference zenon_TC_i zenon_TD_l)). zenon_intro zenon_H15. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_Hd; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_f zenon_TD_l))->(member D (difference zenon_TC_i zenon_TD_l)))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.20/0.54 elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.20/0.54 generalize (difference_defn zenon_TC_i). zenon_intro zenon_H1e. % 0.20/0.54 generalize (zenon_H1e zenon_TD_l). zenon_intro zenon_H1f. % 0.20/0.54 generalize (zenon_H1f zenon_TD_ba). zenon_intro zenon_H20. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1c; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.20/0.54 generalize (zenon_H11 zenon_TD_ba). zenon_intro zenon_H26. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.20/0.54 generalize (difference_defn zenon_TB_f). zenon_intro zenon_H29. % 0.20/0.54 generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a. % 0.20/0.54 generalize (zenon_H2a zenon_TD_ba). zenon_intro zenon_H2b. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H1d; zenon_intro zenon_H2c ]. % 0.20/0.54 exact (zenon_H2e zenon_H1d). % 0.20/0.54 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.20/0.54 exact (zenon_H28 zenon_H30). % 0.20/0.54 exact (zenon_H25 zenon_H27). % 0.20/0.54 apply zenon_H24. zenon_intro zenon_H31. % 0.20/0.54 generalize (difference_defn zenon_TB_f). zenon_intro zenon_H29. % 0.20/0.54 generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a. % 0.20/0.54 generalize (zenon_H2a zenon_TD_ba). zenon_intro zenon_H2b. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H1d; zenon_intro zenon_H2c ]. % 0.20/0.54 exact (zenon_H2e zenon_H1d). % 0.20/0.54 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.20/0.54 exact (zenon_H2f zenon_H31). % 0.20/0.54 exact (zenon_H1c zenon_H22). % 0.20/0.54 exact (zenon_Hd zenon_H17). % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 1470 % 0.20/0.54 max branch formulas: 448 % 0.20/0.54 proof nodes created: 165 % 0.20/0.54 formulas created: 6574 % 0.20/0.54 %------------------------------------------------------------------------------