%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:37:04 EDT 2022 % Result : Theorem 0.51s 0.70s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n012.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 12:51:13 EDT 2022 % 0.13/0.34 % CPUTime : % 0.51/0.70 (* PROOF-FOUND *) % 0.51/0.70 % SZS status Theorem % 0.51/0.70 (* BEGIN-PROOF *) % 0.51/0.70 % SZS output start Proof % 0.51/0.70 Theorem prove_th48 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (forall E : zenon_U, (((subset B C)/\(subset D E))->(subset (difference B E) (difference C D))))))). % 0.51/0.70 Proof. % 0.51/0.70 apply NNPP. intro zenon_G. % 0.51/0.70 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (forall E : zenon_U, (((subset B C)/\(subset D E))->(subset (difference B E) (difference C D))))))) zenon_G); [ zenon_intro zenon_H7; idtac ]. % 0.51/0.70 elim zenon_H7. zenon_intro zenon_TB_i. zenon_intro zenon_H9. % 0.51/0.70 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (forall E : zenon_U, (((subset zenon_TB_i C)/\(subset D E))->(subset (difference zenon_TB_i E) (difference C D)))))) zenon_H9); [ zenon_intro zenon_Ha; idtac ]. % 0.51/0.70 elim zenon_Ha. zenon_intro zenon_TC_l. zenon_intro zenon_Hc. % 0.51/0.70 apply (zenon_notallex_s (fun D : zenon_U => (forall E : zenon_U, (((subset zenon_TB_i zenon_TC_l)/\(subset D E))->(subset (difference zenon_TB_i E) (difference zenon_TC_l D))))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 0.51/0.70 elim zenon_Hd. zenon_intro zenon_TD_o. zenon_intro zenon_Hf. % 0.51/0.70 apply (zenon_notallex_s (fun E : zenon_U => (((subset zenon_TB_i zenon_TC_l)/\(subset zenon_TD_o E))->(subset (difference zenon_TB_i E) (difference zenon_TC_l zenon_TD_o)))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 0.51/0.70 elim zenon_H10. zenon_intro zenon_TE_r. zenon_intro zenon_H12. % 0.51/0.70 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.51/0.70 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.51/0.70 generalize (subset_defn zenon_TB_i). zenon_intro zenon_H17. % 0.51/0.70 generalize (zenon_H17 zenon_TC_l). zenon_intro zenon_H18. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H16; zenon_intro zenon_H19 ]. % 0.51/0.70 exact (zenon_H1b zenon_H16). % 0.51/0.70 generalize (subset_defn zenon_TD_o). zenon_intro zenon_H1c. % 0.51/0.70 generalize (zenon_H1c zenon_TE_r). zenon_intro zenon_H1d. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H20; zenon_intro zenon_H1f | zenon_intro zenon_H15; zenon_intro zenon_H1e ]. % 0.51/0.70 exact (zenon_H20 zenon_H15). % 0.51/0.70 generalize (subset_defn (difference zenon_TB_i zenon_TE_r)). zenon_intro zenon_H21. % 0.51/0.70 generalize (zenon_H21 (difference zenon_TC_l zenon_TD_o)). zenon_intro zenon_H22. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H13; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ]. % 0.51/0.70 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_i zenon_TE_r))->(member D (difference zenon_TC_l zenon_TD_o)))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 0.51/0.70 elim zenon_H26. zenon_intro zenon_TD_bn. zenon_intro zenon_H28. % 0.51/0.70 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.51/0.70 generalize (difference_subset2 zenon_TD_o). zenon_intro zenon_H2b. % 0.51/0.70 generalize (difference_defn zenon_TC_l). zenon_intro zenon_H2c. % 0.51/0.70 generalize (zenon_H2c zenon_TE_r). zenon_intro zenon_H2d. % 0.51/0.70 generalize (zenon_H2b zenon_TE_r). zenon_intro zenon_H2e. % 0.51/0.70 generalize (zenon_H2e zenon_TC_l). zenon_intro zenon_H2f. % 0.51/0.70 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H20 | zenon_intro zenon_H30 ]. % 0.51/0.70 generalize (subset_defn zenon_TD_o). zenon_intro zenon_H1c. % 0.51/0.70 generalize (zenon_H1c zenon_TE_r). zenon_intro zenon_H1d. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H20; zenon_intro zenon_H1f | zenon_intro zenon_H15; zenon_intro zenon_H1e ]. % 0.51/0.70 exact (zenon_H1f zenon_H1e). % 0.51/0.70 exact (zenon_H20 zenon_H15). % 0.51/0.70 generalize (subset_defn (difference zenon_TC_l zenon_TE_r)). zenon_intro zenon_H31. % 0.51/0.70 generalize (zenon_H31 (difference zenon_TC_l zenon_TD_o)). zenon_intro zenon_H32. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H30; zenon_intro zenon_H33 ]. % 0.51/0.70 exact (zenon_H35 zenon_H30). % 0.51/0.70 generalize (zenon_H33 zenon_TD_bn). zenon_intro zenon_H36. % 0.51/0.70 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.51/0.70 generalize (zenon_H2d zenon_TD_bn). zenon_intro zenon_H39. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H38; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H3a ]. % 0.51/0.70 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.51/0.70 generalize (difference_defn zenon_TB_i). zenon_intro zenon_H3f. % 0.51/0.70 generalize (zenon_H19 zenon_TD_bn). zenon_intro zenon_H40. % 0.51/0.70 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.51/0.70 generalize (zenon_H3f zenon_TE_r). zenon_intro zenon_H43. % 0.51/0.70 generalize (zenon_H43 zenon_TD_bn). zenon_intro zenon_H44. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H2a; zenon_intro zenon_H45 ]. % 0.51/0.70 exact (zenon_H47 zenon_H2a). % 0.51/0.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.51/0.70 exact (zenon_H42 zenon_H49). % 0.51/0.70 exact (zenon_H3e zenon_H41). % 0.51/0.70 apply zenon_H3d. zenon_intro zenon_H4a. % 0.51/0.70 generalize (difference_defn zenon_TB_i). zenon_intro zenon_H3f. % 0.51/0.70 generalize (zenon_H3f zenon_TE_r). zenon_intro zenon_H43. % 0.51/0.70 generalize (zenon_H43 zenon_TD_bn). zenon_intro zenon_H44. % 0.51/0.70 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H2a; zenon_intro zenon_H45 ]. % 0.51/0.70 exact (zenon_H47 zenon_H2a). % 0.51/0.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.51/0.70 exact (zenon_H48 zenon_H4a). % 0.51/0.70 exact (zenon_H38 zenon_H3b). % 0.51/0.70 exact (zenon_H29 zenon_H37). % 0.51/0.70 exact (zenon_H13 zenon_H24). % 0.51/0.70 Qed. % 0.51/0.70 % SZS output end Proof % 0.51/0.70 (* END-PROOF *) % 0.51/0.70 nodes searched: 11410 % 0.51/0.70 max branch formulas: 3008 % 0.51/0.70 proof nodes created: 486 % 0.51/0.70 formulas created: 38949 % 0.51/0.70 %------------------------------------------------------------------------------