%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 06:37:02 EDT 2022 % Result : Theorem 0.63s 0.86s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n006.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 13:58:20 EDT 2022 % 0.12/0.33 % CPUTime : % 0.63/0.86 (* PROOF-FOUND *) % 0.63/0.86 % SZS status Theorem % 0.63/0.86 (* BEGIN-PROOF *) % 0.63/0.86 % SZS output start Proof % 0.63/0.86 Theorem prove_intersection_subset_of_union : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (subset (intersection B C) (union B D))))). % 0.63/0.86 Proof. % 0.63/0.86 apply NNPP. intro zenon_G. % 0.63/0.86 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (subset (intersection B C) (union B D))))) zenon_G); [ zenon_intro zenon_Hb; idtac ]. % 0.63/0.86 elim zenon_Hb. zenon_intro zenon_TB_m. zenon_intro zenon_Hd. % 0.63/0.86 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (subset (intersection zenon_TB_m C) (union zenon_TB_m D)))) zenon_Hd); [ zenon_intro zenon_He; idtac ]. % 0.63/0.86 elim zenon_He. zenon_intro zenon_TC_p. zenon_intro zenon_H10. % 0.63/0.86 apply (zenon_notallex_s (fun D : zenon_U => (subset (intersection zenon_TB_m zenon_TC_p) (union zenon_TB_m D))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 0.63/0.86 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13. % 0.63/0.86 generalize (subset_defn (intersection zenon_TB_m zenon_TC_p)). zenon_intro zenon_H14. % 0.63/0.86 generalize (zenon_H14 (union zenon_TB_m zenon_TD_s)). zenon_intro zenon_H15. % 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H13; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.63/0.86 apply (zenon_notallex_s (fun D : zenon_U => ((member D (intersection zenon_TB_m zenon_TC_p))->(member D (union zenon_TB_m zenon_TD_s)))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.63/0.86 elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b. % 0.63/0.86 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.63/0.86 generalize (union_defn zenon_TB_m). zenon_intro zenon_H1e. % 0.63/0.86 generalize (intersection_is_subset zenon_TB_m). zenon_intro zenon_H1f. % 0.63/0.86 generalize (zenon_H1e zenon_TD_s). zenon_intro zenon_H20. % 0.63/0.86 generalize (zenon_H20 zenon_TD_ba). zenon_intro zenon_H21. % 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1c; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ]. % 0.63/0.86 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.63/0.86 generalize (zenon_H1f zenon_TC_p). zenon_intro zenon_H27. % 0.63/0.86 generalize (subset_defn (intersection zenon_TB_m zenon_TC_p)). zenon_intro zenon_H14. % 0.63/0.86 generalize (zenon_H14 zenon_TB_m). zenon_intro zenon_H28. % 0.63/0.86 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H2b; zenon_intro zenon_H2a | zenon_intro zenon_H27; zenon_intro zenon_H29 ]. % 0.63/0.86 exact (zenon_H2b zenon_H27). % 0.63/0.86 generalize (zenon_H29 zenon_TD_ba). zenon_intro zenon_H2c. % 0.63/0.86 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.63/0.86 exact (zenon_H2e zenon_H1d). % 0.63/0.86 exact (zenon_H26 zenon_H2d). % 0.63/0.86 exact (zenon_H1c zenon_H23). % 0.63/0.86 exact (zenon_H13 zenon_H17). % 0.63/0.86 Qed. % 0.63/0.86 % SZS output end Proof % 0.63/0.86 (* END-PROOF *) % 0.63/0.86 nodes searched: 12156 % 0.63/0.86 max branch formulas: 1638 % 0.63/0.86 proof nodes created: 681 % 0.63/0.86 formulas created: 31711 % 0.63/0.86 %------------------------------------------------------------------------------