%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 06:34:38 EDT 2022 % Result : Theorem 226.79s 226.97s % Output : Proof 226.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n013.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 : Mon Jul 11 09:47:44 EDT 2022 % 0.13/0.34 % CPUTime : % 226.79/226.97 (* PROOF-FOUND *) % 226.79/226.97 % SZS status Theorem % 226.79/226.97 (* BEGIN-PROOF *) % 226.79/226.97 % SZS output start Proof % 226.79/226.97 Theorem prove_absorbtion_for_intersection : (forall B : zenon_U, (forall C : zenon_U, ((intersection B (union B C)) = B))). % 226.79/226.97 Proof. % 226.79/226.97 apply NNPP. intro zenon_G. % 226.79/226.97 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((intersection B (union B C)) = B))) zenon_G); [ zenon_intro zenon_H9; idtac ]. % 226.79/226.97 elim zenon_H9. zenon_intro zenon_TB_k. zenon_intro zenon_Hb. % 226.79/226.97 apply (zenon_notallex_s (fun C : zenon_U => ((intersection zenon_TB_k (union zenon_TB_k C)) = zenon_TB_k)) zenon_Hb); [ zenon_intro zenon_Hc; idtac ]. % 226.79/226.97 elim zenon_Hc. zenon_intro zenon_TC_n. zenon_intro zenon_He. % 226.79/226.97 generalize (equal_member_defn zenon_TB_k). zenon_intro zenon_Hf. % 226.79/226.97 generalize (intersection_defn zenon_TB_k). zenon_intro zenon_H10. % 226.79/226.97 generalize (zenon_Hf (intersection zenon_TB_k (union zenon_TB_k zenon_TC_n))). zenon_intro zenon_H11. % 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H13; zenon_intro zenon_H12 ]. % 226.79/226.97 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_k)<->(member D (intersection zenon_TB_k (union zenon_TB_k zenon_TC_n))))) zenon_H14); [ zenon_intro zenon_H16; idtac ]. % 226.79/226.97 elim zenon_H16. zenon_intro zenon_TD_x. zenon_intro zenon_H18. % 226.79/226.97 apply (zenon_notequiv_s _ _ zenon_H18); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_H19 ]. % 226.79/226.97 generalize (zenon_H10 (union zenon_TB_k zenon_TC_n)). zenon_intro zenon_H1d. % 226.79/226.97 generalize (zenon_H1d zenon_TD_x). zenon_intro zenon_H1e. % 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H19; zenon_intro zenon_H20 | zenon_intro zenon_H1b; zenon_intro zenon_H1f ]. % 226.79/226.97 exact (zenon_H19 zenon_H1b). % 226.79/226.97 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H1a. zenon_intro zenon_H21. % 226.79/226.97 exact (zenon_H1c zenon_H1a). % 226.79/226.97 generalize (zenon_H10 (union zenon_TB_k zenon_TC_n)). zenon_intro zenon_H1d. % 226.79/226.97 generalize (zenon_H1d zenon_TD_x). zenon_intro zenon_H1e. % 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H19; zenon_intro zenon_H20 | zenon_intro zenon_H1b; zenon_intro zenon_H1f ]. % 226.79/226.97 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H1c | zenon_intro zenon_H22 ]. % 226.79/226.97 exact (zenon_H1c zenon_H1a). % 226.79/226.97 generalize (union_defn zenon_TB_k). zenon_intro zenon_H23. % 226.79/226.97 generalize (zenon_H23 zenon_TC_n). zenon_intro zenon_H24. % 226.79/226.97 generalize (zenon_H24 zenon_TD_x). zenon_intro zenon_H25. % 226.79/226.97 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H22; zenon_intro zenon_H27 | zenon_intro zenon_H21; zenon_intro zenon_H26 ]. % 226.79/226.97 apply (zenon_notor_s _ _ zenon_H27). zenon_intro zenon_H1c. zenon_intro zenon_H28. % 226.79/226.97 exact (zenon_H1c zenon_H1a). % 226.79/226.97 exact (zenon_H22 zenon_H21). % 226.79/226.97 exact (zenon_H19 zenon_H1b). % 226.79/226.97 apply zenon_He. apply sym_equal. exact zenon_H13. % 226.79/226.97 Qed. % 226.79/226.97 % SZS output end Proof % 226.79/226.97 (* END-PROOF *) % 226.79/226.97 nodes searched: 6346165 % 226.79/226.97 max branch formulas: 35309 % 226.79/226.97 proof nodes created: 160050 % 226.79/226.97 formulas created: 9546198 % 226.79/226.97 %------------------------------------------------------------------------------