%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n023.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 06:34:25 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 % 0.03/0.12 % Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n023.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % 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 22:34:55 EDT 2022 % 0.13/0.34 % 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_idempotency_of_intersection : (forall B : zenon_U, ((intersection B B) = B)). % 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 => ((intersection B B) = B)) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.20/0.54 elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha. % 0.20/0.54 generalize (equal_member_defn zenon_TB_j). zenon_intro zenon_Hb. % 0.20/0.54 generalize (intersection_defn zenon_TB_j). zenon_intro zenon_Hc. % 0.20/0.54 generalize (zenon_Hc zenon_TB_j). zenon_intro zenon_Hd. % 0.20/0.54 generalize (zenon_Hb (intersection zenon_TB_j zenon_TB_j)). zenon_intro zenon_He. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_He); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_H10; zenon_intro zenon_Hf ]. % 0.20/0.54 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)<->(member D (intersection zenon_TB_j zenon_TB_j)))) zenon_H11); [ zenon_intro zenon_H13; idtac ]. % 0.20/0.54 elim zenon_H13. zenon_intro zenon_TD_u. zenon_intro zenon_H15. % 0.20/0.54 apply (zenon_notequiv_s _ _ zenon_H15); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.20/0.54 generalize (zenon_Hd zenon_TD_u). zenon_intro zenon_H1a. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H16; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ]. % 0.20/0.54 exact (zenon_H16 zenon_H18). % 0.20/0.54 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H17. zenon_intro zenon_H17. % 0.20/0.54 exact (zenon_H19 zenon_H17). % 0.20/0.54 generalize (zenon_Hd zenon_TD_u). zenon_intro zenon_H1a. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H16; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H19 | zenon_intro zenon_H19 ]. % 0.20/0.54 exact (zenon_H19 zenon_H17). % 0.20/0.54 exact (zenon_H19 zenon_H17). % 0.20/0.54 exact (zenon_H16 zenon_H18). % 0.20/0.54 apply zenon_Ha. apply sym_equal. exact zenon_H10. % 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: 797 % 0.20/0.54 max branch formulas: 298 % 0.20/0.54 proof nodes created: 87 % 0.20/0.54 formulas created: 3015 % 0.20/0.54 %------------------------------------------------------------------------------