%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 06:37:31 EDT 2022 % Result : Theorem 19.53s 19.71s % Output : Proof 19.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET626+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n027.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 : Mon Jul 11 09:05:18 EDT 2022 % 0.14/0.35 % CPUTime : % 19.53/19.71 (* PROOF-FOUND *) % 19.53/19.71 % SZS status Theorem % 19.53/19.71 (* BEGIN-PROOF *) % 19.53/19.71 % SZS output start Proof % 19.53/19.71 Theorem prove_th102 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))). % 19.53/19.71 Proof. % 19.53/19.71 assert (zenon_L1_ : forall (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TB_l : zenon_U), (~(exists D : zenon_U, ((member D zenon_TB_l)/\(member D zenon_TC_k)))) -> (member zenon_TD_j zenon_TB_l) -> (member zenon_TD_j zenon_TC_k) -> False). % 19.53/19.71 do 3 intro. intros zenon_H6 zenon_H7 zenon_H8. % 19.53/19.71 apply zenon_H6. exists zenon_TD_j. apply NNPP. zenon_intro zenon_Hc. % 19.53/19.71 apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 19.53/19.71 exact (zenon_He zenon_H7). % 19.53/19.71 exact (zenon_Hd zenon_H8). % 19.53/19.71 (* end of lemma zenon_L1_ *) % 19.53/19.71 apply NNPP. intro zenon_G. % 19.53/19.71 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))) zenon_G); [ zenon_intro zenon_Hf; idtac ]. % 19.53/19.71 elim zenon_Hf. zenon_intro zenon_TB_l. zenon_intro zenon_H10. % 19.53/19.71 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((intersect zenon_TB_l (intersection C D))->(intersect zenon_TB_l C)))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 19.53/19.71 elim zenon_H11. zenon_intro zenon_TC_k. zenon_intro zenon_H12. % 19.53/19.71 apply (zenon_notallex_s (fun D : zenon_U => ((intersect zenon_TB_l (intersection zenon_TC_k D))->(intersect zenon_TB_l zenon_TC_k))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 19.53/19.71 elim zenon_H13. zenon_intro zenon_TD_u. zenon_intro zenon_H15. % 19.53/19.71 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 19.53/19.71 generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18. % 19.53/19.71 generalize (zenon_H18 (intersection zenon_TC_k zenon_TD_u)). zenon_intro zenon_H19. % 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H17; zenon_intro zenon_H1a ]. % 19.53/19.71 exact (zenon_H1c zenon_H17). % 19.53/19.71 elim zenon_H1a. zenon_intro zenon_TD_j. zenon_intro zenon_H1d. % 19.53/19.71 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H7. zenon_intro zenon_H1e. % 19.53/19.71 generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18. % 19.53/19.71 generalize (zenon_H18 zenon_TC_k). zenon_intro zenon_H1f. % 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H16; zenon_intro zenon_H6 | zenon_intro zenon_H21; zenon_intro zenon_H20 ]. % 19.53/19.71 generalize (intersection_defn zenon_TC_k). zenon_intro zenon_H22. % 19.53/19.71 generalize (zenon_H22 zenon_TB_l). zenon_intro zenon_H23. % 19.53/19.71 generalize (zenon_H23 zenon_TD_j). zenon_intro zenon_H24. % 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H26; zenon_intro zenon_H25 ]. % 19.53/19.71 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_Hd | zenon_intro zenon_He ]. % 19.53/19.71 generalize (zenon_H22 zenon_TD_u). zenon_intro zenon_H29. % 19.53/19.71 generalize (zenon_H29 zenon_TD_j). zenon_intro zenon_H2a. % 19.53/19.71 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2d; zenon_intro zenon_H2c | zenon_intro zenon_H1e; zenon_intro zenon_H2b ]. % 19.53/19.71 exact (zenon_H2d zenon_H1e). % 19.53/19.71 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H8. zenon_intro zenon_H2e. % 19.53/19.71 exact (zenon_Hd zenon_H8). % 19.53/19.71 exact (zenon_He zenon_H7). % 19.53/19.71 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H8. zenon_intro zenon_H7. % 19.53/19.71 apply (zenon_L1_ zenon_TD_j zenon_TC_k zenon_TB_l); trivial. % 19.53/19.71 exact (zenon_H16 zenon_H21). % 19.53/19.71 Qed. % 19.53/19.71 % SZS output end Proof % 19.53/19.71 (* END-PROOF *) % 19.53/19.71 nodes searched: 620721 % 19.53/19.71 max branch formulas: 13462 % 19.53/19.71 proof nodes created: 20174 % 19.53/19.71 formulas created: 780137 % 19.53/19.71 %------------------------------------------------------------------------------