%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET579+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 06:36:58 EDT 2022 % Result : Theorem 2.43s 2.63s % Output : Proof 2.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET579+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n017.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 : Mon Jul 11 04:00:18 EDT 2022 % 0.12/0.33 % CPUTime : % 2.43/2.63 (* PROOF-FOUND *) % 2.43/2.63 % SZS status Theorem % 2.43/2.63 (* BEGIN-PROOF *) % 2.43/2.63 % SZS output start Proof % 2.43/2.63 Theorem prove_th20 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((forall E : zenon_U, ((member E B)<->((member E C)/\(~(member E D)))))->(B = (difference C D)))))). % 2.43/2.63 Proof. % 2.43/2.63 assert (zenon_L1_ : forall (zenon_TD_i : zenon_U) (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TB_l : zenon_U), (forall E : zenon_U, ((member E zenon_TB_l)<->((member E zenon_TC_k)/\(~(member E zenon_TD_j))))) -> (member zenon_TD_i zenon_TB_l) -> (member zenon_TD_i zenon_TD_j) -> False). % 2.43/2.63 do 4 intro. intros zenon_H5 zenon_H6 zenon_H7. % 2.43/2.63 generalize (zenon_H5 zenon_TD_i). zenon_intro zenon_Hc. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_Hf; zenon_intro zenon_He | zenon_intro zenon_H6; zenon_intro zenon_Hd ]. % 2.43/2.63 exact (zenon_Hf zenon_H6). % 2.43/2.63 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H11. zenon_intro zenon_H10. % 2.43/2.63 exact (zenon_H10 zenon_H7). % 2.43/2.63 (* end of lemma zenon_L1_ *) % 2.43/2.63 apply NNPP. intro zenon_G. % 2.43/2.63 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((forall E : zenon_U, ((member E B)<->((member E C)/\(~(member E D)))))->(B = (difference C D)))))) zenon_G); [ zenon_intro zenon_H12; idtac ]. % 2.43/2.63 elim zenon_H12. zenon_intro zenon_TB_l. zenon_intro zenon_H13. % 2.43/2.63 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((forall E : zenon_U, ((member E zenon_TB_l)<->((member E C)/\(~(member E D)))))->(zenon_TB_l = (difference C D))))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 2.43/2.63 elim zenon_H14. zenon_intro zenon_TC_k. zenon_intro zenon_H15. % 2.43/2.63 apply (zenon_notallex_s (fun D : zenon_U => ((forall E : zenon_U, ((member E zenon_TB_l)<->((member E zenon_TC_k)/\(~(member E D)))))->(zenon_TB_l = (difference zenon_TC_k D)))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 2.43/2.63 elim zenon_H16. zenon_intro zenon_TD_j. zenon_intro zenon_H17. % 2.43/2.63 apply (zenon_notimply_s _ _ zenon_H17). zenon_intro zenon_H5. zenon_intro zenon_H18. % 2.43/2.63 generalize (equal_defn zenon_TB_l). zenon_intro zenon_H19. % 2.43/2.63 generalize (difference_defn zenon_TC_k). zenon_intro zenon_H1a. % 2.43/2.63 generalize (zenon_H1a zenon_TD_j). zenon_intro zenon_H1b. % 2.43/2.63 generalize (zenon_H19 (difference zenon_TC_k zenon_TD_j)). zenon_intro zenon_H1c. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H18; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ]. % 2.43/2.63 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 2.43/2.63 generalize (subset_defn zenon_TB_l). zenon_intro zenon_H22. % 2.43/2.63 generalize (zenon_H22 (difference zenon_TC_k zenon_TD_j)). zenon_intro zenon_H23. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 2.43/2.63 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_l)->(member D (difference zenon_TC_k zenon_TD_j)))) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 2.43/2.63 elim zenon_H27. zenon_intro zenon_TD_i. zenon_intro zenon_H28. % 2.43/2.63 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H6. zenon_intro zenon_H29. % 2.43/2.63 generalize (zenon_H1b zenon_TD_i). zenon_intro zenon_H2a. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H29; zenon_intro zenon_He | zenon_intro zenon_H2b; zenon_intro zenon_Hd ]. % 2.43/2.63 apply (zenon_notand_s _ _ zenon_He); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.43/2.63 generalize (zenon_H5 zenon_TD_i). zenon_intro zenon_Hc. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_Hf; zenon_intro zenon_He | zenon_intro zenon_H6; zenon_intro zenon_Hd ]. % 2.43/2.63 exact (zenon_Hf zenon_H6). % 2.43/2.63 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H11. zenon_intro zenon_H10. % 2.43/2.63 exact (zenon_H2d zenon_H11). % 2.43/2.63 apply zenon_H2c. zenon_intro zenon_H7. % 2.43/2.63 apply (zenon_L1_ zenon_TD_i zenon_TD_j zenon_TC_k zenon_TB_l); trivial. % 2.43/2.63 exact (zenon_H29 zenon_H2b). % 2.43/2.63 exact (zenon_H21 zenon_H25). % 2.43/2.63 generalize (subset_defn (difference zenon_TC_k zenon_TD_j)). zenon_intro zenon_H2e. % 2.43/2.63 generalize (zenon_H2e zenon_TB_l). zenon_intro zenon_H2f. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H20; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ]. % 2.43/2.63 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TC_k zenon_TD_j))->(member D zenon_TB_l))) zenon_H32); [ zenon_intro zenon_H33; idtac ]. % 2.43/2.63 elim zenon_H33. zenon_intro zenon_TD_ca. zenon_intro zenon_H35. % 2.43/2.63 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 2.43/2.63 generalize (zenon_H5 zenon_TD_ca). zenon_intro zenon_H38. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H36; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H39 ]. % 2.43/2.63 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 2.43/2.63 generalize (zenon_H1b zenon_TD_ca). zenon_intro zenon_H3e. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3f; zenon_intro zenon_H3b | zenon_intro zenon_H37; zenon_intro zenon_H39 ]. % 2.43/2.63 exact (zenon_H3f zenon_H37). % 2.43/2.63 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H41. zenon_intro zenon_H40. % 2.43/2.63 exact (zenon_H3d zenon_H41). % 2.43/2.63 apply zenon_H3c. zenon_intro zenon_H42. % 2.43/2.63 generalize (zenon_H1b zenon_TD_ca). zenon_intro zenon_H3e. % 2.43/2.63 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3f; zenon_intro zenon_H3b | zenon_intro zenon_H37; zenon_intro zenon_H39 ]. % 2.43/2.63 exact (zenon_H3f zenon_H37). % 2.43/2.63 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H41. zenon_intro zenon_H40. % 2.43/2.63 exact (zenon_H40 zenon_H42). % 2.43/2.63 exact (zenon_H36 zenon_H3a). % 2.43/2.63 exact (zenon_H20 zenon_H31). % 2.43/2.63 exact (zenon_H18 zenon_H1e). % 2.43/2.63 Qed. % 2.43/2.63 % SZS output end Proof % 2.43/2.63 (* END-PROOF *) % 2.43/2.63 nodes searched: 136903 % 2.43/2.63 max branch formulas: 8836 % 2.43/2.63 proof nodes created: 5099 % 2.43/2.63 formulas created: 186383 % 2.43/2.63 %------------------------------------------------------------------------------