%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 06:38:26 EDT 2022 % Result : Theorem 0.19s 0.54s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 08:00:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.54 (* PROOF-FOUND *) % 0.19/0.54 % SZS status Theorem % 0.19/0.54 (* BEGIN-PROOF *) % 0.19/0.54 % SZS output start Proof % 0.19/0.54 Theorem thIII02 : (forall E : zenon_U, (forall R : zenon_U, (forall A : zenon_U, (((equivalence R E)/\(member A E))->(member A (equivalence_class A E R)))))). % 0.19/0.54 Proof. % 0.19/0.54 apply NNPP. intro zenon_G. % 0.19/0.54 apply (zenon_notallex_s (fun E : zenon_U => (forall R : zenon_U, (forall A : zenon_U, (((equivalence R E)/\(member A E))->(member A (equivalence_class A E R)))))) zenon_G); [ zenon_intro zenon_H11; idtac ]. % 0.19/0.54 elim zenon_H11. zenon_intro zenon_TE_s. zenon_intro zenon_H13. % 0.19/0.54 apply (zenon_notallex_s (fun R : zenon_U => (forall A : zenon_U, (((equivalence R zenon_TE_s)/\(member A zenon_TE_s))->(member A (equivalence_class A zenon_TE_s R))))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 0.19/0.54 elim zenon_H14. zenon_intro zenon_TR_v. zenon_intro zenon_H16. % 0.19/0.54 apply (zenon_notallex_s (fun A : zenon_U => (((equivalence zenon_TR_v zenon_TE_s)/\(member A zenon_TE_s))->(member A (equivalence_class A zenon_TE_s zenon_TR_v)))) zenon_H16); [ zenon_intro zenon_H17; idtac ]. % 0.19/0.54 elim zenon_H17. zenon_intro zenon_TA_y. zenon_intro zenon_H19. % 0.19/0.54 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.19/0.54 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.19/0.54 generalize (equivalence zenon_TE_s). zenon_intro zenon_H1e. % 0.19/0.54 generalize (zenon_H1e zenon_TR_v). zenon_intro zenon_H1f. % 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1d; zenon_intro zenon_H20 ]. % 0.19/0.54 exact (zenon_H22 zenon_H1d). % 0.19/0.54 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.19/0.54 generalize (equivalence_class zenon_TR_v). zenon_intro zenon_H25. % 0.19/0.54 generalize (zenon_H25 zenon_TE_s). zenon_intro zenon_H26. % 0.19/0.54 generalize (zenon_H26 zenon_TA_y). zenon_intro zenon_H27. % 0.19/0.54 generalize (zenon_H27 zenon_TA_y). zenon_intro zenon_H28. % 0.19/0.54 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H1a; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ]. % 0.19/0.54 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.19/0.54 exact (zenon_H2d zenon_H1c). % 0.19/0.54 generalize (zenon_H24 zenon_TA_y). zenon_intro zenon_H2e. % 0.19/0.54 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f ]. % 0.19/0.54 exact (zenon_H2d zenon_H1c). % 0.19/0.54 exact (zenon_H2c zenon_H2f). % 0.19/0.54 exact (zenon_H1a zenon_H2a). % 0.19/0.54 Qed. % 0.19/0.54 % SZS output end Proof % 0.19/0.54 (* END-PROOF *) % 0.19/0.54 nodes searched: 1118 % 0.19/0.54 max branch formulas: 676 % 0.19/0.54 proof nodes created: 77 % 0.19/0.54 formulas created: 7536 % 0.19/0.54 %------------------------------------------------------------------------------