%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 16:00:06 EDT 2022 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n021.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 Jun 20 11:14:18 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.52 (* PROOF-FOUND *) % 0.20/0.52 % SZS status Theorem % 0.20/0.52 (* BEGIN-PROOF *) % 0.20/0.52 % SZS output start Proof % 0.20/0.52 Theorem t65_relat_1 : (forall A : zenon_U, ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))). % 0.20/0.52 Proof. % 0.20/0.52 assert (zenon_L1_ : (~((empty_set) = (empty_set))) -> False). % 0.20/0.52 do 0 intro. intros zenon_H16. % 0.20/0.52 apply zenon_H16. apply refl_equal. % 0.20/0.52 (* end of lemma zenon_L1_ *) % 0.20/0.52 apply NNPP. intro zenon_G. % 0.20/0.52 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.20/0.52 elim zenon_H17. zenon_intro zenon_TA_y. zenon_intro zenon_H19. % 0.20/0.52 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.20/0.52 apply (zenon_and_s _ _ t60_relat_1). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.20/0.52 apply (zenon_notequiv_s _ _ zenon_H1a); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 0.20/0.52 cut (((relation_dom (empty_set)) = (empty_set)) = ((relation_dom zenon_TA_y) = (empty_set))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H21. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H1d. % 0.20/0.52 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 0.20/0.52 cut (((relation_dom (empty_set)) = (relation_dom zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 0.20/0.52 congruence. % 0.20/0.52 elim (classic ((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y))); [ zenon_intro zenon_H23 | zenon_intro zenon_H24 ]. % 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y)) = ((relation_dom (empty_set)) = (relation_dom zenon_TA_y))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H22. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H23. % 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.20/0.52 congruence. % 0.20/0.52 cut ((zenon_TA_y = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.20/0.52 congruence. % 0.20/0.52 generalize (t64_relat_1 zenon_TA_y). zenon_intro zenon_H27. % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.52 exact (zenon_H29 zenon_H1b). % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H21. zenon_intro zenon_H1e. % 0.20/0.52 exact (zenon_H1e zenon_H20). % 0.20/0.52 exact (zenon_H26 zenon_H2a). % 0.20/0.52 apply zenon_H24. apply refl_equal. % 0.20/0.52 apply zenon_H24. apply refl_equal. % 0.20/0.52 apply zenon_H16. apply refl_equal. % 0.20/0.52 cut (((relation_rng (empty_set)) = (empty_set)) = ((relation_rng zenon_TA_y) = (empty_set))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H1e. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H1c. % 0.20/0.52 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 0.20/0.52 cut (((relation_rng (empty_set)) = (relation_rng zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 0.20/0.52 congruence. % 0.20/0.52 elim (classic ((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y)) = ((relation_rng (empty_set)) = (relation_rng zenon_TA_y))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H2c. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H2d. % 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 0.20/0.52 congruence. % 0.20/0.52 cut ((zenon_TA_y = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.20/0.52 congruence. % 0.20/0.52 generalize (t64_relat_1 zenon_TA_y). zenon_intro zenon_H27. % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.52 exact (zenon_H29 zenon_H1b). % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H21. zenon_intro zenon_H1e. % 0.20/0.52 exact (zenon_H21 zenon_H1f). % 0.20/0.52 exact (zenon_H26 zenon_H2a). % 0.20/0.52 apply zenon_H2e. apply refl_equal. % 0.20/0.52 apply zenon_H2e. apply refl_equal. % 0.20/0.52 apply zenon_H16. apply refl_equal. % 0.20/0.52 Qed. % 0.20/0.52 % SZS output end Proof % 0.20/0.52 (* END-PROOF *) % 0.20/0.52 nodes searched: 167 % 0.20/0.52 max branch formulas: 111 % 0.20/0.52 proof nodes created: 21 % 0.20/0.52 formulas created: 828 % 0.20/0.52 %------------------------------------------------------------------------------