%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU303+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 16:01:03 EDT 2022 % Result : Theorem 0.47s 0.63s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU303+3 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.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 : Sun Jun 19 07:01:53 EDT 2022 % 0.13/0.34 % CPUTime : % 0.47/0.63 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.47/0.63 (* PROOF-FOUND *) % 0.47/0.63 % SZS status Theorem % 0.47/0.63 (* BEGIN-PROOF *) % 0.47/0.63 % SZS output start Proof % 0.47/0.63 Theorem t26_finset_1 : (forall A : zenon_U, (((relation A)/\(function A))->((finite (relation_dom A))->(finite (relation_rng A))))). % 0.47/0.63 Proof. % 0.47/0.63 assert (zenon_L1_ : forall (zenon_TA_cr : zenon_U), (forall x : zenon_U, (subset x x)) -> (forall B : zenon_U, ((element B (powerset (relation_image zenon_TA_cr (relation_dom zenon_TA_cr))))->(finite B))) -> (forall B : zenon_U, ((element (relation_rng zenon_TA_cr) (powerset B))<->(subset (relation_rng zenon_TA_cr) B))) -> ((relation_image zenon_TA_cr (relation_dom zenon_TA_cr)) = (relation_rng zenon_TA_cr)) -> (~(finite (relation_rng zenon_TA_cr))) -> False). % 0.47/0.63 do 1 intro. intros zenon_H40 zenon_H41 zenon_H42 zenon_H43 zenon_H44. % 0.47/0.63 generalize (zenon_H41 (relation_rng zenon_TA_cr)). zenon_intro zenon_H46. % 0.47/0.63 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 0.47/0.63 generalize (zenon_H42 (relation_rng zenon_TA_cr)). zenon_intro zenon_H49. % 0.47/0.63 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H4b; zenon_intro zenon_H4a ]. % 0.47/0.63 generalize (zenon_H40 (relation_rng zenon_TA_cr)). zenon_intro zenon_H4a. % 0.47/0.63 exact (zenon_H4c zenon_H4a). % 0.47/0.63 cut ((element (relation_rng zenon_TA_cr) (powerset (relation_rng zenon_TA_cr))) = (element (relation_rng zenon_TA_cr) (powerset (relation_image zenon_TA_cr (relation_dom zenon_TA_cr))))). % 0.47/0.63 intro zenon_D_pnotp. % 0.47/0.63 apply zenon_H48. % 0.47/0.63 rewrite <- zenon_D_pnotp. % 0.47/0.63 exact zenon_H4b. % 0.47/0.63 cut (((powerset (relation_rng zenon_TA_cr)) = (powerset (relation_image zenon_TA_cr (relation_dom zenon_TA_cr))))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 0.47/0.63 cut (((relation_rng zenon_TA_cr) = (relation_rng zenon_TA_cr))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 0.47/0.63 congruence. % 0.47/0.63 apply zenon_H4f. apply refl_equal. % 0.47/0.63 cut (((relation_rng zenon_TA_cr) = (relation_image zenon_TA_cr (relation_dom zenon_TA_cr)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 0.47/0.63 congruence. % 0.47/0.63 apply zenon_H50. apply sym_equal. exact zenon_H43. % 0.47/0.63 exact (zenon_H44 zenon_H47). % 0.47/0.63 (* end of lemma zenon_L1_ *) % 0.47/0.63 apply NNPP. intro zenon_G. % 0.47/0.63 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H40 | zenon_intro zenon_H51 ]. % 0.47/0.63 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((finite (relation_dom A))->(finite (relation_rng A))))) zenon_G); [ zenon_intro zenon_H52; idtac ]. % 0.47/0.63 elim zenon_H52. zenon_intro zenon_TA_cr. zenon_intro zenon_H53. % 0.47/0.63 apply (zenon_notimply_s _ _ zenon_H53). zenon_intro zenon_H55. zenon_intro zenon_H54. % 0.47/0.63 apply (zenon_notimply_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H44. % 0.47/0.63 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 0.47/0.63 generalize (t146_relat_1 zenon_TA_cr). zenon_intro zenon_H59. % 0.47/0.63 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H43 ]. % 0.47/0.63 exact (zenon_H5a zenon_H58). % 0.47/0.63 generalize (t3_subset (relation_rng zenon_TA_cr)). zenon_intro zenon_H42. % 0.47/0.63 generalize (cc2_finset_1 (relation_image zenon_TA_cr (relation_dom zenon_TA_cr))). zenon_intro zenon_H5b. % 0.47/0.63 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_H41 ]. % 0.47/0.63 generalize (t17_finset_1 (relation_dom zenon_TA_cr)). zenon_intro zenon_H5d. % 0.47/0.63 generalize (zenon_H5d zenon_TA_cr). zenon_intro zenon_H5e. % 0.47/0.63 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.47/0.63 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H5a | zenon_intro zenon_H61 ]. % 0.47/0.63 exact (zenon_H5a zenon_H58). % 0.47/0.63 exact (zenon_H61 zenon_H57). % 0.47/0.63 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 0.47/0.63 exact (zenon_H63 zenon_H56). % 0.47/0.63 exact (zenon_H5c zenon_H62). % 0.47/0.63 apply (zenon_L1_ zenon_TA_cr); trivial. % 0.47/0.63 apply zenon_H51. zenon_intro zenon_Tx_dw. apply NNPP. zenon_intro zenon_H65. % 0.47/0.63 generalize (reflexivity_r1_tarski zenon_Tx_dw). zenon_intro zenon_H0. % 0.47/0.63 generalize (zenon_H0 zenon_E). zenon_intro zenon_H66. % 0.47/0.63 exact (zenon_H65 zenon_H66). % 0.47/0.63 Qed. % 0.47/0.63 % SZS output end Proof % 0.47/0.63 (* END-PROOF *) % 0.47/0.63 nodes searched: 3380 % 0.47/0.63 max branch formulas: 965 % 0.47/0.63 proof nodes created: 281 % 0.47/0.63 formulas created: 9192 % 0.47/0.63 %------------------------------------------------------------------------------