%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 15:59:19 EDT 2022 % Result : Theorem 0.78s 0.94s % Output : Proof 0.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jun 19 04:25:44 EDT 2022 % 0.14/0.35 % CPUTime : % 0.78/0.94 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.78/0.94 (* PROOF-FOUND *) % 0.78/0.94 % SZS status Theorem % 0.78/0.94 (* BEGIN-PROOF *) % 0.78/0.94 % SZS output start Proof % 0.78/0.94 Theorem t20_finset_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((finite A)/\((finite B)/\(finite C)))->(finite (cartesian_product3 A B C)))))). % 0.78/0.94 Proof. % 0.78/0.94 assert (zenon_L1_ : forall (zenon_TC_ck : zenon_U) (zenon_TB_cl : zenon_U) (zenon_TA_cm : zenon_U), (~(finite (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))) -> (finite (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)) -> False). % 0.78/0.94 do 3 intro. intros zenon_H3c zenon_H3d. % 0.78/0.94 cut ((finite (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)) = (finite (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))). % 0.78/0.94 intro zenon_D_pnotp. % 0.78/0.94 apply zenon_H3c. % 0.78/0.94 rewrite <- zenon_D_pnotp. % 0.78/0.94 exact zenon_H3d. % 0.78/0.94 cut (((cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck) = (cartesian_product3 zenon_TA_cm zenon_TB_cl zenon_TC_ck))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.78/0.94 congruence. % 0.78/0.94 generalize (d3_zfmisc_1 zenon_TA_cm). zenon_intro zenon_H42. % 0.78/0.94 generalize (zenon_H42 zenon_TB_cl). zenon_intro zenon_H43. % 0.78/0.94 generalize (zenon_H43 zenon_TC_ck). zenon_intro zenon_H44. % 0.78/0.94 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~((cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck) = zenon_Vg))) _ _ zenon_H41 zenon_H44). zenon_intro zenon_H45. % 0.78/0.94 apply zenon_H45. apply refl_equal. % 0.78/0.94 (* end of lemma zenon_L1_ *) % 0.78/0.94 apply NNPP. intro zenon_G. % 0.78/0.94 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ]. % 0.78/0.94 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((finite A)/\((finite B)/\(finite C)))->(finite (cartesian_product3 A B C)))))) zenon_G); [ zenon_intro zenon_H48; idtac ]. % 0.78/0.94 elim zenon_H48. zenon_intro zenon_TA_cm. zenon_intro zenon_H49. % 0.78/0.94 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((finite zenon_TA_cm)/\((finite B)/\(finite C)))->(finite (cartesian_product3 zenon_TA_cm B C))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ]. % 0.78/0.94 elim zenon_H4a. zenon_intro zenon_TB_cl. zenon_intro zenon_H4b. % 0.78/0.94 apply (zenon_notallex_s (fun C : zenon_U => (((finite zenon_TA_cm)/\((finite zenon_TB_cl)/\(finite C)))->(finite (cartesian_product3 zenon_TA_cm zenon_TB_cl C)))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ]. % 0.78/0.94 elim zenon_H4c. zenon_intro zenon_TC_ck. zenon_intro zenon_H4d. % 0.78/0.94 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H4e. zenon_intro zenon_H3c. % 0.78/0.94 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.78/0.94 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 0.78/0.94 generalize (t3_subset (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H53. % 0.78/0.94 generalize (cc2_finset_1 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H54. % 0.78/0.94 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.78/0.94 generalize (fc14_finset_1 (cartesian_product2 zenon_TA_cm zenon_TB_cl)). zenon_intro zenon_H57. % 0.78/0.94 generalize (zenon_H57 zenon_TC_ck). zenon_intro zenon_H58. % 0.78/0.94 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H59 | zenon_intro zenon_H3d ]. % 0.78/0.94 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.78/0.94 generalize (fc14_finset_1 zenon_TA_cm). zenon_intro zenon_H5c. % 0.78/0.94 generalize (zenon_H5c zenon_TB_cl). zenon_intro zenon_H5d. % 0.78/0.94 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.78/0.94 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.78/0.94 exact (zenon_H61 zenon_H50). % 0.78/0.94 exact (zenon_H60 zenon_H52). % 0.78/0.94 exact (zenon_H5b zenon_H5e). % 0.78/0.94 exact (zenon_H5a zenon_H51). % 0.78/0.94 exact (zenon_H56 zenon_H3d). % 0.78/0.94 generalize (zenon_H55 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H62. % 0.78/0.94 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H63 | zenon_intro zenon_H3d ]. % 0.78/0.94 generalize (zenon_H53 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H64. % 0.78/0.94 apply (zenon_equiv_s _ _ zenon_H64); [ zenon_intro zenon_H63; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H65 ]. % 0.78/0.94 generalize (zenon_H46 (cartesian_product2 (cartesian_product2 zenon_TA_cm zenon_TB_cl) zenon_TC_ck)). zenon_intro zenon_H65. % 0.78/0.94 exact (zenon_H67 zenon_H65). % 0.78/0.94 exact (zenon_H63 zenon_H66). % 0.78/0.94 apply (zenon_L1_ zenon_TC_ck zenon_TB_cl zenon_TA_cm); trivial. % 0.78/0.94 apply zenon_H47. zenon_intro zenon_Tx_ea. apply NNPP. zenon_intro zenon_H69. % 0.78/0.94 generalize (reflexivity_r1_tarski zenon_Tx_ea). zenon_intro zenon_H0. % 0.78/0.94 generalize (zenon_H0 zenon_E). zenon_intro zenon_H6a. % 0.78/0.94 exact (zenon_H69 zenon_H6a). % 0.78/0.94 Qed. % 0.78/0.94 % SZS output end Proof % 0.78/0.94 (* END-PROOF *) % 0.78/0.94 nodes searched: 21148 % 0.78/0.94 max branch formulas: 5532 % 0.78/0.94 proof nodes created: 579 % 0.78/0.94 formulas created: 55585 % 0.78/0.94 %------------------------------------------------------------------------------