%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 15:59:56 EDT 2022 % Result : Theorem 2.00s 2.25s % Output : Proof 2.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n003.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 : Sun Jun 19 07:10:58 EDT 2022 % 0.12/0.33 % CPUTime : % 2.00/2.25 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 2.00/2.25 (* PROOF-FOUND *) % 2.00/2.25 % SZS status Theorem % 2.00/2.25 (* BEGIN-PROOF *) % 2.00/2.25 % SZS output start Proof % 2.00/2.25 Theorem t119_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset A B)/\(subset C D))->(subset (cartesian_product2 A C) (cartesian_product2 B D))))))). % 2.00/2.25 Proof. % 2.00/2.25 apply NNPP. intro zenon_G. % 2.00/2.25 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((subset x y)->((subset y z)->(subset x z))))))); [ zenon_intro zenon_H6 | zenon_intro zenon_H7 ]. % 2.00/2.25 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset A B)/\(subset C D))->(subset (cartesian_product2 A C) (cartesian_product2 B D))))))) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 2.00/2.25 elim zenon_H8. zenon_intro zenon_TA_j. zenon_intro zenon_Ha. % 2.00/2.25 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset zenon_TA_j B)/\(subset C D))->(subset (cartesian_product2 zenon_TA_j C) (cartesian_product2 B D)))))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ]. % 2.00/2.25 elim zenon_Hb. zenon_intro zenon_TB_m. zenon_intro zenon_Hd. % 2.00/2.25 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TA_j zenon_TB_m)/\(subset C D))->(subset (cartesian_product2 zenon_TA_j C) (cartesian_product2 zenon_TB_m D))))) zenon_Hd); [ zenon_intro zenon_He; idtac ]. % 2.00/2.25 elim zenon_He. zenon_intro zenon_TC_p. zenon_intro zenon_H10. % 2.00/2.25 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TA_j zenon_TB_m)/\(subset zenon_TC_p D))->(subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m D)))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 2.00/2.25 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13. % 2.00/2.25 apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 2.00/2.25 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 2.00/2.25 generalize (t118_zfmisc_1 zenon_TC_p). zenon_intro zenon_H18. % 2.00/2.25 generalize (zenon_H18 zenon_TD_s). zenon_intro zenon_H19. % 2.00/2.25 generalize (zenon_H19 zenon_TB_m). zenon_intro zenon_H1a. % 2.00/2.25 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 2.00/2.25 exact (zenon_H1c zenon_H16). % 2.00/2.25 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 2.00/2.25 elim (classic ((~((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TB_m zenon_TC_p)))/\(~(subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TC_p))))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 2.00/2.25 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 2.00/2.25 generalize (t118_zfmisc_1 zenon_TA_j). zenon_intro zenon_H23. % 2.00/2.25 generalize (zenon_H23 zenon_TB_m). zenon_intro zenon_H24. % 2.00/2.25 generalize (zenon_H24 zenon_TC_p). zenon_intro zenon_H25. % 2.00/2.25 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 2.00/2.25 exact (zenon_H27 zenon_H17). % 2.00/2.25 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28. % 2.00/2.25 exact (zenon_H21 zenon_H29). % 2.00/2.25 cut ((subset (cartesian_product2 zenon_TB_m zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TD_s)) = (subset (cartesian_product2 zenon_TA_j zenon_TC_p) (cartesian_product2 zenon_TB_m zenon_TD_s))). % 2.00/2.25 intro zenon_D_pnotp. % 2.00/2.25 apply zenon_H14. % 2.00/2.25 rewrite <- zenon_D_pnotp. % 2.00/2.25 exact zenon_H1d. % 2.00/2.25 cut (((cartesian_product2 zenon_TB_m zenon_TD_s) = (cartesian_product2 zenon_TB_m zenon_TD_s))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 2.00/2.25 cut (((cartesian_product2 zenon_TB_m zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 2.00/2.25 congruence. % 2.00/2.25 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.00/2.25 apply zenon_H2d. zenon_intro zenon_H2e. % 2.00/2.25 elim (classic ((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 2.00/2.25 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p)) = ((cartesian_product2 zenon_TB_m zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))). % 2.09/2.26 intro zenon_D_pnotp. % 2.09/2.26 apply zenon_H2b. % 2.09/2.26 rewrite <- zenon_D_pnotp. % 2.09/2.26 exact zenon_H2f. % 2.09/2.26 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TA_j zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 2.09/2.26 cut (((cartesian_product2 zenon_TA_j zenon_TC_p) = (cartesian_product2 zenon_TB_m zenon_TC_p))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 2.09/2.26 congruence. % 2.09/2.26 exact (zenon_H22 zenon_H2e). % 2.09/2.26 apply zenon_H30. apply refl_equal. % 2.09/2.26 apply zenon_H30. apply refl_equal. % 2.09/2.26 apply zenon_H2c. zenon_intro zenon_H29. % 2.09/2.26 generalize (zenon_H6 (cartesian_product2 zenon_TA_j zenon_TC_p)). zenon_intro zenon_H31. % 2.09/2.26 generalize (zenon_H31 (cartesian_product2 zenon_TB_m zenon_TC_p)). zenon_intro zenon_H32. % 2.09/2.26 generalize (zenon_H32 (cartesian_product2 zenon_TB_m zenon_TD_s)). zenon_intro zenon_H33. % 2.09/2.26 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H21 | zenon_intro zenon_H34 ]. % 2.09/2.26 exact (zenon_H21 zenon_H29). % 2.09/2.26 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 2.09/2.26 exact (zenon_H36 zenon_H1d). % 2.09/2.26 exact (zenon_H14 zenon_H35). % 2.09/2.26 apply zenon_H2a. apply refl_equal. % 2.09/2.26 apply zenon_H7. zenon_intro zenon_Tx_cd. apply NNPP. zenon_intro zenon_H38. % 2.09/2.26 apply zenon_H38. zenon_intro zenon_Ty_cf. apply NNPP. zenon_intro zenon_H3a. % 2.09/2.26 apply zenon_H3a. zenon_intro zenon_Tz_ch. apply NNPP. zenon_intro zenon_H3c. % 2.09/2.26 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 2.09/2.26 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 2.09/2.26 generalize (t1_xboole_1 zenon_Tx_cd). zenon_intro zenon_H41. % 2.09/2.26 generalize (zenon_H41 zenon_Ty_cf). zenon_intro zenon_H42. % 2.09/2.26 generalize (zenon_H42 zenon_Tz_ch). zenon_intro zenon_H43. % 2.09/2.26 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 2.09/2.26 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 2.09/2.26 exact (zenon_H47 zenon_H3e). % 2.09/2.26 exact (zenon_H46 zenon_H40). % 2.09/2.26 exact (zenon_H3f zenon_H44). % 2.09/2.26 Qed. % 2.09/2.26 % SZS output end Proof % 2.09/2.26 (* END-PROOF *) % 2.09/2.26 nodes searched: 337301 % 2.09/2.26 max branch formulas: 2544 % 2.09/2.26 proof nodes created: 923 % 2.09/2.26 formulas created: 96038 % 2.09/2.26 %------------------------------------------------------------------------------