%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 2.09s 2.28s % Output : Proof 2.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.11 % Command : run_zenon %s %d % 0.11/0.32 % Computer : n029.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sat Jun 18 20:04:14 EDT 2022 % 0.11/0.32 % CPUTime : % 2.09/2.28 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 2.09/2.28 (* PROOF-FOUND *) % 2.09/2.28 % SZS status Theorem % 2.09/2.28 (* BEGIN-PROOF *) % 2.09/2.28 % SZS output start Proof % 2.09/2.28 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))))))). % 2.09/2.28 Proof. % 2.09/2.28 apply NNPP. intro zenon_G. % 2.09/2.28 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_H5 | zenon_intro zenon_H6 ]. % 2.09/2.28 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_H7; idtac ]. % 2.09/2.28 elim zenon_H7. zenon_intro zenon_TA_i. zenon_intro zenon_H9. % 2.09/2.28 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset zenon_TA_i B)/\(subset C D))->(subset (cartesian_product2 zenon_TA_i C) (cartesian_product2 B D)))))) zenon_H9); [ zenon_intro zenon_Ha; idtac ]. % 2.09/2.28 elim zenon_Ha. zenon_intro zenon_TB_l. zenon_intro zenon_Hc. % 2.09/2.28 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TA_i zenon_TB_l)/\(subset C D))->(subset (cartesian_product2 zenon_TA_i C) (cartesian_product2 zenon_TB_l D))))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 2.09/2.28 elim zenon_Hd. zenon_intro zenon_TC_o. zenon_intro zenon_Hf. % 2.09/2.28 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TA_i zenon_TB_l)/\(subset zenon_TC_o D))->(subset (cartesian_product2 zenon_TA_i zenon_TC_o) (cartesian_product2 zenon_TB_l D)))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 2.09/2.28 elim zenon_H10. zenon_intro zenon_TD_r. zenon_intro zenon_H12. % 2.09/2.28 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 2.09/2.28 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 2.09/2.28 generalize (t118_zfmisc_1 zenon_TC_o). zenon_intro zenon_H17. % 2.09/2.28 generalize (zenon_H17 zenon_TD_r). zenon_intro zenon_H18. % 2.09/2.28 generalize (zenon_H18 zenon_TB_l). zenon_intro zenon_H19. % 2.09/2.28 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 2.09/2.28 exact (zenon_H1b zenon_H15). % 2.09/2.28 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 2.09/2.28 elim (classic ((~((cartesian_product2 zenon_TA_i zenon_TC_o) = (cartesian_product2 zenon_TB_l zenon_TC_o)))/\(~(subset (cartesian_product2 zenon_TA_i zenon_TC_o) (cartesian_product2 zenon_TB_l zenon_TC_o))))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 2.09/2.28 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 2.09/2.28 generalize (t118_zfmisc_1 zenon_TA_i). zenon_intro zenon_H22. % 2.09/2.28 generalize (zenon_H22 zenon_TB_l). zenon_intro zenon_H23. % 2.09/2.28 generalize (zenon_H23 zenon_TC_o). zenon_intro zenon_H24. % 2.09/2.28 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 2.09/2.28 exact (zenon_H26 zenon_H16). % 2.09/2.28 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 2.09/2.28 exact (zenon_H20 zenon_H28). % 2.09/2.28 cut ((subset (cartesian_product2 zenon_TB_l zenon_TC_o) (cartesian_product2 zenon_TB_l zenon_TD_r)) = (subset (cartesian_product2 zenon_TA_i zenon_TC_o) (cartesian_product2 zenon_TB_l zenon_TD_r))). % 2.09/2.28 intro zenon_D_pnotp. % 2.09/2.28 apply zenon_H13. % 2.09/2.28 rewrite <- zenon_D_pnotp. % 2.09/2.28 exact zenon_H1c. % 2.09/2.28 cut (((cartesian_product2 zenon_TB_l zenon_TD_r) = (cartesian_product2 zenon_TB_l zenon_TD_r))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 2.09/2.28 cut (((cartesian_product2 zenon_TB_l zenon_TC_o) = (cartesian_product2 zenon_TA_i zenon_TC_o))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 2.09/2.28 congruence. % 2.09/2.28 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 2.09/2.28 apply zenon_H2c. zenon_intro zenon_H2d. % 2.09/2.28 elim (classic ((cartesian_product2 zenon_TA_i zenon_TC_o) = (cartesian_product2 zenon_TA_i zenon_TC_o))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 2.09/2.28 cut (((cartesian_product2 zenon_TA_i zenon_TC_o) = (cartesian_product2 zenon_TA_i zenon_TC_o)) = ((cartesian_product2 zenon_TB_l zenon_TC_o) = (cartesian_product2 zenon_TA_i zenon_TC_o))). % 2.09/2.28 intro zenon_D_pnotp. % 2.09/2.28 apply zenon_H2a. % 2.09/2.28 rewrite <- zenon_D_pnotp. % 2.09/2.28 exact zenon_H2e. % 2.09/2.28 cut (((cartesian_product2 zenon_TA_i zenon_TC_o) = (cartesian_product2 zenon_TA_i zenon_TC_o))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 2.09/2.28 cut (((cartesian_product2 zenon_TA_i zenon_TC_o) = (cartesian_product2 zenon_TB_l zenon_TC_o))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 2.09/2.28 congruence. % 2.09/2.28 exact (zenon_H21 zenon_H2d). % 2.09/2.28 apply zenon_H2f. apply refl_equal. % 2.09/2.28 apply zenon_H2f. apply refl_equal. % 2.09/2.28 apply zenon_H2b. zenon_intro zenon_H28. % 2.09/2.28 generalize (zenon_H5 (cartesian_product2 zenon_TA_i zenon_TC_o)). zenon_intro zenon_H30. % 2.09/2.28 generalize (zenon_H30 (cartesian_product2 zenon_TB_l zenon_TC_o)). zenon_intro zenon_H31. % 2.09/2.28 generalize (zenon_H31 (cartesian_product2 zenon_TB_l zenon_TD_r)). zenon_intro zenon_H32. % 2.09/2.28 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H20 | zenon_intro zenon_H33 ]. % 2.09/2.28 exact (zenon_H20 zenon_H28). % 2.09/2.28 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 2.09/2.28 exact (zenon_H35 zenon_H1c). % 2.09/2.28 exact (zenon_H13 zenon_H34). % 2.09/2.28 apply zenon_H29. apply refl_equal. % 2.09/2.28 apply zenon_H6. zenon_intro zenon_Tx_cc. apply NNPP. zenon_intro zenon_H37. % 2.09/2.28 apply zenon_H37. zenon_intro zenon_Ty_ce. apply NNPP. zenon_intro zenon_H39. % 2.09/2.28 apply zenon_H39. zenon_intro zenon_Tz_cg. apply NNPP. zenon_intro zenon_H3b. % 2.09/2.28 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 2.09/2.28 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 2.09/2.28 generalize (t1_xboole_1 zenon_Tx_cc). zenon_intro zenon_H40. % 2.09/2.28 generalize (zenon_H40 zenon_Ty_ce). zenon_intro zenon_H41. % 2.09/2.28 generalize (zenon_H41 zenon_Tz_cg). zenon_intro zenon_H42. % 2.09/2.28 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 2.09/2.28 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 2.09/2.28 exact (zenon_H46 zenon_H3d). % 2.09/2.28 exact (zenon_H45 zenon_H3f). % 2.09/2.28 exact (zenon_H3e zenon_H43). % 2.09/2.28 Qed. % 2.09/2.28 % SZS output end Proof % 2.09/2.28 (* END-PROOF *) % 2.09/2.28 nodes searched: 337299 % 2.09/2.28 max branch formulas: 2539 % 2.09/2.28 proof nodes created: 923 % 2.09/2.28 formulas created: 96560 % 2.09/2.28 %------------------------------------------------------------------------------