%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET014+4 : TPTP v8.1.0. Released v2.2.0. % 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 06:32:24 EDT 2022 % Result : Theorem 0.47s 0.70s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET014+4 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % 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 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 10:10:00 EDT 2022 % 0.12/0.34 % CPUTime : % 0.47/0.70 (* PROOF-FOUND *) % 0.47/0.70 % SZS status Theorem % 0.47/0.70 (* BEGIN-PROOF *) % 0.47/0.70 % SZS output start Proof % 0.47/0.70 Theorem thI45 : (forall A : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (((subset X A)/\(subset Y A))<->(subset (union X Y) A))))). % 0.47/0.70 Proof. % 0.47/0.70 apply NNPP. intro zenon_G. % 0.47/0.70 apply (zenon_notallex_s (fun A : zenon_U => (forall X : zenon_U, (forall Y : zenon_U, (((subset X A)/\(subset Y A))<->(subset (union X Y) A))))) zenon_G); [ zenon_intro zenon_Hc; idtac ]. % 0.47/0.70 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He. % 0.47/0.70 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((subset X zenon_TA_n)/\(subset Y zenon_TA_n))<->(subset (union X Y) zenon_TA_n)))) zenon_He); [ zenon_intro zenon_Hf; idtac ]. % 0.47/0.70 elim zenon_Hf. zenon_intro zenon_TX_q. zenon_intro zenon_H11. % 0.47/0.70 apply (zenon_notallex_s (fun Y : zenon_U => (((subset zenon_TX_q zenon_TA_n)/\(subset Y zenon_TA_n))<->(subset (union zenon_TX_q Y) zenon_TA_n))) zenon_H11); [ zenon_intro zenon_H12; idtac ]. % 0.47/0.70 elim zenon_H12. zenon_intro zenon_TY_t. zenon_intro zenon_H14. % 0.47/0.70 apply (zenon_notequiv_s _ _ zenon_H14); [ zenon_intro zenon_H18; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_H15 ]. % 0.47/0.70 generalize (subset (union zenon_TX_q zenon_TY_t)). zenon_intro zenon_H19. % 0.47/0.70 generalize (zenon_H19 zenon_TA_n). zenon_intro zenon_H1a. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1c | zenon_intro zenon_H17; zenon_intro zenon_H1b ]. % 0.47/0.70 exact (zenon_H15 zenon_H17). % 0.47/0.70 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.47/0.70 generalize (subset zenon_TX_q). zenon_intro zenon_H1f. % 0.47/0.70 generalize (zenon_H1f zenon_TA_n). zenon_intro zenon_H20. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1e; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 0.47/0.70 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TX_q)->(member X zenon_TA_n))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.47/0.70 elim zenon_H24. zenon_intro zenon_TX_bl. zenon_intro zenon_H26. % 0.47/0.70 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.47/0.70 generalize (zenon_H1b zenon_TX_bl). zenon_intro zenon_H29. % 0.47/0.70 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.47/0.70 generalize (union zenon_TX_bl). zenon_intro zenon_H2c. % 0.47/0.70 generalize (zenon_H2c zenon_TX_q). zenon_intro zenon_H2d. % 0.47/0.70 generalize (zenon_H2d zenon_TY_t). zenon_intro zenon_H2e. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H2b; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ]. % 0.47/0.70 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.47/0.70 exact (zenon_H33 zenon_H28). % 0.47/0.70 exact (zenon_H2b zenon_H30). % 0.47/0.70 exact (zenon_H27 zenon_H2a). % 0.47/0.70 exact (zenon_H1e zenon_H22). % 0.47/0.70 generalize (subset zenon_TY_t). zenon_intro zenon_H34. % 0.47/0.70 generalize (zenon_H34 zenon_TA_n). zenon_intro zenon_H35. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H1d; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.47/0.70 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TY_t)->(member X zenon_TA_n))) zenon_H38); [ zenon_intro zenon_H39; idtac ]. % 0.47/0.70 elim zenon_H39. zenon_intro zenon_TX_cg. zenon_intro zenon_H3b. % 0.47/0.70 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.47/0.70 generalize (zenon_H1b zenon_TX_cg). zenon_intro zenon_H3e. % 0.47/0.70 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.47/0.70 generalize (union zenon_TX_cg). zenon_intro zenon_H41. % 0.47/0.70 generalize (zenon_H41 zenon_TX_q). zenon_intro zenon_H42. % 0.47/0.70 generalize (zenon_H42 zenon_TY_t). zenon_intro zenon_H43. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H40; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 0.47/0.70 apply (zenon_notor_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.47/0.70 exact (zenon_H47 zenon_H3d). % 0.47/0.70 exact (zenon_H40 zenon_H45). % 0.47/0.70 exact (zenon_H3c zenon_H3f). % 0.47/0.70 exact (zenon_H1d zenon_H37). % 0.47/0.70 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H22. zenon_intro zenon_H37. % 0.47/0.70 generalize (subset zenon_TX_q). zenon_intro zenon_H1f. % 0.47/0.70 generalize (zenon_H1f zenon_TA_n). zenon_intro zenon_H20. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1e; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 0.47/0.70 exact (zenon_H1e zenon_H22). % 0.47/0.70 generalize (subset zenon_TY_t). zenon_intro zenon_H34. % 0.47/0.70 generalize (zenon_H34 zenon_TA_n). zenon_intro zenon_H35. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H1d; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 0.47/0.70 exact (zenon_H1d zenon_H37). % 0.47/0.70 generalize (subset (union zenon_TX_q zenon_TY_t)). zenon_intro zenon_H19. % 0.47/0.70 generalize (zenon_H19 zenon_TA_n). zenon_intro zenon_H1a. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H15; zenon_intro zenon_H1c | zenon_intro zenon_H17; zenon_intro zenon_H1b ]. % 0.47/0.70 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TX_q zenon_TY_t))->(member X zenon_TA_n))) zenon_H1c); [ zenon_intro zenon_H49; idtac ]. % 0.47/0.70 elim zenon_H49. zenon_intro zenon_TX_cw. zenon_intro zenon_H4b. % 0.47/0.70 apply (zenon_notimply_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 0.47/0.70 generalize (zenon_H21 zenon_TX_cw). zenon_intro zenon_H4e. % 0.47/0.70 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 0.47/0.70 generalize (zenon_H36 zenon_TX_cw). zenon_intro zenon_H51. % 0.47/0.70 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H4f ]. % 0.47/0.70 generalize (union zenon_TX_cw). zenon_intro zenon_H53. % 0.47/0.70 generalize (zenon_H53 zenon_TX_q). zenon_intro zenon_H54. % 0.47/0.70 generalize (zenon_H54 zenon_TY_t). zenon_intro zenon_H55. % 0.47/0.70 apply (zenon_equiv_s _ _ zenon_H55); [ zenon_intro zenon_H58; zenon_intro zenon_H57 | zenon_intro zenon_H4d; zenon_intro zenon_H56 ]. % 0.47/0.70 exact (zenon_H58 zenon_H4d). % 0.47/0.70 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.47/0.70 exact (zenon_H50 zenon_H5a). % 0.47/0.70 exact (zenon_H52 zenon_H59). % 0.47/0.70 exact (zenon_H4c zenon_H4f). % 0.47/0.70 exact (zenon_H4c zenon_H4f). % 0.47/0.70 exact (zenon_H15 zenon_H17). % 0.47/0.70 Qed. % 0.47/0.70 % SZS output end Proof % 0.47/0.70 (* END-PROOF *) % 0.47/0.70 nodes searched: 8931 % 0.47/0.70 max branch formulas: 1443 % 0.47/0.70 proof nodes created: 417 % 0.47/0.70 formulas created: 57955 % 0.47/0.70 %------------------------------------------------------------------------------