%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET002+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 06:32:11 EDT 2022 % Result : Theorem 0.21s 0.59s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET002+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n003.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 : Mon Jul 11 02:32:14 EDT 2022 % 0.14/0.35 % CPUTime : % 0.21/0.59 (* PROOF-FOUND *) % 0.21/0.59 % SZS status Theorem % 0.21/0.59 (* BEGIN-PROOF *) % 0.21/0.59 % SZS output start Proof % 0.21/0.59 Theorem thI14 : (forall A : zenon_U, (equal_set (union A A) A)). % 0.21/0.59 Proof. % 0.21/0.59 apply NNPP. intro zenon_G. % 0.21/0.59 apply (zenon_notallex_s (fun A : zenon_U => (equal_set (union A A) A)) zenon_G); [ zenon_intro zenon_Hc; idtac ]. % 0.21/0.59 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He. % 0.21/0.59 generalize (equal_set (union zenon_TA_n zenon_TA_n)). zenon_intro zenon_Hf. % 0.21/0.59 generalize (zenon_Hf zenon_TA_n). zenon_intro zenon_H10. % 0.21/0.59 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_He; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.21/0.59 apply (zenon_notand_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.21/0.59 generalize (subset (union zenon_TA_n zenon_TA_n)). zenon_intro zenon_H16. % 0.21/0.59 generalize (zenon_H16 zenon_TA_n). zenon_intro zenon_H17. % 0.21/0.59 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 0.21/0.59 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_n zenon_TA_n))->(member X zenon_TA_n))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.21/0.59 elim zenon_H1b. zenon_intro zenon_TX_bc. zenon_intro zenon_H1d. % 0.21/0.59 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.21/0.59 generalize (union zenon_TX_bc). zenon_intro zenon_H20. % 0.21/0.59 generalize (zenon_H20 zenon_TA_n). zenon_intro zenon_H21. % 0.21/0.59 generalize (zenon_H21 zenon_TA_n). zenon_intro zenon_H22. % 0.21/0.59 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H25; zenon_intro zenon_H24 | zenon_intro zenon_H1f; zenon_intro zenon_H23 ]. % 0.21/0.59 exact (zenon_H25 zenon_H1f). % 0.21/0.59 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H26 | zenon_intro zenon_H26 ]. % 0.21/0.59 exact (zenon_H1e zenon_H26). % 0.21/0.59 exact (zenon_H1e zenon_H26). % 0.21/0.59 exact (zenon_H15 zenon_H19). % 0.21/0.59 generalize (subset zenon_TA_n). zenon_intro zenon_H27. % 0.21/0.59 generalize (zenon_H27 (union zenon_TA_n zenon_TA_n)). zenon_intro zenon_H28. % 0.21/0.59 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H14; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ]. % 0.21/0.59 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_n)->(member X (union zenon_TA_n zenon_TA_n)))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ]. % 0.21/0.59 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 0.21/0.59 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.21/0.59 generalize (union zenon_TX_bt). zenon_intro zenon_H31. % 0.21/0.59 generalize (zenon_H31 zenon_TA_n). zenon_intro zenon_H32. % 0.21/0.59 generalize (zenon_H32 zenon_TA_n). zenon_intro zenon_H33. % 0.21/0.59 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H2f; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.21/0.59 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H37. zenon_intro zenon_H37. % 0.21/0.59 exact (zenon_H37 zenon_H30). % 0.21/0.59 exact (zenon_H2f zenon_H35). % 0.21/0.59 exact (zenon_H14 zenon_H2a). % 0.21/0.59 exact (zenon_He zenon_H12). % 0.21/0.59 Qed. % 0.21/0.59 % SZS output end Proof % 0.21/0.59 (* END-PROOF *) % 0.21/0.59 nodes searched: 2243 % 0.21/0.59 max branch formulas: 680 % 0.21/0.59 proof nodes created: 127 % 0.21/0.59 formulas created: 13606 % 0.21/0.59 %------------------------------------------------------------------------------