%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 06:33:45 EDT 2022 % Result : Theorem 0.15s 0.48s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.02/0.11 % Command : run_zenon %s %d % 0.11/0.31 % Computer : n004.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 600 % 0.11/0.31 % DateTime : Sun Jul 10 10:49:52 EDT 2022 % 0.11/0.31 % CPUTime : % 0.15/0.48 (* PROOF-FOUND *) % 0.15/0.48 % SZS status Theorem % 0.15/0.48 (* BEGIN-PROOF *) % 0.15/0.48 % SZS output start Proof % 0.15/0.48 Theorem member_of_substitution : (forall X : zenon_U, (exists U : zenon_U, (((member U (universal_class))/\(X = (singleton U)))\/((~(exists Y : zenon_U, ((member Y (universal_class))/\(X = (singleton Y)))))/\(U = X))))). % 0.15/0.48 Proof. % 0.15/0.48 apply NNPP. intro zenon_G. % 0.15/0.48 apply (zenon_notallex_s (fun X : zenon_U => (exists U : zenon_U, (((member U (universal_class))/\(X = (singleton U)))\/((~(exists Y : zenon_U, ((member Y (universal_class))/\(X = (singleton Y)))))/\(U = X))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.15/0.48 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 0.15/0.48 apply zenon_H2e. exists zenon_TX_bt. apply NNPP. zenon_intro zenon_H2f. % 0.15/0.48 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 0.15/0.48 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.15/0.48 apply zenon_H33. zenon_intro zenon_H34. % 0.15/0.48 elim zenon_H34. zenon_intro zenon_TY_cb. zenon_intro zenon_H36. % 0.15/0.48 apply zenon_H2e. exists zenon_TY_cb. apply NNPP. zenon_intro zenon_H37. % 0.15/0.48 apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.15/0.48 exact (zenon_H39 zenon_H36). % 0.15/0.48 apply zenon_H32. apply refl_equal. % 0.15/0.48 Qed. % 0.15/0.48 % SZS output end Proof % 0.15/0.48 (* END-PROOF *) % 0.15/0.48 nodes searched: 640 % 0.15/0.48 max branch formulas: 556 % 0.15/0.48 proof nodes created: 22 % 0.15/0.48 formulas created: 6395 % 0.15/0.48 %------------------------------------------------------------------------------