This paper presents a semi-automated formal verification method based on the famous SVO logic, and discusses its experimental results. We discuss several problems on automating the SVO logic and design its derivative, ASVO logic for automation. Also the proposed method is implemented by the Isabelle/Isar system. As a result, we verified the well-known weakness of the NSSK protocol that is vulnerable to the Denning-Sacco attack, using our Isabelle/ASVO system. Finally, we refined the protocol by following the logical consequence of the ASVO verification.