In database applications involving sensitive data, the dual imperatives of data confidentiality and provable query processing are important. This paper introduces PoneglyphDB, a database system that leverages non-interactive zero-knowledge proofs (ZKP) to support both confidentiality and provability. Unlike traditional databases, PoneglyphDB enhances confidentiality by ensuring that raw data remains exclusively with the host, while also enabling verification of the correctness of query responses by providing proofs to clients. The main innovation in this paper is proposing efficient ZKP designs (called circuits) for basic operations in SQL query processing. These basic operation circuits are then combined to form ZKP circuits for larger, more complex queries. PoneglyphDB's circuits are carefully designed to be efficient by utilizing advances in cryptography such as PLONKish-based circuits, recursive proof composition techniques, and designs with low-order polynomial constraints. We demonstrate the performance of PoneglyphDB with the standard TPC-H benchmark. Our experimental results show that PoneglyphDB can efficiently achieve both confidentiality and provability, outperforming existing state-of-the-art ZKP methods.