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Constraint-based program synthesis techniques have been widely used in numerous settings. However, synthesizing programs that use libraries remains a major challenge. To handle complex or black-box libraries, the state of the art is to provide carefully crafted mocks or models to the synthesizer, requiring extra manual work. We address this challenge by proposing TOSHOKAN, a new synthesis framework as an alternative approach in which library-using programs can be generated without any user-provided artifacts at the cost of moderate performance overhead. The framework extends the classic counterexample-guided synthesis framework with a bootstrapping, log-based library model. The model collects input-output samples from running failed candidate programs on witness inputs. We prove that the framework is sound when a sound, bounded verifier is available, and also complete if the underlying synthesizer and verifier promise to produce minimal outputs. We implement and incorporate the framework to JSKETCH, a Java sketching tool. Experiments show that TOSHOKAN can successfully synthesize programs that use a variety of libraries, ranging from mathematical functions to data structures. Comparing to state-of-the-art synthesis algorithms which use mocks or models, TOSHOKAN reduces up to 159 lines of code of required manual inputs, at the cost of less than 40s of performance overheads.