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Boolean matching is one of the enabling techniques for technology mapping and logic resynthesis of field-programmable gate arrays (FPGAs). Boolean satisfiability (SAT)-based Boolean matching (SAT-BM) has been proposed, but computational complexity prohibits its practical deployment. In this paper, we leverage symmetries present in both Boolean functions and target FPGA architectures to prune the solution space, and we also propose some techniques to reduce the replication runtime for SAT instance generation using the incremental SAT reasoning engine. Experiment shows that our SAT-BM reduces runtime by 226times compared with the original SAT-BM algorithm, making SAT-BM more practical.