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This paper introduces a novel approach for solving the Boolean satisfiability (SAT) problem by combining software and configurable hardware. The suggested technique avoids instance-specific hardware compilation and, as a result, allows the total problem solving time to be reduced compared to other approaches that have been proposed. Moreover, the technique permits problems that exceed the resources of the available reconfigurable hardware to be solved. The paper presents the results obtained with some of the DIMACS benchmarks and a comparison of our implementation with other available SAT solvers based on reconfigurable hardware. The hardware part of the satisfier was realized on Virtex XCV812E FPGA, which has a large volume of embedded memory blocks that provide direct support for the proposed approach.