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We present GridSAT, a parallel and complete satisfiability solver designed to solve non-trivial SAT problem instances using a large number of widely distributed and heterogeneous resources. The GridSAT parallel algorithm uses intelligent backtracking, distributed and carefully scheduled sharing of learned clauses, and clause reduction. Our implementation focuses on dynamic resource acquisition and release to optimize application execution. We show how the large number of computational resources that are available from a Grid can be managed effectively for the application by an automatic scheduler and effective implementation. GridSAT execution speed is compared against the best sequential solver as rated by the SAT2002 competition using a wide variety of problem instances. The results show that GridSAT delivers speed-up for all but one of the test problem instances that are of significant size. In addition, we describe how GridSAT has solved previously unsolved satisfiability problems and the domain science contribution these results make.