We are dealing with solving difficult SAT instances in this paper. We propose a method for preprocessing SAT instances (CNF formulas) by using consistency techniques known from constraint programming methodology and by using our own consistency technique based on clique decomposition of a graph representing conflicts in the input formula. The clique decomposition allows us to make a strong reasoning over the SAT instance, which even in some cases decides the SAT instance itself without search.

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... e implemented our preprocessing method in C++ and compared it with several state-of-the-art SAT solvers on the selected difficult SAT instances. The result of application of our method was speedup in orders of magnitudes compared to the tested SAT solvers.