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In this paper we will present an optimized structural 01X-SAT-solver for bounded model checking of blackbox designs that exploits semantical knowledge regarding the node selection during SAT search. Experimental results show that exploiting the problem structure in this way speeds up the 01X-SAT-solver considerably. Additionally, we give a concise first-order formulation that is more expressive than using 01X-logic. This formulation leads to hard-to-solve QBF formulas for which experimental results from the QBF Evaluation 2006 are presented.