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The need for representing indefinite information led to disjunctive deductive databases, which also fertilized work on disjunctive logic programming. Base on this paradigm, the DLV system has been designed and implemented as a tool for declarative knowledge representation. In this paper, we focus on the usage of DLV for solving problems in a declarative manner and report on experiments that we have run on a suite of benchmark problems. We discuss how problems can be solved in a natural way using a "Guess&Check"-paradigm where solutions are guessed and verified by parts of the program. Furthermore, we describe various front-ends that can be used for solving problems in specific applications. The experiments show that due to the ongoing implementation efforts, which include fine -tuning of the underlying algorithms, successive and significant performance improvements have been achieved during the last two years. The results indicate that DLV is capable of solving some complex problems quite efficiently.