Automated theorem provers use search strategies. Unfortunately, no strategy is uniformly successful on all problems. This motivates us to spend the available resources in terms of processors and time on different strategies. In this paper, we develop the basic concept of the complementarity of strategy sets. The problems of the initial strategy selection are discussed in detail. The paper also contains a short description of an implementation of a strategy parallel theorem prover (p-SETHEO) and an experimental evaluation of the schedule selection algorithm.