One of the critical issue in framework-based software development is a huge introduction cost caused by technical gap between developers and users of frameworks. This paper proposes a technique for deriving framework usages to implement a given requirements specification. By using the derived usages, the users can use the frameworks without understanding the framework in detail. Requirements specifications which describe definite behavioral requirements cannot be related to frameworks in as-is since the frameworks do not have definite control structure so that the users can customize them to suit given requirements specifications. To cope with this issue, a new technique based on satisfiability problems (SAT) is employed to derive the control structures of the framework model. In the proposed technique, requirements specifications and frameworks are modeled based on Labeled Transition Systems (LTSs) with branch conditions represented by predicates. Truth assignments of the branch conditions in the framework models are not given initially for representing the customizable control structure. The derivation of truth assignments of the branch conditions is regarded as the SAT by assuming relations between termination states of the requirements specification model and ones of the framework model. This derivation technique is incorporated into a technique we have proposed previously for relating actions of requirements specifications to ones of frameworks. Furthermore, this paper discuss a case study of typical use cases in e-commerce systems.