Ever since computers have been used to support human designers, a variety of representations have been used to encapsulate engineering knowledge. Computational design synthesis (CDS) approaches utilize this knowledge to generate design candidates for a specified task. However, new approaches are required to enable systematic solution space exploration. This paper presents an approach that combines a graph-based object-oriented knowledge representation with first-order logic and Boolean satisfiability. This combination is used as the foundation for a generic automated approach for requirement-driven computational design synthesis. Available design building blocks and a design task defined through a set of requirements are modeled in a graph-based environment and then automatically transferred into a Boolean satisfiability problem and solved, considering a given solution size. The Boolean solution is automatically transferred back to the graph-based domain. The method is validated through two case studies: synthesis of automotive powertrains and chemical process synthesis for ethyl alcohol production. The contribution of the paper is a new method that is able to determine if an engineering task is solvable for a given set of synthesis building blocks and enables systematic solution space exploration.