We propose a methodology for optimal k-way partitioning with replication of directed hypergraphs via Boolean satisfiability. We begin by leveraging the power of existing and emerging SAT solvers to attack traditional logic bipartitioning and show good scaling behavior. We continue to present the first optimal partitioning results that admit generation and assignment of replicated nodes concurrently. Our framework is general enough that we also give the first published optimal results for partitioning with respect to the maximum subdomain degree metric and the sum of external degrees metric. We show that for the bipartitioning case we can feasibly solve problems of up to 150 nodes with simultaneous replication in hundreds of seconds. For other partitioning metrics, we are able to solve problems up to 40 nodes in hundreds of seconds.