We developed a formal framework for SAT solving using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL (conflict-driven clause learning) calculus is connected to a SAT solver that always terminates with correct answers. The framework offers a convenient way to prove theorems about the SAT solver and experiment with variants of the calculus. Compared with earlier verifications, the main novelties are the inclusion of the CDCL rules for forget, restart, and incremental solving and the use of refinement.