The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional ordered resolution prover and establish its soundness and refutational completeness. Methodologically, we apply stepwise refinement to obtain, from an abstract specification of a nondeterministic prover, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for first-order logic.