  Classically, in saturation-based proof systems, unification has been
considered atomic. However, it is also possible to move unification to the
calculus level, turning the steps of the unification algorithm into inferences.
For calculi that rely on unification procedures returning large or even
infinite sets of unifiers, integrating unification into the calculus is an
attractive method of dovetailing unification and inference. This applies, for
example, to AC-superposition and higher-order superposition. We show that
first-order superposition remains complete when moving unification rules to the
calculus level. We discuss some of the benefits this has even for standard
first-order superposition and provide an experimental evaluation.
