Abstract: We designed a superposition calculus for a clausal fragment of extensional
polymorphic higher-order logic that includes anonymous functions but excludes
Booleans. The inference rules work on $\beta\eta$-equivalence classes of
$\lambda$-terms and rely on higher-order unification to achieve refutational
completeness. We implemented the calculus in the Zipperposition prover and
evaluated it on TPTP and Isabelle benchmarks. The results suggest that
superposition is a suitable basis for higher-order reasoning.