  Urban and Bierman introduced a calculus of proof terms for the sequent
calculus LK with a strongly normalizing reduction relation. We extend this
calculus to simply-typed higher-order logic with inferences for induction and
equality, albeit without strong normalization. We implement thiscalculus in
GAPT, our library for proof transformations. Evaluating the normalization on
both artificial and real-world benchmarks, we show that this algorithm is
typically several orders of magnitude faster than the existing Gentzen-like
cut-reduction, and an order of magnitude faster than any other cut-elimination
procedure implemented in GAPT.
