CERES in higher-order logic

We define a generalization CERES of the first-order cut-elimination method CERES to higher-order logic. At the core of CERES lies the computation of an (unsatisfiable) set of sequents CS(π) (the characteristic sequent set) from a proof π of a sequent S. A refutation of CS(π) in a higher-order resolution calculus can be used to transform cut-free parts of π (the proof projections) into a cut-free proof of S. An example illustrates the method and shows that CERES can producemeaningful cut-free proofs inmathematics that traditional cut-elimination methods cannot reach. © 2011 Elsevier B.V. All rights reserved.