CERES in higher-order logic

We define a generalization CERES ω of the first-order cut-elimination method CERES to higher-order logic. At the core of CERES ω 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 ω can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.