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(�) (the characteristic sequent set) from a proof � of a sequent S. A refutation of CS(�) in a higher-order resolution calculus can be used to transform cut-free parts of � (the proof projections) into a cutfree proof of S. An example illustrates the method and shows that CERES ! can produce meaningful cut-free proofs in mathematics that traditional cutelimination methods cannot reach.

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