System sescription: The proof transformation system CERES

Abstract

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an ACNF, an LK-proof with only atomic cuts. The system CERES, an implementation of the CERES-method has been used successfully in analyzing nontrivial mathematical proofs (see 4).In this paper we describe the main features of the CERES system with special emphasis on the extraction of Herbrand sequents and simplification methods on these sequents. We demonstrate the Herbrand sequent extraction and simplification by a mathematical example. © 2010 Springer-Verlag.