System Description: The Proof Transformation System CERES

The original publication is available at www.springerlink.comInternational audienceCut-elimination is the most prominent form of proof trans- formation 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 resolu- tion) 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 spe- cial emphasis on the extraction of Herbrand sequents and simplification methods on these sequents. We demonstrate the Herbrand sequent ex- traction and simplification by a mathematical example

Proof Transformation by CERES

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 constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an LK-proof with only atomic cuts. In this paper we present an extension of CERES to a calculus LKDe which is stronger than the Gentzen calculus LK (it contains rules for introduction of definitions and equality rules). This extension makes it much easier to formalize mathematical proofs and increases the performance of the cut-elimination method. The system CERES already proved efficient in handling very large proofs