System Description : The Cut - Elimination System 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. The use of resolution and the enormous size of (formalized) mathematically relevant proofs suggest an implementation able to handle rather complex cut-elimination problems. In this paper we present an implementation of CERES: the system CERES. It already implements an improvement based on an extension of LK to the calculus LKDe containing equality rules and rules for introduction of definitions which makes it easier to formalize and interpret mathematical proofs in LK. Furthermore it increases the efficiency of the cut-elimination method. The system CERES already performs well in handling quite large proofs.