System Description: The Proof Transformation System CERES

Abstract : Cut-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.
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Jürgen Giesl and Reiner Hähnle. International Joint Conference on Automated Reasoning, Jul 2010, Edinburgh, United Kingdom. Springer, 6173, pp.427-433, 2010, Lecture Notes in Computer Science / Lecture Notes in ArtificiaI Intelligence. 〈10.1007/978-3-642-14203-1_36〉
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Tsvetan Dunchev, Alexander Leitsch, Tomer Libal, Daniel Weller, Bruno Woltzenlogel Paleo. System Description: The Proof Transformation System CERES. Jürgen Giesl and Reiner Hähnle. International Joint Conference on Automated Reasoning, Jul 2010, Edinburgh, United Kingdom. Springer, 6173, pp.427-433, 2010, Lecture Notes in Computer Science / Lecture Notes in ArtificiaI Intelligence. 〈10.1007/978-3-642-14203-1_36〉. 〈hal-00545482〉

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