Cut-elimination and redundancy-elimination by resolution
Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
CERES: An analysis of Fürstenberg's proof of the infinity of primes
Theoretical Computer Science
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
A Clausal Approach to Proof Analysis in Second-Order Logic
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Towards a clausal analysis of cut-elimination
Journal of Symbolic Computation
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Project presentation: algorithmic structuring and compression of proofs (ASCOP)
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
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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.