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Herbrand-Confluence for Cut Elimination in Classical First Order Logic Hetzl, Stefan Straßburger, Lutz proof theory first-order logic tree languages term rewriting semantics of proofs We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and mathematically more realistic) look at cut-free proofs. We analyze which witnesses they choose for which quantifiers, or in other words: we only consider the Herbrand-disjunction of a cut-free proof. Our main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Stefan Hetzl and Lutz Straßburger 2012 Is Part Of LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2012.320 urn:nbn:de:0030-drops-36815 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.320 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode