## Section: New Results

### Herbrand Confluence

Participants : Stefan Hetzl, Lutz Straßburger.

It is well-known that cut-elimination in the sequent calculus for classical first-order logic is in its most general form, is neither confluent nor strongly normalizing. But if one takes a coarser (and mathematically more realistic) look at cut-free proofs, one can analyze which witnesses they choose for which quantifiers, or in other words: one can only consider the Herbrand-disjunction of a cut-free proof. This yields a surprising confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing cut reduction lead to the same Herbrand-disjunction. This result has been presented at CSL 2012 [25] .