On the non-confluence of cut-elimination

Westudy cut-elimination in first-order classical logic. Weconstruct a sequenceof polynomiallength proofs having a non-elementary number of different cut-free normal forms. These normal forms are different in a strong sense: they not only represent different Herbrand-disjunctions but also differ in their propositional structure. This result illustrates that the constructive content of a proof in classical logic is not uniquely determined but rather depends on the chosen method for extracting it. §