Sequent-style tableaux for first-order logic: structural analysis, cut admissibility, and the correspondence with LK
We give a self-contained development of the first-order block calculus in unsigned sequent-style notation: each node of the refutation tree carries a finite block $\Pi = \Gamma \cup \neg[\Delta]$, negation is governed by explicit rules, and a branch closes on a complementary pair of literals. The calculus is Smullyan's...