Unsound Inferences Make Proofs Shorter
  We give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are non-elementarily shorter than LK-proofs. 
Juan P. Aguilera and Matthias Baaz
math.LO cs.LO