We consider the following problem: Given a proof of the Skolemization of a formula F, what is the length of the shortest proof of F? For the restriction of this question to cut-free proofs we prove corresponding exponential upper and lower bounds.
"On the complexity of proof deskolemization." J. Symbolic Logic 77 (2) 669 - 686, June 2012. https://doi.org/10.2178/jsl/1333566645