Decidability problems for the prenex fragment of intuitionistic logic

We develop a constraint-based technique which allows one to prove decidability and complexity results for sequent calculi. Specifically, we study decidability problems for the prenex fragment of intuitionistic logic. We introduce an analogue of Skolemization for intuitionistic logic with equality, prove PSPACE-completeness of two fragments of intuitionistic logic with and without equality and some other results. In the proofs, we use a combination of techniques of constraint satisfaction, loop-free sequent systems of intuitionistic logic and properties of simultaneous rigid E-unification.