  G\"odel logic with the projection operator Delta (G_Delta) is an important
many-valued as well as intermediate logic. In contrast to classical logic, the
validity and the satisfiability problems of G_Delta are not directly dual to
each other. We nevertheless provide a uniform, computational treatment of both
problems for prenex formulas by describing appropriate translations into sets
of order clauses that can be subjected to chaining resolution. For validity a
version of Herbrand's Theorem allows us to show the soundness of standard
Skolemization. For satisfiability the translation involves a novel, extended
Skolemization method.
