Implementing the First-Order Logic of Here and There

We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic proof search in the sequent calculus is optimized by using free variables and skolemization. The embedding is used in combination with sequent, tableau and connection calculi for intuitionistic first-order logic. All provers are evaluated on a large benchmark set of first-order formulas, providing a foundation for the development of more efficient HT provers.