  An inductive proof can be represented as a proof schema, i.e. as a
parameterized sequence of proofs defined in a primitive recursive way. A
corresponding cut-elimination method, called schematic CERES, can be used to
analyze these proofs, and to extract their (schematic) Herbrand sequents, even
though Herbrand's theorem in general does not hold for proofs with induction
inferences. This work focuses on the most crucial part of the schematic
cut-elimination method, which is to construct a refutation of a schematic
formula that represents the cut-structure of the original proof schema. We
develop a new framework for schematic substitutions and define a unification
algorithm for resolution schemata. Moreover, we show that this new formalism
allows the extraction of a structure from the refutation schema, called a
Herbrand schema, which represents its Herbrand sequent.
