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Formal proofs of interesting mathematical theorems are usually too
large and full of trivial structural information, and hence hard to
understand and analyze. Techniques to extract specific essential
information from these proofs are needed. This book describes four
algorithms to extract a Herbrand sequent of the end-sequent of
proofs written in Gentzen's Sequent Calculus LK for classical
First-Order Logic. Within this calculus, we define a Herbrand
sequent as a generalization of Herbrand disjunction, and its
extraction can be used to summarize the creative information of a
formal proof, which lies on the instantiations chosen for the
quantifiers. One of these algorithms has been implemented in CERes
(Cut-Elimination by Resolution), an automated system for proof
transformations and analysis.
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