Discussion
What follows from a proof complexity lower bound for a proof system?
Answer: D
A lower bound on proof length applies however cleverly the search is directed, so it bounds the whole family of algorithms based on that system. Stronger systems may have short proofs of the same formulas. Soundness and universal hardness do not follow. A result that rules out an entire class of approaches, rather than a particular implementation, is worth knowing before effort is spent optimising within that class.
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