Discussion
What do pigeonhole formulas demonstrate?
Answer: C
The statement that n plus one objects cannot fit into n boxes is easy for a person and provably hard for resolution, requiring exponentially many steps. Solvers based on resolution therefore fail on them at modest sizes, and stronger proof systems are needed. Normal form, soundness and decidability are unaffected. A family of formulas that separates human reasoning from a particular proof system is instructive about the limits of that system rather than about difficulty in general.
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