Short proofs with simple arithmetic?

I can PROVE it, but it may take time."

There's a simple 2-player game based on simple arithmetic, and one
coach knows that her player can always win. She even tells him what
strategy to use. The player suspects the coach of ulterior motives,
and isn't convinced the strategy really works. How quickly can she
convince him?

This talk describes cutting planes proofs for Quantified Boolean
Formulas, and a lower bound technique.