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This cool result relies on an amazing algorithm that was discovered last year: the Cook-Mertz tree evaluation procedure.

See [0] for an exposition, or [1] for a recent popular article about it.

Wait, it's the same Cook who proved that SAT is NP-complete somewhere during the cold war? I had no idea this guy was still around doing research.

It's not the same Cook, but rather his son.

That's almost equally awesome