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Nah, P vs NP is a bigger factor here.

Basically, checking a proof for correctness takes polynomial time in the size of the proof. (Dependending on how you formalize your proofs, that might even be linear.)

Coming up with a reasonable sized proof is much harder. But if we had P=NP, then checking and finding a proof would be about equally hard.

See eg http://www.scottaaronson.com/papers/philos.pdf

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