Why doesn't Godel's Second Incompleteness Theorem rule out a formalizable proof of P!=NP? – cs.stackexchange.com

Why doesn't Godel's Second Incompleteness Theorem rule out a formalizable proof of P!=NP? – cs.stackexchange.com

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I'm sure there must be something wrong with the following reasoning because otherwise a lot of P vs. NP research would be curtailed but I cannot determine my error: For any fixed integer $k>0$ ...

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