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Say you wanted to let a computer search for a proof of P!=NP - which axioms would you start with and which rules to transform the axioms into additional valid statements?

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I wonder if the algorithm to search such a space of axioms and transforms for a solution would itself be P or NP. :)

Almost certainly so super-exponential that NP appears easy in comparison.

As far was most mathematicians and computer scientists would go, ZF and predicate logic together with a fixed definition of turing machines.

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