| http://www.w3.org/ns/prov#value | - re 1- yes, under certain circumstances, a proof is certainly just the trace through a TM. But your example points to a diferent circumstance, SAT is an NP-complete problem, but as often presented, to show it is membership in NP, one gives a certificate of a valuation, which one then uses to verify that the SAT instance has a true valuation.
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