Can a theorem determine its own complexity?

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Much how Gödel spoke of the Incompleteness Theorems, can a theorem determine its own complexity?

Namely, I haven't seen a concise proof of the following that is not possible to determine in the language of logic (Kolmogorov Complexity); yet, to state this mathematically I am unable to do at the moment:

Can it be positively proven when the proof of the theorem is irreducibly complex up to the least amount of computational steps required for a theorem's proof to Q.E.D.