> Therefore enumeration puts everything achievable by humans in the NP complexity.
This is a severe misunderstanding of NP. Hindley Milner type inference is worst case doubly exponential, for example, and we solve that all the time. We just happen to rarely hit the hard instances. I think the statement you're trying to make is something more along the lines of https://en.wikipedia.org/wiki/Skolem%27s_paradox, which is definitely fascinating but doesn't have much to do with P vs NP. Notably, this paradox does not apply to higher order logics like CiC with more than one universe, which lack countable models (which is why your intuitions about provability may not apply there).
This is a severe misunderstanding of NP. Hindley Milner type inference is worst case doubly exponential, for example, and we solve that all the time. We just happen to rarely hit the hard instances. I think the statement you're trying to make is something more along the lines of https://en.wikipedia.org/wiki/Skolem%27s_paradox, which is definitely fascinating but doesn't have much to do with P vs NP. Notably, this paradox does not apply to higher order logics like CiC with more than one universe, which lack countable models (which is why your intuitions about provability may not apply there).