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You discover truth by doing stuff in real world and observing the results. Current LLM have enough intelligence, but all the inputs they have are the “he said she said” by us monkeys, including all omissions and biases.

But many humans can't do a lot of those things and we still consider them "generally intelligent"

None of what you describe would I label within the realm of 'average'

It's not about what the average human can do - it's about what humans as a category are capable of. There will always be outliers (in both directions), but you can, in general, teach a human a variety of tasks, such as performing arithmetic deterministically, that you cannot teach to, for example, a parrot.