Do the following sentences mean the same?
He seems to have not eaten for ages.
He does not seem to have eaten for ages.
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To me the first implies there exists evidence that no eating has taken place: He is extremely skinny, showing the signs of starvation and malnurishment, etc.
The second implies that there is lack of evidence of him eating: There is no food in the fridge, no dirty dishes, no crumbs, no food scraps in the trash, etc.
Logically both come to the same conclusion with a slightly different nuance.