Do the following sentences mean the same?
He seems to have not eaten for ages.
He does not seem to have eaten for ages.
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.