Knights, Knaves and Normals Puzzle
Your solution is correct and also seems valid, though I didn't read it that closely.
I can't resist posting a shortcut analysis.
Assume Ben normal.
Then one of Adam or Carl must be a knight, and the other a knave.
This yields a contradiction, because you can not ever have a knight and knave make the same statement.
Therefore, Ben is not normal.
Therefore, at least one of Adam or Carl must be a knave, since they have both lied about Ben.
Therefore, Ben is also not a knave, and therefore Ben must be a knight.
At this point, everything falls into place.