And if you read their argument and didn't see them prove anything.
Question:

It means their logic was so deep that you couldn't even comprehend it let alone find a rebuttal for it

You must be more specific on which anime girl, otherwise your point is invalid
If someone claims they proved you wrong but don't know where they did, did they actually prove you wrong?
I suppose not. However, I don’t necessarily know how you’re interpreting that statement.
If someone claims they proved you wrong but don't know where they did, did they actually prove you wrong?