A "fierce clash of wits"? The author
might be writing cheques they can't cash here...

Ah well, whatever.
it's already obvious she's intellectually inferior to MC in every way, so it's
definitely not 'fierce clash' , not just 'might' :
can't trick him with her fake persona in chapter 1
ranked lower than MC, even though he was late so wasn't able to personally experience when the crime happened
can't keep even a little composure at her loss
assumed the grandson of the freaking crime king, lived a 'normal life' for no reason
she needed to accuse MC of cheating, challenge him (setting herself for obvious embarrassment),
and mock his bloodline, shattering her fake persona in chapter 1 to everyone else (if they weren't stupid), instead of
just asking him for his answer
and next chapter just makes it more obvious how outclassed she is.