This really doesn't prove anything since files can be deleted or moved.
That's why I always either record or take screen shots with out F3 if I'm accused.
I suggest appealing against the ban and then staff will review the evidence and make a verdict. Though remember be sincere and don't go spamming staff or go off in a rant. Just let them come to a decision. If that doesn't work re-appeal a month later.
If all these steps fail, maybe just buy a Unban!
Good luck
-sav