You're confusing logic with epistemology in the context of legal proceedings and life in general. Epistemically, I prove there's no elephant in my room now bec

You're confusing logic with epistemology in the context of legal proceedings and life in general. Epistemically, I prove there's no elephant in my room now because elephants can't be invisible, because I would feel it or hear it or smell it, etc. You can posit an endless number of additional premises to show that there may still be an elephant in the room, but you end up in logical paradox where any evidence of the elephant being present is inaccessible. At that point, what does it mean to say "there's an elephant in here with me that is completely undetectable, so lack of detection is not evidence of absence?" In terms of epistemology, "proof" means reaching sufficient justification for considering a belief to be true, not validity according to an axiomatic system.