In any circumstance is useless to prove if you didn't cheat if the account was used to cheat.

VAC bans are permanent, non-negotiable, and cannot be removed by Steam Support. If a VAC ban is determined to have been issued incorrectly, it will automatically be removed(that's not your case).

VAC is automated software that bans for the detection of known cheats on either your account or an account linked to yours via mobile number or game library.

VAC bans are delayed from the time of the detection to the time that the ban is actually applied. What you were doing when the ban was applied, is irrelevant.

Keep enjoying your VACation!