The best way to make someone admit they are lying is catching them during the event they lied about.
Plus, you made it worse, because you said you have seen it with your own eyes, that's where 99 % of misunderstandings starts. So many times what you see is not what it really looks like. Be careful about your judgement. Just saying, don't let the ending shame be for you, make sure then claim or get rough.
There's one thin line between being a cop & criminal. One bad judgment call.