Rules have already been provided.
Let me just add common sense;
When you see 7 identical twin moving in perfect sync, you
know it's an illusion. That doesn't tell you which one is the real wizard!
When the PC told you he wanted to disbelieve you should have just done

and told him he can't do that because it made no sense. If he starts quoting rules, tell him you'll look into that after the session.
Use common sense when making call on the fly, read the rules carefully after the game and decide how you'll handle the situation from then on. A lot of players, consciously or not, regularly come up with plausible yet wrong interpretation of the rules that always seem to favor their PC (no kidding). Don't ever let them pull one of those
during the session. Look over the rule with them afterward.
In the same vein, not long ago I had a rogue player say he was going to take a -20 to his Hide check to sneak attack a giant but remain hidden. This wasn't even an interpretation but it came from a splat book I hadn't read yet. I told him no, if he wanted to do that he should have talked to me about this tactic
before the game. Never get bullied by rule lawyers.