What is “liar, liar pants on fire” in latin?

What we’re actually looking for is a Latin proverbial expression that means what the English means. And the English has nothing to do with inflammable pants at all: it just says “Hah! caught you lying!”

I noodled around latin Via Proverbs. The closest I get are:

Mendacem memorem esse oportet.
A liar should have a good memory.
(Quintilian, Institutio Oratoria 4.2.91)

Because if you don’t remember what you lied about, you won’t be able to keep your story straight. And when you get found out, then it’s Liar Liar Pants On Fire.

Or maybe:

Mendacia curta semper habent crura.
Lies always have short legs.
(Mediaeval proverb)

Meaning, lies can’t run far: they’ll get found out eventually.