How to tell the truth from a hundred thousand cold jokes?

The question is: do you think another princess will say that you are fake or true?

Suppose 1, in the morning:

The real princess replied: false.

The fake princess replied: Really.

Scene 2, afternoon:

The real princess replied: false.

The fake princess replied: Really.

That is to say, whether in the morning or afternoon, the real princess can only answer "false" and the false princess can only answer "true", so that true and false princess can be distinguished.

Extended data:

If a proposition is the original proposition, the proposition that is mutually negative with it is the negative proposition of the original proposition. The original proposition and the negative proposition are equivalent propositions. If the original proposition holds, the negative proposition holds. Inverse proposition and negative proposition are equivalent propositions. If the inverse proposition holds, the negative proposition holds.

Proposition and negative proposition are equivalent, that is, if the proposition is true, then the negative proposition is also true. The equivalence between a proposition and its negative proposition exists as an axiom, and you can neither prove it right nor prove it wrong. In fact, this thing can be regarded as an axiom. It is equivalent to the axiom "law of contradiction". Our mathematical system is based on these axioms.