>>12220464"Which door would the other say is the right door?"
Assume one stands before door A (the correct door), and the other before door B (the incorrect door).
Knowing Aqua is delusional and Shion is contradictory, Shion would say that Aqua would say that door A is the correct door. This is because Aqua's answer is always incorrect, so she would always choose the wrong door, and Shion's is equally incorrect in response to it, thus negating the incorrectness.
Likewise, because Aqua is delusional, even though Shion's contradictary response would mean that directly asking her would have her tell you door B is the correct door, since Aqua already chose door B, she would assume that Shion would choose door A so that they could be a matching pair.
Thus, to uncover the truth when two stories are told, you only need ask them what the other is thinking.