The murderer of the girl is the professor, and the mister is the psychologist.
And I don’t think the inspector was caught. At the end of the film, the inspector was taken away deliberately. How could such a shrewd inspector hit the professor to death in a fit of anger? He did this to let the doctor relax his vigilance, and the sentence of the inspector before he left also reminded the doctor, so when the doctor returned home, he first checked whether his wife was asleep, and then took out himself. "Collectibles".
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