Tenchi the Movie 2: The Daughter of Darkness by Tetsu Kimura

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Mayuka is a girl who appears one day and claims to be Tenchi's daughter. As the initial shock wears off, everyone in the Masaki household gets used to Mayuka's presence. However, things only become more interesting as Washu tries to discover Mayuka's background. What Washu found involves demon, the Prince of Jurai, and unrequited emotions.