Souya Kuroi has dreams of people with superpowers fighting a massive dragon in the sky, but his real life is almost as weird. He's had amnesia for about two weeks and been taken in by a maid and an anthropomorphic cat. When a UFO in the shape of a stuffed bear approaches Sorimasaka City and other metros around the world, he's startled to see seven rainbow-sparkling heroes zoom out to confront it – just like in his dream. Even weirder, the maid wants him to leave his shelter to confront these heroes and take the source of their power. 

(Source: Anime News Network)

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The world is under attack, from huge unidentified floating objects. The first attempts to stop them have been unsuccessful, some soldiers have deserted to go home to enjoy their family time.
 
7 heroes show up to fight the unknown threat. They fly up in the sky in a glow of light while they are enveloped in big robot frames.
 
Is this the time for Souya to join the heroes in a fight for humanity?
No, apparently he has to fight off the heroes.

Judgment Nezuya