BLACK ROCK SHOOTER DAWN FALL

It is the year 2062, two decades after the failure of a massive workforce automation project. However, Artemis, the artificial intelligence at the core of that project, had decided to attack humanity, and the resulting war laid waste to Earth. A lone girl, Empress, wakes up in an underground laboratory at a base. She is one of three surviving guardians of humanity. However, she has no memories of what came before. All she knows is what a colonel of the peace-building force tells her. Artemis is constructing a space elevator to link the Moon and Earth, and Empress is ordered to destroy the space elevator before its completion. If the elevator is completed, the hordes of giant mechanized forces being mass-produced on the Moon will descend upon Earth.

Synopsis from Anime News Network