The trainer doesn't work.
Pressing F1 doesn't work. I ran the game first (up to the point where you start building and stuff), ran the game as administrator and not, ran the DX11 version and not, waited hours and still F1 doesn't work.
When I press F4 or F5, they activate even when the trainer isn't even activated yet.
My version of the game is 1.1.0.1043 Beyond Earth with all DLCs in.
EDIT: I also tried running the trainer as administrator and all kinds of stuff besides that if you're curious.