I can relate to everything you're saying here. I know where you are, I've been there too.
There are two important things you will need to learn if you want to get through this with your sanity intact:
1) "Doublethink" as George Orwell called it. Knowing that it's all a farce, that you are playing some character in this big game (and that so are your commanders, and your fellow soldiers) that is the military. Knowing all this, while still playing the game, becoming the person you need to be in order to fit in this particular game, while still staying true to yourself.
Use your cynicism to your advantage. Play an exaggerated version of the soldier they expect you to be. Be a living parody of the military mentality. It will keep you and those clever enough to understand entertained, and it will make you friends.
Remember: IT'S ALL A GAME!
2) The most important lesson, for the military and for life (as an INTP), which is also the hardest to internalize. DON'T EVER DO ANYTHING SO THAT YOU CAN LATER SAY THAT YOU HAVE DONE IT.
I can not stress the importance of this enough. If you continue doing something you don't want to do, or chasing a goal that isn't you, or doing something that isn't you because you think it'll somehow change you into something you aren't and will never be, only because you don't want to have to tell people you broke a contract, you couldn't handle it, etc', you will end up wasting years chasing this goal, and will ultimately fail, because it's not you.
You will learn this, either the hard way or the easy way.
So basically my advice is to open your mind to your current situation and accept it, but also accept who you are. Stay true to yourself and the universe will always guide you to your niche. But do not, under any circumstances, try to force yourself into someone else's niche (although if you've already gotten yourself into the wrong niche, just start being yourself again, and either the niche will change, or you will fall out of it to something that fits you).
I hope this wasn't all too abstract.