I speak the truth by proving it false, and reveal a lie by making it true. What am I?

Should you have it down to a T, then I guess you have no need for me. If an unsolvable riddle comes your way, that's when my help comes into play. It costs you nothing to unlock me. If you know the answer then leave me be!

You raise me one, I raise the stakes; a challenge born from what it takes. The fool withholds me, feeling shame; while a score of me can make your game. What unlocks wisdom is full of neglect; I am the thing you'll least -or most- expect.

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire word signifies a great woman. What is the word?

You can't always see me, but you can feel me. You might not trust me, but you have to accept me eventually.