Pretty unrelated, but proof by contradiction has been really useful for me in real life. It gives you a way to look at logical facts, and remove many axioms, be

Pretty unrelated, but proof by contradiction has been really useful for me in real life. It gives you a way to look at logical facts, and remove many axioms, because it relies on empirical evidence and a set of assumptions that you are trying to invalidate. In that way, it avoids issues with deducing things from a set of pre-prescribed beliefs. In fact, it fights against them.