you can prove a negative. It is one of only two things you can prove. Simple Boolean logic, it is or it is not. If it is, it can not. simple enough. To prove a negative, you must prove a positive that negates the negative. IE: fact: a dog ate all the food. Negative assertion: The cat ate all the food. We know that if A is a fact, B cannot be true. You assert the very same in the latter part of your post, nullifying your opening thoughts.

Either way, there is some evidence down certain 'rabit holes' for intelligent design. Some evidence for the flood, in some cases. Realistically, we just do not understand enough of A to nullify B ~ nor do many people even care. It is just a battle of bloated ego anymore.

As for evolution - I agree with many parts of the theory, but not it's entirety.