Or any one of the open questions that exist in science of the same sort - this is true in chemistry but not biology, but seems to be true in their own reference frame. This creature wanted to do this versus had a chemical reaction. So are free will and determinism not true because they conflict? What if I observe one or the other? Does that make it more or less true because I'm the observer? Or both or neither?
And not all non- truths conflict with all other non-truths, just some of them. Not to mention the bit about a rational mind believing true things is nonsensical unless you make that your definition of truth. Given an unlimited amount of truths there will be some incredibly large (smaller infinite) subset that conflict.
I just gave two interrelated examples off the top of my head.