Uh, appolose, in Science - I mean true, pure science, not anything skewed by financial research - if you have two contradictory readings or scenario you don't reach for supernatural, you realize that you're missing something that currently remains unknown.
For example, initially, when Einstein and others we're getting into relativity, etc. such contradictions seemed to occur - the key one being that light, no matter how measured, always seemed to be going at the same speed irrespective of the observer. At first this seemed contradictory to other measurements that would imply it should differ.
However, Einstein didn't reach for supernatural, he realised that they were all missing something fundamental, and that the contradictory readings were simply confirming this.
So far as we know currently, and can confirm via tests, he was right, because he then went on to work out the missing element - that the speed of light can remain the same because time can vary to allow for it, respective to different frames of reference.
I guess you're posing a thought experiment - but so far, in my view, there has never been (and never will be) a genuine case of true contradictory results.
As always, it will just mean we're missing something crucial that can appear to cause a contradiction when in fact there is none (once you work out he missing crucial factor).