Prove the non-contradiction of facts against situations we that we hypothesize about. Make a choice. Apart from the third step, all this has been said before. Facts are statements of a type that can only be contradicted by other facts, but no contradiction can be found. Proof of non-contradiction is analysis.
Formal analysis includes logic and mathematics.
If humans were infinitely wise proof of non-contradiction would be tautology . If we wish to transpose facts that apply in one circumstance to a situation about which we hypothesize, we need to transpose the facts by methods free from contradiction. It is not rocket science, but suppose we did wish to send a rocket to Mars, and all the facts we knew concerned how rockets flew on Earth. We would use mathematics to prove non-contradiction of everything we knew about how rockets flew on Earth to how we presume they would fly on Mars. Before sending one there, we still will not know all the facts about how rockets will behave on Mars.