In the face of two accounts that cannot both be true, it is helpful to apply a coherence test to the differing accounts and provisionally accept the account that best explains the available data without introducing contradictions. If both propositions meet these criteria equally well, the simplest proposition is likely to be correct.
Determining the truth of a statement requires analysis of the proposition's coherence. An argument is coherent if it is internally consistent and accurate to the degree that evidence can be examined for its veracity. A coherent argument must explain, or not be in conflict with, all of the observed facts, and it must not contain or imply propositions that contradict each other.
If one story contains an internal contradiction, for example, it can safely be discounted as untrue or logically impossible. The opposing story might also be wrong, but a self-contradictory story is definitely wrong. This is also true of stories that make claims known to be false, as a claim with a false premise is unlikely to be true. In the event that both accounts are internally consistent and agree with the known evidence, the explanation that requires the fewest unsupported assumptions must be accepted as being provisionally true, pending the discovery of new evidence.