The Truth of God can indeed be tested. To do so requires extrapolating and determining the effects the belief has on every other belief one holds and then testing that entire complex against the alternative complex centered on around a disbelief in God.
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Claim #2 The Coherence Theory of Truth is the best known system that allows us to prove the truths we can and infer the truths we cannot. The Coherence theory of truth provides us with a mechanism for testing both provable and unprovable truth. Coherence theory holds that a belief is true if we can incorporate it in an orderly and logical manner into a larger and complex system of beliefs or, even more simply still, a belief is true when it fits in with the set of all our other beliefs without creating a contradiction.
Coherence theory holds that a statement is true when it can be fully integrated into a group of complex ideas, the whole set of which is then tested against reality. Similarly an idea is false when it cannot be integrated into a group of complex ideas or if upon integration the set fails when tested against reality.
Another and more common word for an unprovable truth is an a priori truth.
See:
The Coherence Theory of Truth