Is there an "undecided" assertion of which a proof that it's not undecidable is known? Just a curiosity:

Is there an assertion of which a proof (formalizable, say, in ZFC) is not known but a proof that it's not undecidable (in ZFC) is known?

Edit: after the comments, I think the actual question was 

Is there an ("interesting") assertion of which neither a proof (formalizable, say, in ZFC) of it or its negation is known but a proof that it's not undecidable (in ZFC) is known?

 A: It shouldn't be hard to find a large number $N$ such that no one knows a proof that $N$ is prime and no one knows a proof that $N$ is not prime. Yet the question of the primality of $N$ can't be undecidable - there is a simple (if impractical) algorithm for deciding it. 
A: There's tons of assertions like that in finite combinatorics.  For example the Ramsey numbers R(5,5) and R(6,6) can be "straightforwardly" (i.e. given impractically large computing resources) found by direct enumeration.  It's known that $43\le R(5,5) \le 49$ and $102\le R(6,6)\le 165$.  But Wikipedia's article on Ramsey theory quotes Joel Spencer:

Erdős asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5, 5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6, 6). In that case, he believes, we should attempt to destroy the aliens.

The article Graham's number has another interesting example.
A: If it's known that some statement $S$ is decidable in ZFC, then you can just run a computer program that enumerates all ZFC-proofs and stops when it finds a proof of $S$ or a proof of $\neg S$.  By hypothesis, this algorithm is guaranteed to terminate.  Therefore, the only possible obstacle separating decidable statements from decided ones is computational complexity.
In other words, the only possible instances of what you're looking for are statements that have already been proved up to a finite computation.  Until they were actually proved, the Kepler Conjecture and Catalan's Conjecture were perhaps the most interesting examples of this type.  I can't think of other examples of comparable interest offhand, but maybe others can.
