The wikipedia-article for the P-NP problem  says there are three possible answers to the P-NP-problem:
- $P\neq NP$
- $P=NP$ is independent of ZFC
The third possible solution seems to be very interesting. Assuming it is true, there could still exist a turing machine which solve e.g. $SAT$ in polynomial time, but it cannot be proved. Assume now someone has found this turing machine.
It should never be possible to prove that this turing machine solves $SAT$ in polynomial time (because we "know" $P=NP$ is independent of ZFC), but the machine does it.
This situation sound very strange to me: Someone has a turing machine, but it is not possible to prove that it solves a specific problem ($SAT$). More specifc: If someone has proven that $P=NP$ is independent of ZFC then there exists a proof which says that it is not possible to prove for any turing machine that is solves $P=NP$ in polynomial time. Even if someone has found this turing machine.
Did i understand this right? Or did i understand something wrong? Because it sounds very strange to me that someone has an algorithm and it can be proved that it is impossible to prove what exactly this algorithm does.