Complexity of (SAT to 3-SAT) Problem?
This has been answered on the CS Theory StackExchange site:
https://cstheory.stackexchange.com/a/19833/5038

(I'm posting an answer here, so this question does not get treated as a question-without-an-answer and get periodically rotated back onto the front page by the Community user.  Normally, questions without any upvoted or accepted answer are re-displayed on the front page every so often.  Since this question now has been solved answered elsewhere, there doesn't seem any need for that.  As long as someone upvotes or accepts this answer, that should prevent this question from being rotated back onto the front page.  I'm ticking the community wiki box so I won't get any rep from this answer.)