If all NP-complete problems can be converted to 3-SAT problems I had an idea that would not solve the NP problem but might be a practical solution.
What you could do is simply, make a huge table of 3-SAT problems and whether they are solvable or not. Store this on a giant server.
Then it takes less than polynomial time to look at a 3-SAT problem and look it up in a table.
Two questions, for practical purposes, how big a table would be useful? Does such a table already exist?