Yea those would be those "details". I wouldn't even have the slightest clue how to begin proving that NP problems are equivalent for the purpose of (dis)proving that P=NP, much less proving the entire thing. I guess that may have to do with why nobody has solved it. 
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"Prohibition will work great injury to the cause of temperance. It is a species of intemperance within itself, for it goes beyond the bounds of reason in that it attempts to control a man's appetite by legislation, and makes a crime out of things that are not crimes. A Prohibition law strikes a blow at the very principles upon which our government was founded." --Abraham Lincoln
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