Sufficient for any practical use is not "solved" in the mathematical sense. Also, AFAIK, a general solution to P=NP could still be very time consuming to calcu

Sufficient for any practical use is not "solved" in the mathematical sense. Also, AFAIK, a general solution to P=NP could still be very time consuming to calculate (even if you prove polynomial time solutions, that could still be a very high order polynomial). That is, your general solution to the problem could be only slightly better than O(n!) and satisfy.