I said typically. These are NP problems you can always find edge cases that are impossible to solve. For these edge cases we can always reformulate the problem

I said typically. These are NP problems you can always find edge cases that are impossible to solve. For these edge cases we can always reformulate the problem, aka use different definition of variables and constraints that can better inform the search. We are talking about real world applications, not toying with pathogenic benchmark toy examples.