As an example [Dixon GinsbergDixon Ginsberg2002], suppose that we have a partial
assignment
and constraints

Now we can unit propagate to conclude by virtue of (31) and by virtue of (32); it isn't hard to conclude that the conflict set is in that either or must be true if (31) and (32) are to be simultaneously satisfiable. But if we simply add (31) and (32) and simplify, we get

which still allows and to both be false. This difficulty can be addressed by deriving a cardinality constraint that is guaranteed to be falsified by the current partial solution being investigated [Dixon GinsbergDixon Ginsberg2002]; Chai and Kuehlmann Chai:pb have developed a still stronger method.