@xiggi - I would say that the manipulations are not trivial. Three algebraic steps at the least, and all the while, it is not certain that you are getting anywhere! That was my point: we have not seen enough new SAT problems to know that the approach is going to be worth the time. If you had told me that this was a current-SAT problem, I definitely would pursue your approach. In fact, with a little tweaking (so that the answer would not be negative) and this would be a fine grid-in question.