But it can take exponential time and space to convert a general SAT problem to disjunctive normal form; for an example exchange " and " in the above exponential blow-up example for conjunctive normal forms.2007 2nd Bio-Inspired Models of Network, Information and Computing Systems."A machine program for theorem-proving" (PDF).

Different SAT solvers will find different instances easy or hard, and some excel at proving unsatisfiability, and others at finding solutions.The green vertices form a 3-clique and correspond to the satisfying assignment x false, y true.

Not-all-equal 3-satisfiability edit Main article: Not-all-equal 3-satisfiability Another variant is the not-all-equal 3-satisfiability problem (also called NAE3SAT ).In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values true or false in such a way that the formula evaluates to true.