 Conjunctive normal form

A Boolean formula is in conjunctive normal form when it is a logical conjunction of Boolean clauses. It is true precisely when every Boolean clause is true under the same Boolean valuation; an empty logical conjunction is true. For example, $(x\vee \neg y)\wedge (z)$ has two Boolean clauses with widths two and one. Width counts Boolean literal occurrences within a Boolean clause, whereas the Boolean clause count counts the conjuncts. 2-SAT bounds width by two, and 3-SAT bounds width by three. A Boolean formula with an empty Boolean clause is an unsatisfiable Boolean formula.