Definition:CNF Satisfiability Problem

Problem
A Conjunctive Normal Form Boolean Satisfiability problem is a Boolean Satisfiability Problem where all the clauses in $L$ all take the form
 * $\bigvee_{i \mathop = 1}^n v_i$

where $v_i$ is either a single variable or a the negation of a single variable.

Example

 * $x_1 \lor x_2$
 * $\neg x_1$
 * $x_1 \lor \neg x_2 \lor \neg x_3 \lor x_4 \lor x_5 \lor \neg x_6 \lor x_7$

are all in conjunctive normal form.


 * $x_1 \implies x_2$
 * $\neg (x_1 \lor x_2)$
 * $x_1 \land x_2$

are not in conjunctive normal form.

Also see

 * CNF Satisfiability Problem is NP-Complete