Definition:Boolean Satisfiability Problem

Problem
Given a set of propositional variables $X$ and a list of one or more logical expresions $L$ constructed using only the variables, the four unary functions ($\operatorname{True}$, $\operatorname{False}$, identity, and $\neg$) and the sixteen Binary Truth Functions find values for all $x \in X$ such that all the expressions in $L$ are true.

Example
If $L$ is defined by:
 * $ \neg x_1 \lor \neg x_2$
 * $x_3$
 * $x_3 \implies x_2$

then a solution is:
 * $ x_1 = \operatorname{False}$
 * $x_2 = \operatorname{True}$
 * $x_3 = \operatorname{True}$

Also see
The Boolean Satisfiability Problem was the first known NP-Complete problem, as proved in the Cook Levin Theorem.