Page "Boolean satisfiability problem" Paragraph 33
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As mentioned briefly above, though the problem is NP-complete, many practical instances can be solved much more quickly.
Many practical problems are actually " easy ", so the SAT solver can easily find a solution, or prove that none exists, relatively quickly, even though the instance has thousands of variables and tens of thousands of constraints.
Other much smaller problems exhibit run-times that are exponential in the problem size, and rapidly become impractical.
Therefore, almost all SAT solvers include time-outs, so they will terminate even if they cannot find a solution.
Finally, different SAT solvers will find different instances easy or hard, and some excel at proving unsatisfiability, and others at finding solutions.
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