[jcd748]

SAT is NP-complete, but there are certain properties that allow theorem provers to show that a particular instance is overconstrained (and therefore unsatisfiable), or underconstrained (and many solutions exist). It's at a particular point, so-called phase transitions, where one finds the very hard instances. As an example, when characterizing 3-SAT instances by grouping by their ratio of clauses to variables, the very hard instances are grouped around a value of ~4.3.