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## 4.3.1 Modal Depth 3

Our method can be used to generate interesting test sets with modal depth d = 3. This depth is not at all interesting with previous methods—either the formulae are immensely difficult, such as for p = 0, or the behavior is dominated by trivial unsatisfiability, such as for p = 0:5.

For interesting levels of difficulty, we do have to reduce C to values below 2:5. If C is much larger, the formulae are too hard. However, with C  2:5 we can produce interesting test sets, as shown in Figure 12. (The relevant asymmetry between the satisfiable and unsatisfiable rates curves for N  5 is due to the high amount of tests exceeding the time limit.) Here the problems are hard even for N  5 but doable, and there are no problems with trivially (un)satisfiable formulas.