Before revision: Consider SAT with the following restrictions. An input formula is in CNF form, and, there exists an ordering of the clauses in which clauses containing any fixed literal appear contiguously. We call this restricted SAT CONTIGUOUS SAT.
After revision: We define the problem segment cover as follows. We are given a set of pairs of sub-intervals of the unit interval. The problem asks if there is a choice of a single interval from each pair such that the union of the chosen intervals covers the entire unit interval.