An instance is a CNF instance of the NP core: a structure whose elements are clauses and variables, with the positive and negative occurrences of variables in clauses. A literal occurrence of a clause $c$ is a pair $(x, s)$ of a variable and a sign such that $x$ occurs in $c$ with sign $s$. The instance has width at most two when no clause has three distinct literal occurrences, and it is a yes-instance of 2SAT when it has width at most two and is satisfiable. 2SAT is the decision problem of the structures isomorphic to such an instance. Instances of larger width are no-instances: the width bound is part of the problem, not a promise.