Nothing about formulas, literals, satisfiability or encodings is defined here. A formula is a formula of $lax-429075$ — a list of clauses, a clause a list of literals, a literal a variable index with a sign — its satisfiability is that submission's $Satisfiable$, and its binary word is that submission's $encodeCNF$. The only new notion is the width condition, so that 2-SAT is literally a subset of SAT, with membership in the two languages witnessed by the same formula.

A clause is allowed to have fewer than two literals. A unit clause is a clause of one literal; the empty clause is a clause no assignment satisfies, so a formula containing one is not satisfiable. Both are handled by the algorithm, and the classical results hold for them: the restriction to clauses of exactly two literals is a convenience that this development does not need.

The variables of a formula are the indices its literals mention, however large; a formula on the single variable $1000$ has one variable. The count of distinct variables is what the running time of the algorithm is measured by, besides the length of the word.