A formula is satisfiable if there exists an assignment of true or false to variables that makes all clauses true simultaneously. You need every single clause to be satisfied. If no such assignment exists, the formula is unsatisfiable. No matter what values you choose, at least one clause will be false. -SAT determines satisfiability in linear time using the SCC structure. This is the central question: can you satisfy all constraints at once?
The SCC condition answers this in m time without trying all possibilities.