In clausal logic, an SLD refutation demonstrates that the input set of clauses is unsatisfiable. This sentence is unsatisfiable (a contradiction) because of the universal quantifier formula 2. These methods can sometimes but not always prove unsatisfiability of an unsatisfiable constraint store. In principle, whenever the constraint store is unsatisfiable the algorithm could backtrack. This operation may not detect inconsistency even if the constraint store is unsatisfiable. He established complexity results for detecting minimally unsatisfiable formulas. Runs of DPLL-based algorithms on unsatisfiable instances correspond to tree resolution refutation proofs. Once a branch contains a literal and its negation, its corresponding formula is unsatisfiable. If all conjunctions are proved unsatisfiable, the original set of formulae is unsatisfiable. For example, runs of DPLL algorithm on unsatisfiable instances correspond to tree-like Resolution refutations. Otherwise, an unsatisfiable set can generate an infinite-growing tableau. In a complete logic, a formula is contradictory if and only if it is unsatisfiable. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. As a result, if this set is detected unsatisfiable, the interpreter backtracks. If the answer is "no", the formula is unsatisfiable.