This problem investigates resolution, a method for proving the unsatisfiability of cnf-formulas. let φ = c1 ∧c2 ∧···∧cm be a formula in cnf, where the ci are its clauses. let c = {ci| ci is a clause of φ}. in a resolution step, we take two clauses ca and cb in c, which both have some variable x, where x occurs positively in one of the clauses and negatively in x ∨z1 ∨z2 ∨···∨zl), where the yi the other. thus, ca = (x ∨ y1 ∨ y2 ∨ · · · ∨ yk) and cb = ( and zi are literals. we form the new clause (y1 ∨y2 ∨···∨yk ∨ z1 ∨z2 ∨···∨zl) and remove repeated literals. add this new clause to c. repeat the resolution steps until no additional clauses can be obtained. if the empty clause () is in c, then declare φ unsatisfiable.