A clause is a disjunction of literals (atoms or negations of atoms).

Select two clauses C₁ and C₂ that have exactly one atom that is positive in one clause and negated in the other.

Form a new clause, consisting of all literals of both clauses except for the two complementary literals, and add it to the set of clauses.

Theorem: The new clause produced by resolution is a logical consequence of the two parent clauses.

Proof: Let the parent clauses be C₁ = L &or C₁' and C₂ = ¬ L &or C₂'; the resolvent is H = C₁' &or C₂'. Suppose that C₁ and C₂ are true in an interpretation I.
Case 1: L = true in I. Then since C₂ = ¬ L &or C₂', C₂' must be true in I and H is true in I.
Case 2: L = false in I. Then since C₁ = L &or C₁', C₁' must be true in I and H is true in I.

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