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Resolution – Properties of Clausal Forms

    (1) If l appears in some clause of S , but l c does not appear in any clause, then, if we delete all clauses in S containing l , the new clausal form S' is satisfiable if and only if S is satisfiable

    Example: Satisfiability of is equivalent to satisfiability of

    (2) Suppose C = { l } is a unit clause and we obtain S' from S by deleting C and l c from all clauses that contain it; then, S is satisfiable if and only if S' is satisfiable

    Example: is satisfiable iff is satisfiable


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