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What is the empty clause?

  • A.A clause whose variables have all been instantiated
  • B.A clause with no literals, which is unsatisfiable
  • C.A clause containing only positive literals
  • D.A clause that has been removed by subsumption

Answer: B

The empty clause asserts a disjunction of nothing, which is false in every model, so deriving it proves the clause set contradictory. It is the goal of every resolution refutation. Positive clauses, subsumed clauses and ground clauses are different notions. That the target of a proof is a syntactic object with no content, rather than a statement of the conclusion, is initially disconcerting and follows directly from the refutation strategy. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

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