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What is a proof by refutation?

  • A.Deriving a contradiction from the premises and the negated goal
  • B.Showing that the goal is false in some particular model
  • C.Refuting an opponent's argument rather than proving one's own
  • D.Deriving the goal directly from the premises by forward inference

Answer: A

Refutation converts an entailment question into a satisfiability question, which is what resolution and every satisfiability based prover exploit. Direct derivation is possible in other proof systems but resolution is only refutation complete. Counter-models and rhetorical refutation are different notions. Adopting a proof strategy because it suits the available machinery, rather than because it is the most natural, is a recurring practical compromise. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

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