Resolution Example[Chang and Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.]

  1. The customs officials searched everyone who entered the country who was not a V.I.P.
  2. Some of the drug pushers entered the country, and they were only searched by drug pushers.
  3. No drug pusher was a V.I.P.
  4. Conclusion: Some of the officials were drug pushers.

  1. &forall x ( E(x) &and ¬ V(x) &rarr &exist y ( S(x,y) &and C(y)) )
  2. &exist x ( P(x) &and E(x) &and &forall y ( S(x,y) &rarr P(y) ) )
  3. &forall x ( P(x) &rarr ¬ V(x) )
  4. &exist x ( P(x) &and C(x) )

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