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

  1. No used car dealer buys a used car for his family.
  2. Some people who buy used cars are absolutely dishonest.
  3. Conclusion: Some absolutely dishonest people are not used car dealers.

  1. &forall x ( U(x) &rarr ¬ B(x) )
  2. &exist x ( B(x) &and D(x) )
  3. &exist x ( D(x) &and ¬ U(x) )

  1. ¬ U(x) &or ¬ B(x)
  2. a. B(a) b. D(a)
  3. ¬ ( &exist x ( D(x) &and ¬ U(x) ) )
    &forall x ¬ ( D(x) &and ¬ U(x) )
    &forall x ( ¬ D(x) &or U(x) )
    ¬ D(x) &or U(x)
  4. (1, 2.a.) ¬ U(a)
  5. (3, 4) ¬ D(a)
  6. (2.b, 5.) □

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