Sep 29, 2003
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- Converting "scoped exists" into clauses
	- use a Skolem function
	- parameterized by all universal vars that appear before

- More proof handouts
	- solved problems 1 and 3 today

- things to be careful about
	- negate goal *before* converting to clauses
		- why?

Problem 1:
   Given
        - The law says it is a crime for an American to sell
          weapons to hostile notions. The country Nono, an enemy
          of America, has some missiles, and all of its missiles
          were sold to it by Colonel West, an American.
   Prove
        - West is a criminal.

Problem 2:
   Given
        - Everyone who loves all animals is loved by someone.
        - Anyone who kills an animal is loved by no one.
        - Jack loves all animals.
        - Either Jack or Curiosity killed the cat, who is named Tuna.
   Find
        - Who killed the cat?

Problem 3:
   Given
        - Sam, Clyde, and Oscar are elephants.
        - Sam is green.
        - Clyde is gray and likes Oscar.
        - Oscar is either green or gray (but not both).
        - Oscar likes Sam.
   Prove
        - there is a gray elephant that likes a green elephant.

Problem 4:
   Given
        - No used car dealer buys a used car for his/her family.
        - Some people who  buy used cars are dishonest.
  Prove
        - Some dishonest people are not used car dealers.