CS451/551                     Artificial Intelligence                 Spring 2002

Assignment #3                due: Thursday,  4/3/02


The Assignment:
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Download OTTER from http://www-unix.mcs.anl.gov/AR/otter
If you want you can run my version directly.  The executable
called otter is in my public directory.

For each of the following problems, you are given a set of 
axioms and a conclusion, representing a theorem.  You should
convert each problem to clausal form and give a resolution proof
of the theorem.  More specifially, I want the following for each
problem:

A.  A listing of the meaning of each atom used.
B.  A list of all your clauses, with some explanation 
    of their meaning.
C.  A proof of the theorem.
D.  After you have proved the theorem for yourself, I 
    want you to represent it in OTTER and prove it using
    OTTER.  For each problem, you should hand in the OTTER
    input file and the OTTER output file.

The Problems:
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1.  Last night, there was a party.  Ann and Bill and Carl and Dave
were invited.  Whenever, there is a party, Carl always comes when
Ann and Bill come.  But Carl will not come if Dave comes.  We know
that Ann came to the party.  Prove that either Bill or Dave did not
come to the party.

2.  There was another party.  Ann and Bill and Carl and Dave
were invited.  Not all of them came.  Whenever there is a party,
Bill comes when Ann comes.  Also, Carl comes when Bill comes.
Also, Dave comes when Carl comes.  Also, Ann comes when Dave comes.
Prove that nobody came to the party.

3.  There was another party.  Ann and Bill and Carl and Dave
were invited.  There were at least two people at the party.
If Ann came then everybody else came.  And Bill always comes
when Carl comes.  Prove that Bill came to the party.

4.  There was another party.  This time only Ann and Bill and
Carl were invited.  Either Ann or Bill came, but not both.  Either
Bill or Carl came, but not both.  Prove if either Ann or Carl came 
to the party, then both Ann and Carl came to the party.

5.  Suppose there are only five people in the world.  Three of
the people are male and two are female.  Each female is married
to at most one male.  Prove that not all of the males are married.