Mini-Project 1: First-Order Theorem Proving

Due: February 5, 2010

In this mini-project you will use the Otter theorem prover to encode
some simple knowledge bases and prove simple consequences from those
knowledge bases. 

Unfortunately, debugging knowledge bases and successfully running a
theorem prover can be quite tedious for moderately sophisticated
problems. Thus, in this project the knowledge bases and queries will
be extremely simple. The project is primarily intended to give you
some basic experience using Otter, so that in the future if the need
arises you have a good starting point.

Otter is quite simple to use in concept. You can download Otter at,

http://www.cs.unm.edu/~mccune/otter/

for both Windows and Unix/Linux. 

You should begin by reading the introduction to Otter written by Tom
Bylander, which can be found at,

http://www.cs.utsa.edu/~bylander/cs3793/otter-intro.pdf

The examples given in that introduction use clausal knowledge
bases. Otter is also able to accept formulas written in full
first-order logic. To see the syntax you can look at section 4.5 of
the Otter manual,

http://www.cs.unm.edu/~mccune/otter/Otter33.pdf

For some problems it may be convenient to provide Otter with non-clausal formulas and let it do the conversion automatically. 

Your assignment is to use Otter for the following five problems:

1) Use Otter to prove that the graph in Figure 9.5 is colorable.

2) Repeat (1) but with a new graph that is not colorable with three colors. Use Otter to show that the graph is not colorable. The graph can small. 

3) Using the KB described in section 9.3 page 281 (formulas 9.3-9.10)
   use Otter to prove that West is a criminal.

4) Repeat 3, but this time use Otter to prove that "there exists 
   someone who is a criminal".

5) Using the "cat knowledge base" on page 299 (formulas A-F), use
   Otter to prove that that curiosity did kill the cat. 

For each of these you should provide me with your Otter input file 
and the corresponding Otter output, showing the proof that Otter found.

You can package these all up and email them directly to me at
afern@eecs.oregonstate.edu.