Use resolution and proof by contradiction to reprove Example.ExampleWe prove the following...

Use resolution and proof by contradiction to reprove Example.

Example

We prove the following using resolution:

1.

2.

We use (2.3.4) to replace hypothesis 1 with the two hypotheses

We use the first of De Morgan’s laws (2.3.3) to replace hypothesis 2 with the two hypotheses

The argument becomes

1.

2.

3.

4.

Applying (2.3.1) to expressions 1 and 3, we immediately derive the conclusion

In automated reasoning systems, proof by resolution is combined with proof by contradiction. We write the negated conclusion as clauses and add the clauses to the hypothesis. We then repeatedly apply (2.3.1) until we derive a contradiction.