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# 15-815 Automated Theorem Proving

# Lecture 33: Ground Superposition

After concluding the discussion and properties of the lexicographic
path ordering, we show it may be used to strongly restrict paramodulation
inferences. The resulting calculus is called *(ground) superposition*

On first-order Horn clauses, (ground) superposition can be applied
by introducing a new constant *true* and replacing every atomic
predicate *P* by an equation *P = true*. This is related
to the notion of *analytic cut* (cut with subformulas of a goal
sequent) which may be employed in the inverse method.

### Reading

### Key Concepts

- Paramodulation
- Reduction order
- Superposition
- Equality resolution
- Horn sequents
- Ordered resolution

### Links

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Frank Pfenning
fp@cs