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# 15-815 Automated Theorem Proving

# Lecture 34: Constrained Paramodulation

We generalize the superposition to allow schematic sequents and
consider the consequences. Besides superposition we also consider
paramodulation with constrained sequents and the so-called
*basic paramodulation* strategy which yields a further
improvement.

Another important component of search in the presence of equality
is redundancy elimination (in particular by simplification according
to oriented equations), leading to saturation-based theorem
proving procedures. Using the examples of groups, we briefly
touch upon the central redundancy elimination techniques.

### Reading

### Key Concepts

- Paramodulation
- Basic paramodulation
- Paramodulation with constraints
- Saturation

### Links

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Frank Pfenning
fp@cs