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.