# Superposition calculus and equality factoring

Superposition with equal rights resolution and also equal rights factoring is claimed to be a full calculus for first - order logic. The objective of equal rights factoring is primarily to get rid of paraduplicate literals like $p(X)$|$p(Y)$, which is great.

Yet all the documents I carry the subject concur that factoring uses just to favorable equal rights. To put it simply, it does not take care of paraduplicate adverse literals like $\lnot p(X)$|$\lnot p(Y)$. Just how do you manage those?

The solution (many thanks to Stephan Schulz, writer of the E theory prover, individual interaction) is that factoring on favorable literals is adequate ; along with the various other reasoning regulations, this will certainly create conditions that will certainly settle with the adverse literals to address the trouble, if it can be addressed in all.

Related questions