  Motivated by applications of first-order theorem proving to software
analysis, we introduce a new inference rule, called subsumption demodulation,
to improve support for reasoning with conditional equalities in
superposition-based theorem proving. We show that subsumption demodulation is a
simplification rule that does not require radical changes to the underlying
superposition calculus. We implemented subsumption demodulation in the theorem
prover Vampire, by extending Vampire with a new clause index and adapting its
multi-literal matching component. Our experiments, using the TPTP and SMT-LIB
repositories, show that subsumption demodulation in Vampire can solve many new
problems that could so far not be solved by state-of-the-art reasoners.
