Two apparently different approaches to automating deduction are mentioned in the title of the thesis; they are the subject of a debate on
"big engines vs. little engines of proof". The contributions in this thesis advocate that these two strands of research can interplay in subtle and
sometimes unexpected ways, such that mutual pervasion can lead to intriguing results: Superposition can be, firstly, run on top of decision
procedures; secondly, employed as proof-theoretic means underneath combined decision procedures; and thirdly, used as a decision procedure
for many interesting theories, turning a big engine into a little one.