Existing implementation of Scott's reduction?
You might check the FO2 solver by Tomer Kotek: https://forsyte.at/alumni/kotek/fo2-solver/
This is the only existing FO2 solver (Tony Tan with his student are working on developing something too).
Answering the question, the authors implemented an improved version of Scott Normal Form, called therein &quot;Skolemized Scott Normal Form&quot;. All the details are available here: https://arxiv.org/pdf/1610.02101.pdf