It has quantifiers so it would be predicate calculus (first-order logic) - https://en.wikipedia.org/wiki/First-order_logic

I thought the question was more about the syntax of the logic language (which I think is rather idiosyncratic), but I can see that maybe they were asking about the relevant part of math.

(It might be worth noting that the webapp is not exactly first-order logic because it has some extra operators from modal logic.)