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Here is how I solved it. The language has binary relationship $\prec,$ unary function $\textit{pick}: \mathbb{N} \rightarrow \mathbb{R},$ constant function $\textit{count}: \emptyset \rightarrow \mathbb{N}.$ The language uses regular quantifiers as well as counting quantifiers. The theory defines $\prec$ as a linear order. Other axioms are ( \forall x \; \...