Consider a quantified Boolean formula $f$. We can convert it into Skolem Normal Form formula $f^*$ such that $f$ is satisfiable iff $f^*$ is satisfiable, by replacing variables that are existentially quantified with Skolem functions (that satisfy certain conditions).
It seems to me that $|f^*|$ can be exponentially larger than $|f|$, but I'm struggling to find a good reference for that.
I see that in this question: How to generate Skolem function in practice, the answer states that we don't need to compute the Skolem functions in practice, but I'm actually interested in computing them.
I don't know if my intuition is correct (about $|f^*|$ potentially having an exponential blow-up), but if it is, I'd be grateful if someone could point me towards such a reference.
Edit: My intuition stems from the fact that if there were a polynomial upper bound on those Skolem functions, then that would put QBF in $\Sigma_2^p$--- ($\exists$ Skolem functions)($\forall$ assignments)[formula is true].