I have a propositional formula of the form

$$\bigvee_{i=1}^n \neg \left( x_i \Leftrightarrow \left(\bigvee_{j=1}^{f(i)} y_{ij} \right) \right)$$

where the $x_i$'s are propositional variables and the $y_{ij}$'s are propositional literals (i.e., propositional variables or their negation) and $f : \mathbb{N} \to \mathbb{N}$ is just a function.

I would like to have this formula in Conjunctive Normal Form (CNF) using these general symbols.

The leading "quantifer" is a disjunction and I do not know how to change it to a conjunction in an efficient manner. Of course, it can be done manually for each specific instance, but that is very slow even on a computer.