Skolemization eliminates existential quantifiers by replacing each
existentially quantified variable with a * Skolem constant* or
* Skolem function*.

In effect, we are saying ``If there exists (at least) one, give the algebraic
name *a* to it.'' Having named the existential variable, we can eliminate
the quantifier.

In general, an existential variable is replaced by a * Skolem function*
of all the universal variables to its left. (A Skolem constant is a function
of no variables.)

Each Skolem constant or function that is introduced must be a new one, distinct from any constant or function symbol that has been used already.

Example: *&exist x &forall y &forall z &exist w P(x, y, z, w)*

This is Skolemized as *P(a, y, z, f(y, z))*. *&exist x* has no universals
to its left, so it is Skolemized as a constant, *a*. *&exist w* has
universals *y* and *z* to its left, so it is Skolemized as a function of
*y* and *z*.

After Skolemizing, universal quantifiers are eliminated; all remaining variables are understood to be universally quantified.