Order of Quantifiers
The order in which quantifiers appear is very important; it must be maintained.
Consider the ambiguous sentence, Every man loves some woman. This sentence could be interpreted as:
∀ x [Man(x) → ∃ y [Woman(y) ∧ Loves(x,y)]]
and Skolemized:
Man(x) →
[Woman(lover(x)) ∧ Loves(x,lover(x))]
∃ y ∀ x [Man(x) → [Woman(y) ∧ Loves(x,y)]]
and Skolemized:
Man(x) → [Woman(a) ∧ Loves(x,a)]