A doubt on converting NOT gate to CNF formula
Your formula does actually look like $x_2 = F(x_1)$, it's just written with different symbols.

First, we can rewrite the two clauses using implication. Since $(a \to b) \iff (\neg a \lor b)$, we can rewrite the formula as

$$
(\neg x_1 \to x_2) \land (x_2 \to\neg x_1)
$$

Now, you can recognize that this is $(a \to b) \land (b \to a)$, which is to say $a \iff b$.

$\iff$ as a boolean operator behaves the same way as $=$; it evaluates to true when its left hand side and right hand side are the same. So your formula is equivalent to

$$ x_2 \iff \neg x_1 $$

Viewing this as a constraint (assuming $x_1$ can be treated as "fixed"), $x_2$ is fixed as $x_2 := \neg x_1 $