How to convert this first order sentence into conjunctive normal form? This is one of my homework, but it seems to be so complicated that I really do not know where to start :(

$$ \exists x\;\forall y\;\forall z \Bigl({\rm person}(x)\land \bigl(({\rm likes}(x,y)\land y\ne z)\to \neg {\rm likes}(x,z)\bigr)\Bigr) $$

Any help is appreciated!
 A: We start with removing implications, note that $\alpha \to \beta \equiv \neg \alpha \lor \beta$, this gives us $$
 \exists x\;\forall y\;\forall z \Bigl({\rm person}(x)\land \bigl(\neg ({\rm likes}(x,y)\land y\ne z)\lor \neg {\rm likes}(x,z)\bigr)\Bigr) $$
Now we move the negations to the innermost position, using $\neg(\alpha \land \beta) \equiv \neg \alpha \lor \neg \beta$ and $\neg(\alpha \lor \beta) \equiv \neg \alpha \land \neg \beta$ giving 
$$\exists x\;\forall y\;\forall z \Bigl({\rm person}(x)\land \bigl( \neg {\rm likes}(x,y)\lor y= z \lor \neg {\rm likes}(x,z)\bigr)\Bigr) $$
As the quantifiers are already at their outmost positions, we now skolemize, that is replace $\forall x_1\ldots \forall x_n\exists v. \phi(x_1, \ldots, x_n, v)$ by $\phi(x_1, \ldots, x_n, f(x_1, \ldots, x_n, v))$, so here we replace the $x$ by a constant symbol $p$, giving
$$\forall y\;\forall z \Bigl({\rm person}(p)\land \bigl( \neg {\rm likes}(p,y)\lor y= z \lor \neg {\rm likes}(p,z)\bigr)\Bigr) $$
Now we drop the universals 
$${\rm person}(p)\land \bigl( \neg {\rm likes}(p,y)\lor y= z \lor \neg {\rm likes}(p,z)\bigr)$$
As this is a CNF, we are done.
