Логическо програмиране 2004/05 - упражнения

Да се приведат формулите в Скулемова нормална форма:

1. $$\neg \forall X(\exists Y(p(X,Y)\rightarrow(q(g(X))\rightarrow\exists X\forall Y(r(X,Y)))))$$
2. $$\forall X\exists Y(p(X,Y)) \rightarrow \forall X\exists Y(q(X,Y))$$
3. $$\neg\exists X((\forall Y(q(X,Y))\rightarrow p(f(X)))\rightarrow \exists X\forall Y(\neg r(X,Y))$$
4. $$\exists X(\exists Y(p(X,Y))\rightarrow \neg q(g(X)) \rightarrow \forall X\exists Y(\neg r(U,X,Y)))$$
5. $$\neg(\exists X((\exists Y(p(X,Y)))\rightarrow \forall Y(q(Y)))$$
6. $$\forall Y(\forall X(p(X,Y)\rightarrow\neg\exists X(p(X,g(Z))\vee\forall Z(\neg q(X,Z))))$$
7. $$\exists X\neg(\neg(\exists Y(p(Y,f(Z)) \& \exists Z(\neg q(X,Z))))\rightarrow\forall Y(p(X,Y)))$$