Question $4$: $[20$ points$]$ A formula is in prenex normal form $($PNF$)$ if it is of the form

$Q_1{x}_1{Q}_2{x}_{2}cdots{Q}_n{x}_{n}B$ where $Q_i(i=1,$dotsn$)$ is $AA$ or $EE$ and the formula $B$ is

quantifier free. For example, AAxEEy$(P(x,y)vvQ(x))$ is in PNF form, but

AAxP$(x)vvEEyQ(y)$ is not in PNF form. Convert the following statement

to PNF form:

AAx$((EEyR(x,y{)}^{{?}^{?}}$AAynotS$(x,y))$not$(EEyR(x,y{)}^{{?}^{?}}P))$

Fact: Every formula can be written in PNF form!