Consider the following logic program P
$\begin{align*} A(x) &\gets B(x,y), C(y) \\ &\gets B(x,x) \end{align*}$
Which of the following first order sentences is equivalent to P?

$(\forall x) [(\exists y) [B(x,y) \land C(y)] \Rightarrow A(x)] \land \neg (\exists x)[B(x,x)]$

$(\forall x) [(\forall y) [B(x,y) \land C(y)] \Rightarrow A(x)] \land \neg (\exists x)[B(x,x)]$

$(\forall x) [(\exists y) [B(x,y) \land C(y)] \Rightarrow A(x)] \vee \neg (\exists x)[B(x,x)]$

$(\forall x) [(\forall y) [B(x,y) \land C(y)] \Rightarrow A(x)] \land (\exists x)[B(x,x)]$