Kenneth Rosen Edition 7 Exercise 1.6 Question 29 (Page No. 80)

Question

Use rules of inference to show that if $\forall x (P(x) \vee Q(x))$, $\forall x (\sim Q(x) \vee S(x)), \forall x (R(x) \rightarrow \sim S(x)),$ and $\exists x \sim P(x)$ are true, then $\exists x \sim R(x)$ is true.