Propositional Logic Proof using I.P. or C.P or rules of inference I'm attempting to solve a proof my professor asked. We are able to use any of the rules of inference, Indirect Proof or Conditional Proof. Every time I think am making progress I run into a brick wall. Here is the question.


*

*$Q \lor (R \rightarrow S)$

*$[R \rightarrow  (R \rightarrow  S)] \rightarrow (T \lor U)$

*$(T \rightarrow Q) \land (U \rightarrow V)$

*Conclusion: $Q \lor V$


I believe the easiest solution would be to attain $(T \lor U)$ from line 2 and then use as a Constructive Dilemma with line 3 but I'm really struggling to get past the $[R \rightarrow  (R \rightarrow  S)]$ part in order to get $(T \lor U)$. If anyone can help it would be greatly appreciated.
edit* I got by the previously mentioned part, but I am now struggling to get $(R \rightarrow S)$ from line one.
Translations:


*

*"$\supset = \rightarrow$"(if...then)

*"$\bullet = \land$"(and)

*~ = $\lnot$(not)



here is my work thus far. I have been trying any and everything for the past 4 hours and I have no idea where I am going from here. 

We can "formalize" Dave's answer, using Indirect Proof  : 
1) $\lnot (Q \lor V) \equiv (\lnot Q \land \lnot V)$ --- assumed [1] and using (DM)
2) $\lnot Q$ --- from 1) by (Simp)
3) $R \rightarrow S$ --- from premise 1. and 2) by (DS)
4) $(R \land R) \rightarrow S$ --- from 3) by (Taut) 
5) $R→(R→S)$ --- from 4) by (Exp)
6) $T \lor U$ --- from premise 2. and 5) by (MP)
7) $Q \lor V$ --- from 6) and premise 3. by (CD)
but 7) contradicts 1); thus we have :

9) $Q \lor V$ --- by Indirect Proof, discharging [1].

Conclusion :


$Q∨(R→S), [R→(R→S)]→(T∨U), (T→Q)∧(U→V) \vdash Q \lor V$.


