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. 

It turns out $R \rightarrow (R \rightarrow S)$ is actually equivalent to $R \rightarrow S$.  You can show this in a couple of different ways: use Material Equivalence twice, plus the associative and commutative laws for disjunction, or alternatively, use exportation.  (For the latter, though, you'd need some extra lines to justify turning $R \wedge R$ into $R$, since this doesn't appear to be one of your allowed equivalences.)
How to fit this into an overall solution, based on Indirect Proof: Suppose the desired conclusion is false, which by De Morgan and Simplification gives you both $\neg Q$ and $\neg V$.  By Disjunctive Syllogism you then obtain $R \rightarrow S$, and after applying the aforementioned equivalence followed by Modus Ponens, you arrive at $T \vee U$.  Simplifying the third premise and applying a Constructive Dilemma gets you to $Q \vee V$, a contradiction.
