Prove using natural deduction that $(R \rightarrow (P \rightarrow Q))\vdash (Q\rightarrow P) \lor (P \rightarrow Q)$ I ran into some trouble proving the following:

$(R \rightarrow (P \rightarrow Q))\vdash (Q\rightarrow P) \lor (P \rightarrow Q)$

My approach thus far:

Honestly I'm really stuck. So basically my hypothesis requires this $R$, hence the first thing that came to my mind is the Law of Excluded Middle. Using $R$ is trivial. The problem comes with $\neg R$. I can't seem to proceed from there.

Any help or insights is deeply appreciated.
Since the conclusion $(Q→P)∨(P→Q)$ is a tautology, one does not need the premise to prove the conclusion. One can prove this using the Law of the Excluded Middle (LEM) in the following manner:





Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
You can use the exportation law

$ ( R \to (P \to Q)) \Leftrightarrow (( R \land P ) \to Q) $

to reduce this question to 
prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$

Which you have already asked.