The premises are:
- (P $\rightarrow$ J) $\rightarrow$ ($\lnot$C $\rightarrow$ M)
- $\lnot$J $\rightarrow$ $\space$ $\lnot$P
- ($\lnot$ J $\land$ E) $\rightarrow$ $\space$ $\lnot$C
- $\lnot$M $\rightarrow$ $\space$ P
The conclusion is: $\lnot$(J $\land$ $\space$ $\lnot$P) $\rightarrow$ C
You don't necessarily have to answer the question, but I would like to know whether there is such a thing as being too complex for proving with rules of inference. I believe checking the validity would be much easier with a truth tree.
If it can be done with rules of inference, how would I go about doing it?