$(p \land q ) \iff (r \implies s)$
$(s \vee \neg t)$
So, $\neg s \implies ((r \implies \neg p) \vee \neg t)$
My lecturer has written in our notes that this statement is invalid, but I'm not so sure. I've attached my workings and have found there to be a contradiction whilst using the 'no counterexample' method (i.e. assume the premise to be T whilst the conclusion F, if there is a contradiction then the statement is valid) to find the validity of this statement. Thus, I think this inference is valid.
My question is: is the above inference valid or not?
Thank you so much in advanced for your help! :)