For me, the trick here was to forget about the words "success" and "failure" because they have too much semantics embedded. I had to re-word the problem like this: call f3, if first argument of f1 and f2 are called. All other roads lead to f4. Both f1 and f2 has to be called in the chain no matter what.
Also, this is the first time I've seen such a pattern. Is there a practical application of such pattern? I think it's ok to have a single level of closure to continue execution, but if it goes to that many levels like the sample problem, it'll be a nightmare to maintain for people who have not seen your code yet.
Interested in seeing how my solution was off, and if I was thinking about it the wrong way. Any luck?