We showed in class that every strongly, exactly consistent s.c.f is strongly firm (I don't know if this is the right translation - we defined strong firmness as the equivalence of $*,\alpha,\beta$ effectiveness, which simply means that $\beta$ effectiveness $\Rightarrow$ * effectiveness).
I was wondering - is the converse statement true? That is: is every strongly firm s.c.f also strongly and exactly consistent? I thought about this for a bit and it seems the answer should be negative, however I haven't been able to come up with a suitable example.
Thanks!