If $s \vDash t \rightarrow u$ and $s \vdash \neg t \rightarrow \neg u$, then is $s$ unsatisfiable?
Let $v$ be a valuation. Then $(v(s) = T \rightarrow v(t)= F \wedge v(u) = T) \land (v(s) = T \rightarrow v(t) = T \lor v(u) = F)$
But I get stuck here?