Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities

We show that positivity of {\it every} partial transpose of $N$-partite quantum states implies new inequalities on Bell correlations which are stronger than standard Bell inequalities by a factor of $2^{(N-1)/2}$. A violation of the inequality implies the system is in a bipartite distillable entangled state. It turns out that a family of $N$-qubit bound entangled states proposed by D\"ur {[Phys. Rev. Lett. {\bf 87}, 230402 (2001)]} violates the inequality for $N\geq 4$.