In this paper we present a new consensus protocol for Bitcoin-like peer-to-peer systems, where the right to generate a block is given to the party which provides non-interactive proofs of retrievability for the past state snapshots. This Proof-of-Work scheme has better resistance to specialized hardware than Bitcoin and Permacoin. Unlike blockchain systems being used today, a network using the protocol of ours is safe if majority of nodes are rational in terms of storing full blocks. By using that we also show that one useful application of our protocol is the construction of a prunable blockchain system without a security loss.