In this paper we propose Aleph, a leaderless, fully asynchronous, Byzantine fault tolerant consensus protocol for ordering messages exchanged among processes. It is based on a distributed construction of a partially ordered set and the algorithm for reaching a consensus on its extension to a total order. To achieve the consensus, the processes perform computations based only on a local copy of the data structure, however, they are bound to end with the same results. Our algorithm uses a dual-threshold coin-tossing scheme as a randomization strategy and establishes the agreement in an expected constant number of rounds. In addition, we introduce a fast way of validating messages that can occur prior to determining the total ordering. This version of the protocol is deprecated. For current version see arXiv:1908.05156.