This paper presents an architecture and one concrete realization of a novel reasoning system named \emph{Distributed Non-Axiomating Reasoning System}. The system uses the so-called \emph{Non-Axiomatic Logic}, a formalism in the domain of artificial general intelligence designed for practical realizations of systems that work under the assumption of insufficient knowledge and resources. The main novelty of the proposed architecture is in the layered and distributed organization of its backend knowledge base. That is, the knowledge base is designed with scalability and fault-tolerance in mind. It allows the system to reason over very large knowledge bases with real-time responsiveness, while serving high numbers of concurrent users. Finally, one concrete practical application of the developed system is presented as well.