Intelligent agents are considered as significant means towards realizing the semantic web vision. On the Semantic Web, integrating ontologies and rules enables software agents to interoperate between them, however, this leads to a problem, that no studies have focused on effective distributed reasoning for integrating ontologies and rules in multiple knowledge-bases. The methods that have been presented for distributed reasoning not only get a lot of times and memory, but also do not lead to a complete and sound reasoning. In this paper, to solve this problem, we present a distributed reasoning system that deals with the representation of the knowledge-base of order sorted logic. This logic is able to describe the hierarchy of predicates and inheritance of expressions that there are in our natural language. To have a distributed reasoning, our proposed method uses the expansion of rigid and valid-non-rigid properties between knowledge-bases. Furthermore, with considering time and the situation of properties for reasoning, the non-rigid properties have not been ignored, in fact, in their valid time and situation, they are used. With this method, we achieve a complete reasoning and, moreover, the extracted knowledge is completely considered in the knowledge-bases and we have a distributed reasoning with high efficiency and sound without missing any information.