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In large computer network, isolation of the primary source of failure is a challenging task. In this paper, we present a novel approach of modeling network fault diagnosis. With the model based on reachable theorems, we design an automated fault identification algorithm and analyze its performance and validity named as DAFMA. To judge the consistency between the fault effect of the given failure sources and the testing one, an efficient algorithm is also proposed named as FFEAJ. DAFMA can be carried out automatically in computer because both DAFMA and FFEAJ are based on matrix and Boolean operations. Finally, to illustrate the details of DAFAM, four classical fault effects are classified and the working steps of DAFAM are described.