Analysis of logical relationships between inputs and outputs of a computational system can significantly reduce the test execution effort via minimizing the number of required test cases. Unfortunately, the available specification documents are often insufficient to build a complete and reliable model of the tested system. In this paper, we demonstrate the use of a data mining method, called Info-Fuzzy Network (IFN), which can automatically induce logical dependencies from execution data of a stable software version, construct a set of non-redundant test cases, and identify faulty outcomes in new, potentially faulty releases of the same system. The proposed approach is applied to the Unstructured Mesh Finite Element Solver (UMFES) which is a general finite element program for solving 2D elliptic partial differential equations. Experimental results demonstrate the capability of the IFN-based testing methodology to detect several kinds of faults injected in the code of this sophisticated application.