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Within this elaboration a generic system, subsequently referred to as System applying High Order Computational Intelligence in Data Mining (SHOCID), applying Computational Intelligence-paradigms, methods and techniques in the field of Data Mining, is being introduced. Currently available Data Mining systems are usually targeted on particular problem statements and require the user to understand how the underlying paradigms work, in contrary to the introduced one. SHOCID does not only fall back on complex Data Mining and Computational Intelligence techniques; it additionally does not require the user to understand how the result of a mining process is being achieved. Depending on the problem, the system is able to combine techniques and is, in some degree, able to decide on its own which strategy suits best. Within this elaboration known but adapted, as well as new approaches to Data Mining are being introduced, with focus on genericity and result-orientation for highlighting the aim of the research project: the provision of highly complex Computational Intelligence-techniques for mining data without the necessity of understanding these, implemented through a result-oriented interface and based on generic system architecture. The system's advantages are brought out by detailing one of its combinatorial data processing strategies as well as by describing algorithmically how training data for Feed Forward Artificial Neural Networks is synthesized. Finally, we provide an outline of the implemented techniques with focus on how the system makes use of them, always focusing on genericity.