In business process life-cycle management and reengineering through process mining, it is crucial for the process mining system to discover structurally safe and complete business process models from process logs. However, most process mining systems typically suffer from discovering inaccurate and unstructured business process models due to various types of anomalous traces hidden in process logs. In this paper, we therefore propose a process log preprocessing approach that purifies a corresponding process log dataset by selecting a group of reasonable process log traces and applying to discover an essential business process model satisfying the structural completeness requirement of matched-pairing and proper-nesting properties. The theoretical basis of the proposed approach is the mathematical graph model of information control net model that is the typical representation of business process models. Finally, we practically demonstrate the conceptual excellence and functional correctness of the proposed preprocessing approach through experimental verifications using real business process enactment log datasets available in the 4TU Center for Research Data.