We describe the Inspire system which participated in the first competition on inductive logic programming (ILP). Inspire is based on answer set programming (ASP). The distinguishing feature of Inspire is an ASP encoding for hypothesis space generation: given a set of facts representing the mode bias, and a set of cost configuration parameters, each answer set of this encoding represents a single rule that is considered for finding a hypothesis that entails the given examples. Compared with state-of-the-art methods that use the length of the rule body as a metric for rule complexity, our approach permits a much more fine-grained specification of the shape of hypothesis candidate rules. The Inspire system iteratively increases the rule cost limit and thereby increases the search space until it finds a suitable hypothesis. The system searches for a hypothesis that entails a single example at a time, utilizing an ASP encoding derived from the encoding used in XHAIL. We perform experiments with the development and test set of the ILP competition. For comparison we also adapted the ILASP system to process competition instances. Experimental results show that the cost parameters for the hypothesis search space are an important factor for finding hypotheses to competition instances within tight resource bounds.