Inductive logic programming is a technique that generates logic programs which keep to a given specification using a background knowledge. We propose a new task in the field of pro- gram synthesis called Time-gated Partition-selection Inductive Logic Programming, consisting of splitting the background knowledge into partitions and selecting only the relevant partitions to a given set of examples. In order to show an initial direction of research and demonstrate the effectiveness of the approach, we have constructed a set of partitioning functions and a selection function. These were implemented using existing graph clustering and community detection algorithms applied to static call graphs of existing programs in the target language and using a linear time evaluation selection function. By comparing the inductive logic programming approach Popper to a version of Popper with its search space reduced using this technique, we show that these partitioning- and selection functions can improve the generated programs on three out of four different domains. Finally we show that there is a difference in partition quality by comparing the results to a random partitioning function. This work establishes background knowledge partitioning- and selection as a useful tool in program synthesis research.