The detection of all inclusion dependencies (INDs) in an unknown dataset is at the core of any data profiling effort. Apart from the discovery of foreign key relationships, INDs can help perform data integration, integrity checking, schema (re-)design, and query optimization. With the advent of Big Data, the demand increases for efficient INDs discovery algorithms that can scale with the input data size. To this end, we propose S-indd++ as a scalable system for detecting unary INDs in large datasets. S-indd++ applies a new stepwise partitioning technique that helps discard a large number of attributes in early phases of the detection by processing the first partitions of smaller sizes. S-indd++ also extends the concept of the attribute clustering to decide which attributes to be discarded based on the clustering result of each partition. Moreover, in contrast to the state-of-the-art, S-indd++ does not require the partition to fit into the main memory- which is a highly appreciable property in the face of the ever growing datasets. We conducted an exhaustive evaluation of S-indd ++ by applying it to large datasets with thousands attributes and more than 266 million tuples. The results show the high superiority of S-indd++ over the state-of-the-art. S-indd++ reduced up to 50~% of the runtime in comparison with Binder, and up to 98~% in comparison with S-indd.