Contemporary process discovery methods take as inputs only positive examples of process executions, and so they are one-class classification algorithms. However, we have found negative examples to also be available in industry, hence we propose to treat process discovery as a binary classification problem. This approach opens the door to many well-established methods and metrics from machine learning, in particular to improve the distinction between what should and should not be allowed by the output model. Concretely, we (1) present a formalisation of process discovery as a binary classification problem; (2) provide cases with negative examples from industry, including real-life logs; (3) propose the Rejection Miner binary classification procedure, applicable to any process notation that has a suitable syntactic composition operator; and (4) apply this miner to the real world logs obtained from our industry partner, showing increased output model quality in terms of accuracy and model size.