Title: Deep Reasoning Networks:  Thinking Fast and Slow, for Pattern De-mixing. Abstract: We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving pattern de-mixing problems, typically in an unsupervised or weakly-supervised setting.  DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic-gradient-based neural network optimization.  We illustrate the power of DRNets on de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku) and on a substantially more complex task in scientific discovery that concerns inferring crystal structures of materials from X-ray diffraction data (Crystal-Structure-Phase-Mapping). DRNets significantly outperform the state of the art and experts' capabilities on Crystal-Structure-Phase-Mapping, recovering more precise and physically meaningful crystal structures. On Multi-MNIST-Sudoku, DRNets perfectly recovered the mixed Sudokus' digits, with 100% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models.