Recently, there is an increasing interest in obtaining the relational structures of the environment in the Reinforcement Learning community. However, the resulting "relations" are not the discrete, logical predicates compatible with the symbolic reasoning such as classical planning or goal recognition. Meanwhile, Latplan (Asai and Fukunaga 2018) bridged the gap between deep-learning perceptual systems and symbolic classical planners. One key component of the system is a Neural Network called State AutoEncoder (SAE), which encodes an image-based input into a propositional representation compatible with classical planning. To get the best of both worlds, we propose First-Order State AutoEncoder, an unsupervised architecture for grounding the first-order logic predicates and facts. Each predicate models a relationship between objects by taking the interpretable arguments and returning a propositional value. In the experiment using 8- Puzzle and a photo-realistic Blocksworld environment, we show that (1) the resulting predicates capture the interpretable relations (e.g., spatial), (2) they help to obtain the compact, abstract model of the environment, and finally, (3) the resulting model is compatible with symbolic classical planning.