This work deals with logical formalization and problem solving using automated solvers. We present the automatic translator TouIST that provides a simple language to generate logical formulas from a problem description. Our tool allows us to model many static or dynamic combinatorial problems and to benefit from the regular improvements of SAT, QBF or SMT solvers in order to solve these problems efficiently. In particular, we show how to use TouIST to solve different classes of planning tasks in Artificial Intelligence.