- In multi-agent path finding (MAPF) on graphs, the task is to find paths for distinguishable agents so that each agent reaches its unique goal vertex from the given start while collisions between agents are forbidden. A cumulative objective function is often minimized in MAPF. The main contribution of this paper consists in integrating independence detection technique (ID) into a compilation-based MAPF solver that translates MAPF instances into propositional satisfiability (SAT). The independence detection technique in search-based solvers tries to decompose a given MAPF instance into instances consisting of small groups of agents with no interaction across groups. After the decomposition phase, small instances are solved independently and the solution of the original instance is combined from individual solutions to small instances. The presented experimental evaluation indicates significant reduction of the size of instances translated to the target SAT formalism and positive impact on the overall performance of the solver.