The task in multi-agent path finding (MAPF) is to find non-conflicting paths connecting agents' start and goal positions. The MAPF problem is often compiled to Boolean satisfiability (SAT) and solved by existing SAT solvers. Contemporary compilation approaches of MAPF to SAT regard the SAT solver as an external tool whose task is to return an assignment of all decision variables of a Boolean model of the input MAPF instance. We present in this paper a novel compilation scheme called DPLL(MAPF) in which the consistency checking of partial assignments of decision variables with respect to the MAPF rules is integrated directly into the SAT solver. This scheme allows for far more automated compilation where the SAT solver and the consistency checking procedure work together simultaneously to create the Boolean model and to search for its satisfying assignment.