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In this work, we focus on decomposing large multi-agent path planning problems with global temporal logic goals (common to all agents) into smaller sub-problems that can be solved and executed independently. Crucially, the sub-problems' solutions must jointly satisfy the common global mission specification. The agents' missions are given as Capability Temporal Logic (CaTL) formulas, a fragment of signal temporal logic, that can express properties over tasks involving multiple agent capabilities (sensors, e.g., camera, IR, and effectors, e.g., wheeled, flying, manipulators) under strict timing constraints. The approach we take is to decompose both the temporal logic specification and the team of agents. We jointly reason about the assignment of agents to subteams and the decomposition of formulas using a satisfiability modulo theories (SMT) approach. The output of the SMT is then distributed to subteams and leads to a significant speed up in planning time. We include computational results to evaluate the efficiency of our solution, as well as the trade-offs introduced by the conservative nature of the SMT encoding.