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Two common approaches for automating IoT smart spaces are having users write rules using trigger-action programming (TAP) or training machine learning models based on observed actions. In this paper, we unite these approaches. We introduce and evaluate Trace2TAP, a novel method for automatically synthesizing TAP rules from traces (time-stamped logs of sensor readings and manual actuations of devices). We present a novel algorithm that uses symbolic reasoning and SAT-solving to synthesize TAP rules from traces. Compared to prior approaches, our algorithm synthesizes generalizable rules more comprehensively and fully handles nuances like out-of-order events. Trace2TAP also iteratively proposes modified TAP rules when users manually revert automations. We implemented our approach on Samsung SmartThings. Through formative deployments in ten offices, we developed a clustering/ranking system and visualization interface to intelligibly present the synthesized rules to users. We evaluated Trace2TAP through a field study in seven additional offices. Participants frequently selected rules ranked highly by our clustering/ranking system. Participants varied in their automation priorities, and they sometimes chose rules that would seem less desirable by traditional metrics like precision and recall. Trace2TAP supports these differing priorities by comprehensively synthesizing TAP rules and bringing humans into the loop during automation.