Reasoning across spacelike surfaces in the Frauchiger-Renner thought experiment

The Frauchiger-Renner argument purports to show that the standard framework of quantum mechanics yields a contradiction when used to reason about systems containing agents who are themselves using quantum mechanics to perform deductions. This has been framed as an obstacle to taking quantum mechanics to be a complete theory. I formalize the argument in two closely related ways and elucidate the source of the paradox, clarifying the flaw in the original argument.