Electronic voting systems are among the most security critical distributed systems. Different trust concepts are implemented to mitigate the risk of conspiracies endangering security properties. These concepts render systems often very complex and end users no longer recognize whom they need to trust. Correspondingly, specific trust considerations are necessary to support users. Recently, resilience terms have been proposed in order to express, which entities can violate the addressed security properties in particular by illegal collaborations. However, previous works derived these resilience terms manually. Thus, successful attacks can be missed. Based on this approach, we propose a framework to formally and automatically derive these terms. Our framework comprises a knowledge calculus, which allows us to model knowledge and reason about knowledge of collaborating election entities. The introduced framework is applied to deduce previously manually derived resilience terms of three remote electronic voting systems, namely Polyas, Helios and the Estonian voting system. Thereby, we were able to discover mistakes in previous derivations.