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This paper introduces a general framework for generate-and-test-based solvers for epistemic logic programs that can be instantiated with different generate and test programs, and it provides sufficient conditions on those programs for the correctness of the solvers built using this framework. It also introduces a new generator program that incorporates the propagation of epistemic consequences and shows that this can exponentially reduce the number of candidates that need to be tested while only incurring a linear overhead. We implement a new solver based on these theoretical findings and experimentally show that it outperforms existing solvers by achieving a ~3.3x speed-up and solving 87% more instances on well-known benchmarks.