We describe the first automatic approach for merging coreference annotations obtained from multiple annotators into a single gold standard. This merging is subject to certain linguistic hard constraints and optimization criteria that prefer solutions with minimal divergence from annotators. The representation involves an equivalence relation over a large number of elements. We use Answer Set Programming to describe two representations of the problem and four objective functions suitable for different datasets. We provide two structurally different real-world benchmark datasets based on the METU-Sabanci Turkish Treebank and we report our experiences in using the Gringo, Clasp, and Wasp tools for computing optimal adjudication results on these datasets.