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Given 2 Kripke structures M1 and M2, if there exists a simulation from M1 to M2 and a simulation from M2 to M1, is there a bisimulation from M1 to M2?

Yes your intuition is correct. The fact is that the 2 relations can be disjoint when considering just one-sided simulation relations but for bisimulation we need 1 relation with symmetry which is ...
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