MYKOLAYIVKA, Ukraine—For Ukraine's army, the two-day battle here last week was a breakthrough victory that forced pro-Russia rebels to abandon their nearby military stronghold of Slovyansk.

But in this small, impoverished town, residents are reeling from artillery strikes that destroyed homes and killed at least a dozen people, including retiree Viktor Fanailov and his wife, Emma, whose relatives say they are still looking for body parts amid the rubble.

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