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You beat a dead horse when you are trying to get an impossible goal, when you continue fighting a lost battle or keep arguing after a final decision has been made. A similar expression is to try to get water out of a dry well.
In ancient Rome, a playwright Plautus used this expression in one of his plays in the year 195 B.C. In it, a farmer whipped a dead horse so as to make it move a heavy load. This situation teaches us that sometimes we try to get worthless pursuits.