For example, if A is lying, then B is telling the truth, and then C is lying. C is right about A but wrong about B, so this assumption holds.

If A is telling the truth, then B must be lying, C is telling the truth, but C is wrong, which shows that this assumption is not valid.

Besides, C can't tell the truth. If C is telling the truth, then A is lying, if A is lying, then B is telling the truth, but C is saying that B is lying, which is contradictory.

So: there is only one possibility, that is, A is lying, B is telling the truth, and C is lying.