The original story about the woodcutter is cruel.
The honest woodcutter only claimed the old axe because it was indeed his and left the lake after thanking the goddess for returning his axe to him. After returning to the village, he told about his experience to the villagers, where another woodcutter thought of a devious idea.
The cunning woodcutter brought his own old axe to the lake, dropped it, and faked his tears to imitate the honest woodcutter. The goddess of the lake similarly appeared with the gold axe, the silver axe, and his old axe, where he claimed that he had dropped all of them. The goddess gave all three axes to the cunning woodcutter, and he left the place with glee. However, he soon got tired because the axes were two heavy for him to carry, which made him slip his footing while crossing a bridge. Thus, the cunning woodcutter drowned to death.