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The Goya work was an etching from the Los Caprichos series. The Dali work was his interpretation of Goya's etching, CNN reported.
Goya's image suffered a broken frame and glass, while the Dali work, had damage to the image itself, as well as a broken frame and glass, CNN reported.
The paintings have been sent to experts to see how badly they were damaged, Metro reported.
The Ministry of Internal Affairs said the women touched the display by accident when they tried to take a photo with the art behind them.
Yekaterinburg officials have refused to open a criminal case against the women, despite a written request from the center's deputy director requesting justice for the paintings, CNN reported.