No prescriptive right that might otherwise accrue to extract ground water shall arise or accrue to, nor shall any statute of limitations operate in regard to the ground water in the four counties after the year 1956 in favor of any person required to file a notice of extraction and diversion of water, until that person files with the board the first “Notice of Extraction and Diversion of Water” substantially in the form mentioned in Section 5002. As to each person who fails to file that notice by the end of the year in 1957, it shall be deemed for the period from that time until the first notice of the person is filed, that no claim of right to the extraction of ground water from any source in the four counties has been made by the person, and that water extracted by the person from the ground water source during that period has not been devoted to or used for any beneficial use. The beneficial use of water from any ground water source within the four counties in any year by the person shall be deemed not to exceed the quantity reported in the notice filed for that year.