Christening record for Alice Caine shows mother's name as Susanna. The first female grand child is named Susanna. Father's name is Anthony.
The image associated with the marriage record source below does shows birth records, not marriage records.
Sources
England Marriages, 1538–1973 , database, FamilySearch (https://familysearch.org/ark:/61903/1:1:NFV8-BMH : 10 December 2014), Solomon Cundy and Alice Kane, 12 Jan 1718; citing St. Dennis, Cornwall, England, reference item 14 p 62; FHL microfilm 1,595,485.
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