The best way is not to touch the main layout files, instead it is best to create your own theme with only one local.xml layout file, as described here. To remove links from the top menu, you need to add these lines to the local.xml file:
<default>
<reference name = "top.links">
<remove name = "checkout_cart_link" />
</reference>
</default>
I believe that this will remove the statement and links to my links in the top menu. If this does not work, try changing top.links to topLinks , as in page.xml it is declared as = "topLinks"
<reference name = "topLinks">
<remove name = "checkout_cart_link" />
</reference>
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