How are Multiple Connectors Processed?

The query builder parses query terms from the left to the right. 

Use parentheses to group complex search phrases connected with Boolean connectors and other operators.

E.g.: (("Iran and Iraq") AND (USA NEAR/5 China)) OR ((Syria NEAR/3 Hezbollah) AND ("Russian Arms Supplies"))

This query asks for documents that have satisfied the conditions in first double parentheses OR have satisfied the conditions within the second set of double parentheses.