Count unique values based on several criteria

My formula is

=COUNTIFS(A:A;"User";D:D;"A";E:E;"9")

It counts the number of entries with these values. Now I need to exclude the entries for which the value in column C is duplicate. Please see the sample workbook.
In this case, the value in C2 should be counted, however, other entries with "a1" in column C with the same user, date and type should be excluded as duplicates. G2 should return 3 instead of 4.

Any tips?