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?

Using COUNTIFS

=SUMPRODUCT(((A2:A10="User")*(D2:D10="A")*(E2:E10=9))/COUNTIFS(A2:A10;A2:A10&"";C2:C10;C2:C10&"";D2:D10;D2:D10&"";E2:E10;E2:E10&""))

more traditional would be an Array

=SUM(IF(FREQUENCY(IF((A2:A10="user")*(D2:D10="A")*(E2:E10=9);MATCH(C2:C10;C2:C10;0));ROW(C2:C10)-ROW(C2)+1)>0;1))
confirmed with CTRL + SHIFT + ENTER

in both cases note limited ranges - both are inefficient