find Sum of # of days w/o counting overlapping days twice with multiple paramaters

I a was able to locate the below formula to count days without including the overlapping counts, however this only to only work for situations where the specific cell range is known. =SUM(1*(MMULT(((MIN(A2:A5)-ROW(A2)+ROW(OFFSET(A2,0,0,MAX(B2:B5)-MIN(A2:A5)+1,1)))>=TRANSPOSE(A2:A5))*((MIN(A2:A5)-ROW(A2)+ROW(OFFSET(A2,0,0,MAX(B2:B5)-MIN(A2:A5)+1,1)))<=TRANSPOSE(B2:B5)),C2:C5)>0))-1

I currently have 1000+ rows of start/end dates that belong to only about 200 unique "files". I am looking to do a vlookup from one sheet, where the file has one occurrence, to the sheet with all of the dates. Any thoughts on how to incorporate that look up?