How to create a flag column that identifies a scheduling conflict

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I am trying to create a checkbox column that gets checked when the conditions of a formula are met. Essentially, I am trying to flag a row if someone is assigned to that row who already has an assignment for that same date AND if the start and end times overlap.

Example:

Interpreter= John; Date= 6/1/2025; Start Time= 8:00 AM; End Time = 10:00 AM

Now if John is assigned to another row that has Date= 6/1/2025; Start Time=9:00 AM; End Time= 10:00 AM, then the conflict column should be checked. I also understand that both rows will be checked which is fine.

I first created column to change my start and end time to military format which I got from another community post:

=VALUE((VALUE(LEFT([Start Time]@row , FIND(":", [Start Time]@row ) - 1)) - IF(VALUE(LEFT([Start Time]@row , FIND(":", [Start Time]@row ) - 1)) = 12, 12, 0) + IF(RIGHT([Start Time]@row , 2) = "pm", 12, 0)) + MID([Start Time]@row , FIND(":", [Start Time]@row ) + 1, 2))

***(I had also tried a more simple TIME([Start Time]@row , 1, 2) but I realize that the new column I am trying to create might not work well with the semicolons)

Here is the formula I am using to indicate if there is a conflict:

=IF([Conflict Override]@row = 1, 0, IF(Interpreter@row <> "", IF(COUNTIFS(ReqID:ReqID, ReqID@row , [Start Date]:[Start Date], [Start Date]@row , [Military End Times]:[Military End Times], @cell >= [Military Start Times]@row , [Military Start Times]:[Military Start Times], @cell <= [Military End Times]@row ) > 1, 1), ""))

Now, I am not sure how to explain this next part because it doesn't make sense to me but, the above formula works for the whole sheet only when the Military Start Times and Military End Times is NOT a column formula AND is ONLY in the first row. In fact, the conflict is being checked correctly for rows where the military time columns do not have data.

Any help would be appreciated.

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