Out of the at least five "tees" (or outlets?) on the drawing section provided, the one I guess the most "in the middle" of the image does not appear to be a "bullhead". If this is a plan view, and if this is drawn correctly, I agree however that tee branch or outlet does appear to be pointed "up".
By "bull head side" I'm going to assume that you mean "Branch outlet". The hidden lines are applied a bit inconsistently on the 4 tees you've highlighted, but the preponderance of the information on the drawing I would build all of them with the branch pointed up.
"Belief" is the acceptance of an hypotheses in the absence of data.
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You have 4x tees, the discharge branches of all four of the 4x tees are "up" in your plan view, hidden line dwg.
You also have two more problems:
1. Unless there is an elevation view to this pipe rack, your draftsman failed to specify how far "up" the the branch rises on the nbr 4 tee running to the right side before it goes back back down to its remaining horizontal run.
2. Your draftsman/checker/designer failed to specify how far "up" the vertical run (the pipe going to the cutoff valve blocking the "future run" of pipe coming out of the valve) is to be, what the height the center of the blocking valve is to be, and where the operator of that valve is to stand when he needs to open or close that valve. Looks like a butt-welded valve is the only thing possible per the sketch, but that allowed/required in the piping spec's for these lines?