help determine where main trunk runs

Hello. I am trying to determine where the main trunk of my waste line runs.

Almost all of the items are marked in their approximate location on my sketch. If you look in the link here image here

• You will note a few things, the main stack goes into my foundation under my stairs on the western wall. A drain my furnace drains to 2 feet away.
• There is already a 4” stub for a toilet and (I assume) its corresponding vent at 2 feet diagonal from that coming out of the floor.
• The washer and dryer are located on the eastern wall, with vent and drain.
• Lastly, the cleanout for my house is in my front yard, one level up.

Not marked on sketch:

• I am thinking that the trunk runs from the cleanout to the main stack, cutting left at the last few feet.

Considering I do not do this for a living, and looking at the placement of the other pieces of the puzzle, would anyone be able to give me their ideas. I am not afraid of hard work. I am planning the remodel of my basement. I have been contemplating renting an electric jackhammer and trenching my basement floor so that I can plumb a new shower, toilet and sink (in red).

Please excuse the any incorrect terminology.