Bathroom layout

We moved into a new home here a few months ago and I’m just starting to finish the basement. I started to frame it out and now I’m to the point the I need to figure out the layout of the bathroom so that I can frame it so a toilet, shower (or tub/shower) and vanity will fit. The problem is, I haven’t a clue what the builders had in mind when the put these pipes in place. Also I will lose some space when I go to put a 2X4 wall up about an inch away from the concrete wall. Any ideas on how to figure out my framing?

Here are some pics to help out with the visual.

The first T pipe is 9†away from concrete wall
The toilet is 14†away from concrete wall
The last is 35†away from wall
Side to side from T pipe to toilet is 15.5â€
And between Toilet and outer pipe is 28â€

It seems to me that the T pipe and the toilet is to close together as well as to close to the wall (especially when you frame it out)

Any help or direction would be gratefully appreciated!

The toilet requires a 12 " rough in and 30" wide centered on the drain.
Things aren't adding up too well as far as the lav sink and toilet go in any direction. I'm not too sure what the civil engineer overseeing the plumber was thinking...

To keep the toilet with a 12" rough-in, you could put strapping on the wall instead of building a standard studwall then install the drywall. If there are any electrical boxes on that wall, as long as you don't try to run lots of wires through any one, a shallow box should fit.

Is the mid-sized pipe 1.5" or 2"? Looks like it might be 1.5". If so, you can only put in a tub unless you tear things out - code requires a 2" line for a shower only.

There are no obvious vents, so that could also be a major problem. Each fixture should be vented. There are limits on wet venting - I don't know if what you have would work.

layout

None of the pipes work for a conventional layout, so you will have to get creative with your wall placement. AAV's do not work good for lower level plumbing.

Rent a jackhammer and put everything where you want it rather than settle and try to make that mess fit. Really, do it right and call the builder to ask him what the hell we was thinking when he did this or was he really thinking at all.