Years ago I saw a toilet that was installed in a basement of a home that was converted from a septic tank to city sewer service and the drain remained at 4' above the basement floor. This friend of mine installed a flush up toilet (I believe it was a McPferson). This toilet worked in two stages. When flushing was required. The first stage was the desinigration stage where a jet action broke down all the solids and the final stage was the syphoning stage where it was pulled up through a 3/4" copper drain into the elevated sewer pipe without the use of a check valve in the line. The only drawback was that this special toilet would not work in a residence where a well was the water source because it had to have a constant 35-40 psi to function. I believe it used about 11/2 gal per flush. Sounds unbelieveable but I saw it with my own eyes. Grey water from the sink or a shower are easy to pump up into the elevated drain.