Answer sounds like you are going to need to install a sump for the sink to drain into and then you put a sump pump at the bottom and connect it into the houses main line.
Follow this with two short stubs of pipe and two 45 degree elbows to move the discharge riser back to the wall. From the remaining opening in the box lid, use a similar arrangement to bring the vent pipe up from the box and back to the wall (Photo 13). Note the lid gasket for the vent opening is sized to the hub of the fitting.
Finish up the sink-to-sump assembly by trimming the sink's tailpiece to length and joining it to the sump box with a 1 1/2-in. Trap (Photo 14). The trickiest part of running the remainder of the piping is identifying an existing vent that you can tap.
Vents can take many forms, but to the uninitiated, they generally have the look of pipes that don't do anything. In the case of a basement bath or any other secondary stack in the basement, the vent is the piping that extends upward from the drain tee of the fixture. Where no basement drains are present, a vent for upstairs fixtures will often take off just below the toilet tee on a full-sized stack and disappear into an upstairs wall.
Expect these vents to be 1 1/2 to 2 in. In our case, we tapped the vent serving a first-floor bath that was located next to the primary stack. While the location for each vent may be different, the connections won't vary much.
As far as making the cuts is concerned, a hacksaw will cut plastic, copper and galvanized iron.
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