Craftsman LT4000 spitting/sputtering and backfiring after riding for 5mins

[EngineMan]

the fuel solenoif does not stop the engine normally.
the magneto cut out stops the engine.
The fuel solenoid blocks off the main jet to prevent toxic unburned fuel vapours from ending all life on earth Oh and making the exhaust go bang.

That is true, so he needs to check the kill side of things ie (wiring) key switch.

 

[gregjo1948]

When it sputters and stops, pull off the gas line after the pump & before the carb, (aim it away from hot parts) crank it over to see if it's pumping fuel. If it's not, could be faulty pump or the hose that pulls vacuum from the valve cover. gregjo1948