My 13hp briggs and stratton model # 28m707 engine starts, runs for about 20 seconds and then stalls

Check the fuel solenoid if it has one. Its located directly in the bottom of the carburetor. Unscrew it and hook up the 2 wires to your battery. Every time you touch the wire on the battery terminal you should see it plung in. If it doesn't then you need a new one. If it does then it's obvious you have other issues. Like maybe remove Nd cleN your carburetor. Spark must be ok because it does fire up.

Try replacing fuel. Empty tank by disconnecting fuel line into carburetor. With tank empty, drain carburetor fuel bowl by loosening bowl nut. If there's a filter on the fuel line, replace. Retighten bowl nut, reattach fuel line and refill with fresh fuel.

If problem doesn't go away, a thorough carb cleaning is likely needed.