Here is a schematic of the system:

Here is the cycle animated, springs are omitted for clarity:

Here are some step by step details of the cycle:

The system is shown here ready to fire. The fuel/air mixture is retained by a spring, while the pressure from the compressed air reservoir keeps the chamber exhaust valve closed as well as the ammunition feed locked.

Pulling the trigger ignites the fuel/air mixture and the overpressure pushes the firing chamber piston forward, allowing the gasses to escape and fire the projectile in the process. At the end of this travel, this piston pushes a switch that temporarily actives the 5/2 solenoid.

This shuts off the fuel (butane) feed while also venting the compressed air line. Return springs push the ammunition feed to the open position allowing a new projectile to load, as well as opening the chamber exhaust valve to vent any burned gasses. Once the solenoid is deactivated (through the operation of a capacitor relay) the compressed air feed is restored allowing the system to reset ready for another shot.
Here is the video of the prototype in action:
[youtube][/youtube]
Thanks to Hector for sharing the details and Kasia for the moral support
