Please stop posting multiple short posts in a row, and just make your point, stringing along like this is not appreciated.

You have made a few mistakes so far:

1. You changed the sign of the exhaust velocity in the equation between equation 1 and 2.

2. If you want p in your equation 1 and 2 to represent the momentum of a rocket body, you need a term that accounts for the momentum that the propellant had before it was ejected.

3. A ship propeller displacing seawater is an example where there is an external force. There are forces between the water and the propeller, and the water is external to the system of interest.

4. Your equation 3 makes no sense, because Δm is undefined, you have used it both for an increment of an external medium, and for something in a diagram that you have not explained, but seems to represent a closed system.

5. Your postulate is contradicted by everything known about physics and every experiment ever performed.