Simple example of necessity logic

Simple example of necessity logic

B: Ensure a sufficient amount of heat
D: Buy a lighter
A: Start a campfire
A-C:Assumption(s)Injection(s)
1. Fuel is necessary to start a fire
C: Have fuel
D': Buy wood

In order to Start a campfire I must Ensure a sufficient amount of heat and in order to Ensure a sufficient amount of heat I must Buy a lighter. But, in order to Start a campfire I must also Have fuel and in order to Have fuel I must Buy wood. I can't both Buy a lighter and Buy wood.

RelationAssumption(s)Injection(s)
D-D'1. I don't have money to buy both.
2. I don't already have either wood or a lighter lying around.
3. I can't borrow money.
B-D1. I don't have matches.
2. I don't have a magnifying glass and/or the sun isn't shining.
3. I can't borrow a lighter/matches from someone.
C-D'1. I have nothing I can use as a fuel-source.
2. I can't get wood for free anywhere.
A-B1. Heat is necessary to start a fire
A-C1. Fuel is necessary to start a fire