Figure $5\mathrm{.}14$ depicts a part of the actual DS$1$ engine design. To achieve thrust in an engine, fuel and oxidizer must be injected. The whole design is highly redundant to ensure its operation even in the presence of multiple failures $($mainly stuck or inoperative valves$).$ Note that whether the valves are black or white, and whether or not they have a bar, are irrelevant for this question.

Each valve can be ok $($or not$)$ and can be open $($or not$).$ The aim of this question is to axiomatize the domain so that we can do two tasks.

$($a$)$ Given an observation of the lack of thrust in an engine and given which valves are open, using consistency$-$based diagnosis, determine what could be wrong.

$($b$)$ Given the goal of having thrust and given the knowledge that some valves are ok$,$ determine which valves should be opened.

For each of these tasks, you must think about what the clauses are in the knowledge base and what is assumable.

The atoms should be of the following forms:

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is true if valve

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is open. Thus the atoms should be

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is true if valve

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is working properly.

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is true if the output of valve

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is pressurized with gas. You should assume that

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and

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are true.

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is true if engine

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has thrust.

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is true if no thrust exists in either engine.

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is true if there is no thrust.

To make this manageable, only write rules for the input into engine

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$.$ Test your code using AIPython or Prolog on a number of examples.