Which answer correctly fills in the blanks in the correct order?

Preliminary Definitions:

Suppose that $S$ is some ethical standard such as the principle of utility $($it doesn't have to be that particular standard$).$ Let $F$ be the conjunction of all true factual claims about the world $-$ a complete world state description. Let $O$ be a purely normative claim $-$ an 'ought' claim. Suppose that the following claim is true:

$1.)O$ is deducible from the conjunction of $S$ and $F.$

Hume's Guillotine tells us that:

HG$)$ It is not possible to logically deduce a purely normative claim from any purely factual claims.

Thus, it follows that:

$2.)$ It is not the case that $O$ is deducible from $F.$

From $1$ and $2,$ it follows that:

$3.)$ It is not the case that $S$ is deducible from $F.$

To deduce $3$ from $1$ and $2$ by the indirect proof strategy $),$ suppose that the negation of $3$ is true:

$4.)S$ is deducible from $F.$

It is a logical truth that:

$5.)F$ is deducible from $F.$

By $,$ it follows from $5$ that:

$6.)$ The conjunction of $S$ and $F$ is deducible from $F.$

From $6$ and $1,$ it logically follows from $6$ by $$ that:

$7.)O$ is deducible from $F.$

Thus, we have a contradiction in the conjunction of $2$ and $7.$ Thus, a contradiction lolgically follows from the assumption of $4.$ Thus, $4$ is false. But $3$ is the negation of $4,$ so $3$ must be true.