$.$ Consider the following definite $($Horn$)-$clause KB:

Notation: $$: for all, $$: exists, &: and, $=>$: implication, $<=>$: biconditional, ~: not

$$x$$y Smoker$($x$)$ & Friends$($y$,$x$)=>$ Smoker$($y$)$

$$x$$y Friends$($x$,$y$)=>$ Friends$($y$,$x$)$

Friends$($Adam$,$Betty$)$

Friends$($Carl$,$David$)$

Friends$($Eddie$,$Adam$)$

Friends$($Eddie$,$David$)$

Smoker$($Eddie$)$:

Answer: Are Betty, Carl smokers? Show your work.

Assume we perform forward$-$chaining starting from this KB $($with all of the rules and facts already loaded$)$ and show the specific conclusions added in their exact order as rules are matched and fired. Assume rules and facts are always matched in the exact order given above and that newly inferred facts are immediately added to the end of the list.