Define a recursive Prolog rule$($s$)$ remove$\_$them$($Lst$1,$ Lst$2,$ Result$)$ where Result is a list of the elements of the list Lst$1$ that do not appear in the list Lst$2.$

Write a Prolog rule clean$\_$list$/2$ where the first argument is a list and the $2$nd argument is a list of the numbers in the list. You will use this for #$2$ & #$3.$

For example:

$1-$ clean$\_$list$([1,$two,'three',four,$5,6],$X$).$

X $=[1,5,6].$

Write a Prolog rule get$\_$values$/2$ which replaces all sub$-$lists of the first argument with the sum of its elements.

For example:

get$\_$values$([[1,2],3,[4,5]],[3,3,9])$

In football, a touchdown is $6$ points, a field goal is $3$ points, a safety is $2$ points and an extra point is $1$ point. Also, the number of extra points must be less than or equal to the number of touchdowns. Write a prolog rule called fbscore$/5$ which has as arguments the number of touchdowns, field goals, safeties, extra points, and total points in a football game. For simplicity, you can assume that there is some maximum number of each type of scoring. You should not assume any particular variable is ground. For example:

fbscore$(7,2,1,5,$ X$).$

$\%$ X $=55.$

fbscore$($T$,$ F$,$ S$,$ X$,10).$

$\%$ T $=$ F$,$ F $=$ X$,$ X $=0,$

$\%$ S $=5.$

We flatten a list L by first removing all lists within L and replacing them with their members. Write a Prolog rule flattenit$/2$ which flattens a list. For example:

:$-$ flattenit$([$a$,$b$,$c$,[$d$,$e$],$f$,[$c$,$ a$,$ b$]],[$a$,$b$,$c$,$d$,$e$,$f$,$c$,$a$,$b$]).$

:$-$ flattenit$([1,2,3,4,[5,6,[7,8]]],[1,2,3,4,5,6,7,8]).$

:$-$ flattenit$([1,2,[3,4,[5,6],7],8,[2,4,5,8]],[1,2,3,4,5,6,7,8,2,4,5,8]).$

Note: there is a built$-$in called flatten $-$ you should not use that in your answer