Solve $($d$)$ and $($e$)$ in as much detail as possible

Problem points$).$ Give proofs in natural deduction

of the following sequents $($where $P,Q$ and $F$ have arity $1,R$ has arity

$2,$ and $S$ has arity $0)$:

$($a$)$ AAxAAyR$(x,y)|--$EEzR$(z,z),$

$($b$)$ EEx$(P(x)S)|--$AAxP$(x)S,$

$($c$)$ EEx$(P(x)F(x)),$AAx$(P(x{)}^{{?}^{?}}Q(x))|--$AAxP$(x{)}^{{?}^{?}}$EExF$(x),$

$($d$)S$EExP$(x)|--$EEx$(SP(x)).$

$($e$)$ Russell's paradox