Show that the following arguments are valid using inference rules:

$($a$)$ phar$\frac{r}{b}ar(q),p(r^{{?}^{?}}{s}^{{?}^{?}}t)\frac{,}{b}ar(s)\frac{,}{b}ar(t)|--q|$

$($b$)(p^{{?}^{?}}q)r,(\frac{?}{\text{b}\text{a}\text{r}}(q)v\frac{v}{b}ar(t))s,(\frac{?}{\text{b}\text{a}\text{r}}(s{)}^{{?}^{?}}u),$pharr$(\frac{?}{\text{b}\text{a}\text{r}}(u)vvt)|--r|$

$($c$)\frac{?}{\text{b}\text{a}\text{r}}(q)p,q(svvt),u\frac{}{b}ar(s),u\frac{,}{b}ar(t)|--p|$

$($d$)(\frac{?}{\text{b}\text{a}\text{r}}(p)v\frac{v}{b}ar(q))(r^{{?}^{?}}s),rw\frac{,}{b}ar(w)|--p|$