Official solution
(p \[ \wedge \] (p \[\to\] q) \[\wedge\] (q \[\to\] r)) \[\to\] r
\[\equiv\] (p \[\wedge\] (\[\sim\] p \[\vee\] q) \[\vee\] (\[\sim\] q \[\vee\] r)) \[\to\] r
\[\equiv\] ((p \[\wedge\] q) \[\wedge\] (\[\sim\] p \[\vee\] r)) \[\to\] r
\[\equiv\] (p \[\wedge\] q \[\wedge\] r) \[\to\] r
\[\equiv\] \[\sim\] (p \[\wedge\] q \[\wedge\] r) \[\vee\] r
\[\equiv\] (\[\sim\] p) \[\vee\] (\[\sim\] q) \[\vee\] (\[\sim\] r) \[\vee\] r
\[\Rightarrow\] tautology