$2.$ Consider the following $($not fully parenthesized$)$ formula, in the first$-$order language of arithmetic, where $0$ is a nonlogical constant symbol $($x$)$x$=0($x$)$x$=0(1)$

$($a$)$ Identify all the prime subformulae of the above, and display them by boxing as in $4\mathrm{.}1\mathrm{.}25$

$($b$)$ Using boxing indicate the Boolean abstraction of the formula

$($c$)$ Can you prove formula $(1)$ in predicate logic without the benefit of any nonlogical axioms that speak of $"0"?$