How to prove that predicate is expressible?

Question

I have to prove, that predicate "x is transposition" in $S_5$ group. I can use such symbols, as *, 1, -1, =. However, I don't know any algorithm or way, which can to prove this statement.

Answer 1

Andre Nicolas has deleted his answer, but you I think you could do this as $x*x=1$, $x \ne 1$, and there exists $y$ such that $y*y*y=1$, $y \ne 1$, and $x*y=y*x$.