González-Acuña's trivial Artin presentation conjecture

Let $A$) be an Artin $n$-presentation, meaning a presentation with generators $x_1,\ldots,x_n$ and relators $r_1,\ldots,r_n$ satisfying the Artin condition. Write $|A|$ for the group presented by $A$, and let $A\sim A'$ denote the equivalence relation defined using automorphisms of $S_n$ preserving the normal closure of $y_1,\ldots,y_n$. Let

$$T=(x_1,\ldots,x_n:x_1,\ldots,x_n).$$

González-Acuña's conjecture. If $A$ is an Artin $n$-presentation such that $|A|=1$, then $A\sim T$. This is one of the conjectures relating Artin presentations of the trivial group to the Poincaré conjecture. Since the source states that these conjectures are now theorems following Perelman's proof of the Poincaré conjecture, the claim is resolved.