I'm wondering if I can make the following transformation by universal instantiation of $x$ for $A(xyx)$?
$$\forall x \exists z F[A(xyx)z] \mapsto \exists z F[A(A(xyx)yA(xyx))z]$$
it feels kinda weird to transform something simple like $x$ into something with multiple parts like $A(xyx)$.... otherwise, I don't see any violation of rules.