# What can't guarded fragment of FO express?

I have some basic confusions about the definition of the guarded fragment of first-order logic. Hopefully someone can tell me where I'm wrong.

GF in FO is defined by:

1. Atomic formulas, $$x=y$$ and $$R(x_1,...,x_n)$$, are guarded formulas.
2. If $$\phi,\psi$$ are guarded formulas, so are $$\neg \phi$$ and $$\phi \wedge \psi$$.
3. For variables $$\{x_j,...,x_m\} \subseteq \{x_i,...,x_n\}$$ and guarded fomula $$\phi$$ and atomic formula $$A$$, $$\exists x_j\ A(x_i,...,x_n) \wedge \phi(x_j,...,x_m)$$ is a guarded formula.

My reasoning is: for arbitrary FO formula of form $$\exists x\ \phi$$, I can just pick some relation $$T$$ that's always true and over all variables, and it's then equivalent to $$\exists x \ T \wedge \phi$$, a guarded formula. Other forms follow from this. So FO reduces to GF.

But that's obviously not true. I can't figure out where my mistake is. Could someone let me know where I got it wrong?

For example, isn't $$\forall x\ \exists y\ \forall z\ \phi$$ equivalent to $$\forall x\ (T \to \exists y\ (T \wedge \forall z\ (T \to \phi)))$$