Time ordering in correlation function in QFT

In Peskin and Shroeder, "An Introduction to Quantum Field theory", chapter 4, the author derives the 2 point correlation function:

$$langle Omega|P{phi(x)phi(y)}|Omega rangle = lim_{Trightarrow infty(1-iepsilon)} frac{langle 0|P left [U(T,x^0)phi_I(x)U(x^0,y^0)phi_I(y)U(y^0,-T)right ]|0rangle}{langle 0 | U(T,-T)|0rangle }, tag{1}$$

where $P$ is the time ordering operator and $U(t,t’)$ is the evolution operator $$U(t,t’) =expleft { -i int_t^{t’}dt H_I(t)right }
= lim_{Trightarrow infty(1-iepsilon)} frac{langle 0|P left [phi_I(x)phi_I(y)expleft { -i int_T^Tdt H_I(t)right }right ]|0rangle}{langle 0 | expleft { -i int_T^Tdt H_I(t)right }|0rangle }. tag{2}$$

My question is how do the various U() factors like $U(T,x^0)$, $U((x^0,y^0)$ and $U(y^0,T)$ simplify to a final $expleft { -i int_T^Tdt H_I(t)right }$ in the numerator from Eq. 1 to Eq. 2?

My problem is that $U()$ does not commute with $phi_I$, so, for example, one cannot really shift $U(T,x^0)$ to the right of $phi_I(x)$ in Eq. 1. $x^0$ is the $0^{th}$ component of $x$, and hence $U(T,x^0)$ and $phi_I(x)$ are at the same time $x^0$, and thus the time ordering operator $P$ cannot be used to shift $U(T,x^0)$ to the right of $phi_I(x)$. To my understanding, time ordering can be used to shiit terms only if they are at different times (according to their time sequence)