Alignment of item number in list containing a minipage

This may be solved with \valign

\newcommand{\MyMiniPage}{%
  \leavevmode\vtop{\hrule height 0pt \kern-\baselineskip
  \valign{\vfill##\vfill\cr
    \hbox to 1in{$\begin{aligned}
    a &= b\\
    c &= d
  \end{aligned}$\hfill}\cr
  \hbox to1in{$\begin{aligned}
    y &= z
  \end{aligned}$\hfill}\cr}}
}

I put everything into a \vtop, where I care to set the first line aligned with the \item; then it's just a "trivial" \valign. :)

--- Added after having seen the example ---

In the case of an included standalone file the approach is different:

\documentclass{standalone}

\usepackage{standalone}
\usepackage{paralist}

\newcommand{\iteminput}[2][\topskip-1bp]{%
  \leavevmode\vtop{\hrule height 0pt\kern-\dimexpr#1\relax
    \input{#2}}}

\usepackage{mathtools}
\usepackage{nccmath} % Removing fixes align, but changes spacing
\begin{document}
\input{ListsProblem-Minipage.tex}  % These two correctly yields
\input{ListsProblem-Minipage.tex}  % the desired 4 columns

\begin{enumerate}[(a)]
    \item First item
    \item \iteminput{ListsProblem-Minipage.tex}
    \item Third item
\end{enumerate}
\end{document}

The command \iteminput has an optional argument in case the default back up in the \vtop is not correct

\iteminput[<dimension>]{filename}