How to adjust long (multiline equation) in two columns using IEEEtrans class

Question

Following the answer given here, I am trying to adjust long multiline equations. However, when I try to add more equations, the solution doesn't seems to be working in my case. I want an output something like that:

(I have obtained it via \documentclass[preview]{standalone}. However, now I want to embed it in IEEEtrans class.

\documentclass[lettersize,journal]{IEEEtran}
\usepackage{mathtools,amssymb,lipsum}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\usepackage{cuted}
\setlength\stripsep{3pt plus 1pt minus 1pt}
\usepackage{empheq}
\title{equation}
\begin{document}
\section{equations}
\begin{strip}
  \begin{align}
   \begin{gathered}
\textbf{R(Reg_S)} = {} \forall X1 \in x1 \wedge \forall X3 \in x3 ; | ; \  X3[1] \coloneqq X1[1]  \wedge X3[3] \coloneqq X1[3] \wedge  X3[4] \coloneqq X1[4] \wedge X3[5]

\coloneqq X1[6] \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
   \end{gathered}
   \begin{gathered}
\textbf{R(Reg_S)} = {} \forall X1 \in x1 \wedge \forall X3 \in x3 ; | ; \  X3[1] \coloneqq X1[1]  \wedge X3[3] \coloneqq X1[3] \wedge  X3[4] \coloneqq X1[4] \wedge X3[5]

\coloneqq X1[6] \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
   \end{gathered}
   \begin{gathered}
\textbf{R(Reg_S)} = {} \forall X1 \in x1 \wedge \forall X3 \in x3 ; | ; \  X3[1] \coloneqq X1[1]  \wedge X3[3] \coloneqq X1[3] \wedge  X3[4] \coloneqq X1[4] \wedge X3[5]

\coloneqq X1[6] \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
   \end{gathered}
  \end{align}
\end{strip}
\maketitle
\end{document}

Answer 1

You can fit equations in a column with a mix of align and split. However, because 1 column really has little space, I had to do a trick with \mathrlap and \hspace. You can also make them span two columns and have more flexibility in formatting.

Below is code that demonstrate both cases. I chose \wedge as a point of split but you have to decide what's best for clarity.

Here's the code:

\documentclass[letterpaper,journal]{IEEEtran}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{cuted}
\usepackage{empheq}
\usepackage{kantlipsum}
\setlength\stripsep{3pt plus 1pt minus 1pt}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\title{Equation}
\author{Name Name}
\begin{document}
\maketitle
\section{Equations}
\kant[1]:
\begin{align}
  \begin{split}
    \mathrlap{\mathbf{R(Reg_S)} = \forall X1 \in x1}
    & \
    & \hspace{2em} \begin{aligned}[t]
                     & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \
                     & \wedge X3[3] \coloneqq X1[3] \
                     & \wedge  X3[4] \coloneqq X1[4] \
                     & \wedge X3[5] \coloneqq X1[6] \
                     & \wedge {x3}' \coloneqq x3 \
                     & \cup {X3[1], X3[3], X3[4], X3[5]} 
                   \end{aligned}
  \end{split} \
  \begin{split}
    \mathrlap{\mathbf{R(Reg_S)} = \forall X1 \in x1}
    & \
    & \hspace{2em} \begin{aligned}[t]
                     & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \
                     & \wedge X3[3] \coloneqq X1[3] \
                     & \wedge X3[4] \coloneqq X1[4] \
                     & \wedge X3[5] \coloneqq X1[6] \
                     & \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]}
                   \end{aligned}
  \end{split} \
  \begin{split}
    \mathrlap{\mathbf{R(Reg_S)} = \forall X1 \in x1}
    & \
    & \hspace{2em} \begin{aligned}[t]
                     & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \
                     & \wedge X3[3] \coloneqq X1[3] \
                     & \wedge X3[4] \coloneqq X1[4] \
                     & \wedge X3[5] \coloneqq X1[6] \
                     & \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
                   \end{aligned}
  \end{split}
\end{align}
\kant[2-5]
\begin{strip}
  \begin{align}
    \begin{split}
      \mathbf{R(Reg_S)} = \forall X1 \in x1
      & \begin{aligned}[t]
          & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \wedge X3[3] \coloneqq X1[3] \wedge  X3[4] \coloneqq X1[4] \wedge X3[5] \coloneqq X1[6] \
          & \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
        \end{aligned}
    \end{split} \
    \begin{split}
      \mathbf{R(Reg_S)} = \forall X1 \in x1
      & \begin{aligned}[t]
          & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \wedge X3[3] \coloneqq X1[3] \wedge X3[4] \coloneqq X1[4] \wedge X3[5] \coloneqq X1[6] \
          & \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]}
        \end{aligned}
    \end{split} \
    \begin{split}
      \mathbf{R(Reg_S)} = \forall X1 \in x1
      & \begin{aligned}[t]
          & \wedge \forall X3 \in x3 ; | ; X3[1] \coloneqq X1[1] \wedge X3[3] \coloneqq X1[3] \wedge X3[4] \coloneqq X1[4] \wedge X3[5] \coloneqq X1[6] \
          & \wedge {x3}' \coloneqq x3 \cup {X3[1], X3[3], X3[4], X3[5]} 
        \end{aligned}
    \end{split}
  \end{align}
\end{strip}
\kant[6-8]
\end{document}

The screenshot

Since split breaks column continuation, such that text continues in the next column before the split, I'd personally prefer to put an equation in one column or either at the top or bottom of a page--for the latter case, a package stfloats might be of help.