You're requesting something that's very subjective. It doesn't look stuffed to me, as long as you're using the appropriate terminology and/or definitions. Perhaps using words instead of symbols will allow for things looking less stuffed:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\noindent
If the following two conditions hold:
\begin{enumerate}
\item $ (a, b_1) \in R \wedge (a, b_3) \in R \Rightarrow (a, b_2) \in R $
for all $ a \in S_i, b_1, b_2, b_3 \in S_j $ with $ b_1 < b_2 < b_3 $.
\item $ (a_1, b_2) \in R \wedge (a_2, b_1) \in R \Rightarrow (a_1, b_1) \in R \wedge (a_2, b_2) \in R $
for all $ a_1, a_2 \in S_i, b_1, b_2 \in S_j $ with $ a_1 < a_2 $ and $ b_1 < b_2 $.
\end{enumerate}
\noindent
If the following two conditions hold:
\begin{enumerate}
\item $\bigl( (a, b_1) \in R \bigr) \wedge \bigl( (a, b_3) \in R \bigr) \Rightarrow (a, b_2) \in R$
for all $a \in S_i$ and $b_1, b_2, b_3 \in S_j$ with $b_1 < b_2 < b_3$.
\item $\bigl( (a_1, b_2) \in R \bigr) \wedge \bigl( (a_2, b_1) \in R \bigr) \Rightarrow \bigl( (a_1, b_1) \in R \bigr) \wedge \bigl( (a_2, b_2) \in R \bigr)$
for all $ a_1, a_2 \in S_i$ and $b_1, b_2 \in S_j$ with $a_1 < a_2$ and $b_1 < b_2$.
\end{enumerate}
\noindent
If the following two conditions hold:
\begin{enumerate}
\item $\bigl( (a, b_1) \in R \bigr)$ and $\bigl( (a, b_3) \in R \bigr)$ implies that $(a, b_2) \in R$
for all $a \in S_i$ and $b_1, b_2, b_3 \in S_j$ with $b_1 < b_2 < b_3$.
\item $\bigl( (a_1, b_2) \in R \bigr)$ and $\bigl( (a_2, b_1) \in R \bigr)$ implies that $\bigl( (a_1, b_1) \in R \bigr)$ and $\bigl( (a_2, b_2) \in R \bigr)$
for all $ a_1, a_2 \in S_i$ and $b_1, b_2 \in S_j$ with $a_1 < a_2$ and $b_1 < b_2$.
\end{enumerate}
\end{document}
I'd advise against adjusting the inter-word spacing just for the sake of this list.
\documentclass{...}
, the required\usepackage
's,\begin{document}
, and\end{document}
. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – Thruston Mar 9 '16 at 17:47