\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t34\_midsp\_2 (TMZhz8wFVZPUxyGBHpajMDQ1z63GbDHmU3c)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_midsp\_2~X1~X0){\unicdcdcdhd}(l1\_midsp\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~(u1\_midsp\_2~X0~X1))){\unicdbdjdcd}((k9\_midsp\_2~X0~X1~X2~X2=k11\_midsp\_2~\\
X0~X1){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=k11\_midsp\_2~X0~X1){\unicdbdjdcd}(X2=X3)){\unicdcdcdhd}(\\
(k9\_midsp\_2~X0~X1~X2~X3=k4\_algstr\_0~(u1\_midsp\_2~X0~X1)~(k9\_midsp\_2~\\
X0~X1~X3~X2)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=k9\_midsp\_2~X0~X1~X4~X5){\unicdbdjdcd}(k9\_midsp\_2~\\
X0~X1~X3~X2=k9\_midsp\_2~X0~X1~X5~X4)){\unicdcdcdhd}(({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~(\\
u1\_midsp\_2~X0~X1))){\unicdbdjdcd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(k9\_midsp\_2~X0~X1~X9~X7=X8)))){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X3~X2=k9\_midsp\_2~\\
X0~X1~X4~X2){\unicdbdjdcd}(X3=X4)){\unicdcdcdhd}(((k3\_midsp\_1~X0~X2~X3=X4){\unicdbdjdcd}(k9\_midsp\_2~X0~\\
X1~X2~X4=k9\_midsp\_2~X0~X1~X4~X3)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X4=k9\_midsp\_2~\\
X0~X1~X4~X3){\unicdbdjdcd}(k3\_midsp\_1~X0~X2~X3=X4)){\unicdcdcdhd}(((k3\_midsp\_1~X0~X2~X3=k3\_midsp\_1~\\
X0~X4~X5){\unicdbdjdcd}(k9\_midsp\_2~X0~X1~X2~X5=k9\_midsp\_2~X0~X1~X4~X3)){\unicdcdcdhd}(((k9\_midsp\_2~\\
X0~X1~X2~X5=k9\_midsp\_2~X0~X1~X4~X3){\unicdbdjdcd}(k3\_midsp\_1~X0~X2~X3=k3\_midsp\_1~\\
X0~X4~X5)){\unicdcdcdhd}(((k9\_midsp\_2~X0~X1~X2~X3=X6){\unicdbdjdcd}(k10\_midsp\_2~X0~X1~X2~X6=\\
X3)){\unicdcdcdhd}((k10\_midsp\_2~X0~X1~X2~X6=X3){\unicdbdjdcd}(k9\_midsp\_2~X0~X1~X2~X3=X6)))))))))))))))))))\end{array}
\label{hyp:ehddddpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}\\
(l1\_midsp\_1~X0))){\unicdcdcdhd}((v4\_midsp\_2~X1~X0){\unicdcdcdhd}(l1\_midsp\_2~X1~X0))){\unicdbdjdcd}(\\
m1\_subset\_1~(k11\_midsp\_2~X0~X1)~(u1\_struct\_0~(u1\_midsp\_2~X0~X1)))\end{array}
\label{hyp:egehpflgbdbdpfngjgegdhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfngjgegdhahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_midsp\_2~X1~X0){\unicdcdcdhd}(l1\_midsp\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k10\_midsp\_2~X0~X1~X2~(k11\_midsp\_2~\\
X0~X1)=X2)))\end{array}$$
\end{theorem}
\end{document}
