\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{t31\_midsp\_2 (TMaNRHcx5R3VxsRDZFhTrYskdHDXwZyS8ns)}
\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 $ k3\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_midsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((k3\_midsp\_1~X0~\\
X2~X3=k3\_midsp\_1~X0~X4~X5){\unicdbdjded}(k9\_midsp\_2~X0~X1~X2~X3=k1\_algstr\_0~(\\
u1\_midsp\_2~X0~X1)~(k9\_midsp\_2~X0~X1~X2~X4)~(k9\_midsp\_2~X0~X1~X2~X5))))))))\end{array}
\label{hyp:ehddadpfngjgegdhahpfcd}
\end{equation}
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 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k3\_midsp\_1~X0~X1~X2=X3){\unicdbdjded}(k8\_midsp\_1~X0~X1~\\
X3=k8\_midsp\_1~X0~X3~X2)))))\end{array}
\label{hyp:ehcdddpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_midsp\_1~X0)){\unicdcdcdhd}\\
(l1\_midsp\_2~X1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~(u1\_midsp\_2~X0~X1)){\unicdcdcdhd}(l2\_algstr\_0~\\
(u1\_midsp\_2~X0~X1)))\end{array}
\label{hyp:egehpffhbdpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~X0))){\unicdcdcdhd}((l1\_midsp\_2~X1~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(m1\_subset\_1~(k9\_midsp\_2~X0~X1~X2~X3)~(u1\_struct\_0~(u1\_midsp\_2~\\
X0~X1)))\end{array}
\label{hyp:egehpflgjdpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_midsp\_2~X0~X1=k1\_algstr\_0~\\
X0~X1~X1))\end{array}
\label{hyp:egbdpfngjgegdhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfngjgegdhahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_midsp\_2~X1~X0){\unicdcdcdhd}(l1\_midsp\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k3\_midsp\_1~X0~X2~X3=X4){\unicdbdjded}(k9\_midsp\_2~X0~X1~X2~X3=k1\_midsp\_2~(u1\_midsp\_2~\\
X0~X1)~(k9\_midsp\_2~X0~X1~X2~X4)))))))\end{array}$$
\end{theorem}
\end{document}
