\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{t32\_cohsp\_1 (TMTGkCzMnqocigFqUemEYw6iYQgTGvMLfJv)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(k4\_tarski~X1~X2 \in k5\_cohsp\_1~X0){\unicdbdjded}((v1\_finset\_1~X1){\unicdcdcdhd}((X1 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(X2 \in k1\_funct\_1~X0~X1))))\end{array}
\label{hyp:ehcdedpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_classes1~\\
(k9\_xtuple\_0~X0)){\unicdbdjdcd}((v8\_cohsp\_1~X0){\unicdbdjded}((v3\_cohsp\_1~(k9\_xtuple\_0~\\
X0)){\unicdcdcdhd}((v6\_cohsp\_1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X1 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}((X2 \in k1\_funct\_1~X0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \preoh (v1\_finset\_1~X3){\unicdcdcdhd}((\\
r1\_tarski~X3~X1){\unicdcdcdhd}(X2 \in k1\_funct\_1~X0~X3)))))))))\end{array}
\label{hyp:ehcdbdpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(v1\_relat\_1~(k7\_cohsp\_1~\\
X0))\end{array}
\label{hyp:ggdgjdpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (k4\_tarski~X2~X3 \in X0){\unicdbdjdcd}(k4\_tarski~X2~X3 \in X1)))\end{array}
\label{hyp:egddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_classes1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in X0){\unicdcdcdhd}\\
(r1\_tarski~X2~X1)){\unicdbdjdcd}(X2 \in X0))\end{array}
\label{hyp:egbdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k7\_cohsp\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  (\\
X2=k4\_tarski~X3~X4){\unicdcdcdhd}((X3 \in k9\_xtuple\_0~X0){\unicdcdcdhd}((X4 \in k1\_funct\_1~X0~\\
X3){\unicdcdcdhd}({\unicdcdadad} X5 .  ((X5 \in k9\_xtuple\_0~X0){\unicdcdcdhd}((r1\_tarski~X5~X3){\unicdcdcdhd}(X4 \in \\
k1\_funct\_1~X0~X5))){\unicdbdjdcd}(X3=X5)))))))\end{array}
\label{hyp:egbdhdpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdgpgigdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v8\_cohsp\_1~X0))){\unicdbdjdcd}\\
((v1\_classes1~(k9\_xtuple\_0~X0)){\unicdbdjdcd}(r1\_tarski~(k7\_cohsp\_1~X0)~(\\
k5\_cohsp\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
