\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{t5\_tdgroup (TMasCxQ8ASh25XtxPZqyBvvqsg9tGxA5P1n)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_tdgroup : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\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 $ r1\_tdgroup : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tdgroup : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_analoaf : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tdgroup : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v12\_vectsp\_1~X0){\unicdcdcdhd}\\
((v1\_tdgroup~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))))){\unicdbdjdcd}((u1\_struct\_0~(k2\_tdgroup~\\
X0)=u1\_struct\_0~X0){\unicdcdcdhd}(u1\_analoaf~(k2\_tdgroup~X0)=k1\_tdgroup~\\
X0))\end{array}
\label{hyp:ehedpfeheghgchpgfhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_tdgroup~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)))))\end{array}
\label{hyp:egehpflgbdpfeheghgchpgfhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v12\_vectsp\_1~X0){\unicdcdcdhd}\\
((v1\_tdgroup~X0){\unicdcdcdhd}(l2\_algstr\_0~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}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_tdgroup~X0~X1~X2~X3~X4){\unicdbdjded}\\
(k4\_tarski~(k4\_tarski~X1~X2)~(k4\_tarski~X3~X4) \in u1\_analoaf~(k2\_tdgroup~\\
X0)))))))\end{array}
\label{hyp:egedpfeheghgchpgfhah}
\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~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}((X1=k1\_tdgroup~X0){\unicdbdjded}({\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}((k4\_tarski~(k4\_tarski~X2~X3)~(k4\_tarski~X4~\\
X5) \in X1){\unicdbdjded}(k1\_algstr\_0~X0~X2~X5=k1\_algstr\_0~X0~X3~X4))))))))\end{array}
\label{hyp:egcdpfeheghgchpgfhah}
\end{equation}
\begin{theorem}\label{thm:ehfdpfeheghgchpgfhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v12\_vectsp\_1~X0){\unicdcdcdhd}\\
((v1\_tdgroup~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_tdgroup~X0~X1~X2~X3~X4){\unicdbdjded}\\
(k1\_algstr\_0~X0~X1~X4=k1\_algstr\_0~X0~X2~X3))))))\end{array}$$
\end{theorem}
\end{document}
