\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{t7\_gr\_cy\_2 (TMTFqGKBbfTv1GjCo7Q26tqitCoJqPt1W8F)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_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 $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_group\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_gr\_cy\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_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}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
k5\_numbers){\unicdcdcdhd}(X2=k5\_group\_1~X0~X3~X1))){\unicdbdjded}(X0=k5\_group\_4~X0~(k6\_domain\_1~\\
(u1\_struct\_0~X0)~X1))))\end{array}
\label{hyp:ehgdpfhgchpfdgjhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~X2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehedcdpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k5\_group\_4~X0~(k6\_domain\_1~(u1\_struct\_0~\\
X0)~X2)=k5\_group\_4~X1~(k6\_domain\_1~(u1\_struct\_0~X1)~X3))))))\end{array}
\label{hyp:ehddpfhgchpfdgjhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v15\_algstr\_0~\\
X1){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}((v1\_gr\_cy\_1~X0){\unicdbdjdcd}(v1\_gr\_cy\_1~X1)))\end{array}
\label{hyp:ehcdadpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(((v15\_algstr\_0~X1){\unicdcdcdhd}\\
(m1\_group\_2~X1~X0)){\unicdcdcdhd}((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)))){\unicdbdjdcd}\\
(r1\_group\_2~X0~X1~X1)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1))))\end{array}
\label{hyp:egehpfngbdpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_gr\_cy\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(g3\_algstr\_0~(u1\_struct\_0~X0)~(u2\_algstr\_0~\\
X0)=k5\_group\_4~X0~(k6\_domain\_1~(u1\_struct\_0~X0)~X1))))\end{array}
\label{hyp:eghdpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}(v3\_group\_1~\\
X1))\end{array}
\label{hyp:dgdgbdpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v15\_algstr\_0~X0){\unicdbdjdcd}(X0=g3\_algstr\_0~\\
(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdfdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdpfhgchpfdgjhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(((v8\_struct\_0~X0){\unicdcdcdhd}(X0=k5\_group\_4~X0~(k6\_domain\_1~\\
(u1\_struct\_0~X0)~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~\\
X2~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdcdcdhd}(r1\_group\_2~\\
X0~X2~(k5\_group\_4~X0~(k6\_domain\_1~(u1\_struct\_0~X0)~(k5\_group\_1~\\
X0~X3~X1))))))))\end{array}$$
\end{theorem}
\end{document}
