\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{t4\_grsolv\_1 (TMS163ShfwknU2y4tgVR6tKjVwfttV9Ef3e)}
\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\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k10\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\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 .  ((v15\_algstr\_0~\\
X1){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~\\
X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~X3~X2){\unicdcdcdhd}(\\
m1\_group\_6~X3~X0~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}(m1\_group\_2~\\
X4~X0)){\unicdbdjdcd}((r1\_group\_2~X0~X4~(k10\_group\_2~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_group\_3~X5~X4){\unicdcdcdhd}(m1\_group\_6~X5~X0~X4)){\unicdbdjdcd}(\preoh (X5=k10\_group\_2~\\
X0~X1~X3){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_group\_2~X6~(k5\_group\_6~X2~X3)){\unicdbdjdcd}(\preoh r1\_group\_6~\\
(k5\_group\_6~X4~X5)~X6)))))))))\end{array}
\label{hyp:ehddpfhgchdhpgmgghpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_6~X2~X0~X1){\unicdbdjdcd}(m1\_group\_2~X2~X0))\end{array}
\label{hyp:egehpfngbdpfhgchpgfhahpfgd}
\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}((m1\_group\_2~X1~X0){\unicdcdcdhd}\\
(m1\_group\_2~X2~X0))){\unicdbdjdcd}(k10\_group\_2~X0~X1~X2=k10\_group\_2~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdadpfhgchpgfhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedpfhgchdhpgmgghpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v15\_algstr\_0~\\
X1){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~\\
X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~X3~X2){\unicdcdcdhd}(\\
m1\_group\_6~X3~X0~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}(m1\_group\_2~\\
X4~X0)){\unicdbdjdcd}((r1\_group\_2~X0~X4~(k10\_group\_2~X0~X2~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_group\_3~X5~X4){\unicdcdcdhd}(m1\_group\_6~X5~X0~X4)){\unicdbdjdcd}(\preoh (X5=k10\_group\_2~\\
X0~X3~X1){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_group\_2~X6~(k5\_group\_6~X2~X3)){\unicdbdjdcd}(\preoh r1\_group\_6~\\
(k5\_group\_6~X4~X5)~X6)))))))))\end{array}$$
\end{theorem}
\end{document}
