\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{t79\_group\_6 (TMKY3WNR8i1ZepxTEdmscFkArr89DWSYpXy)}
\maketitle
Let $ v2\_struct\_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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k8\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_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}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_group\_6~\\
X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((r2\_group\_6~(k5\_group\_6~X1~(k9\_group\_6~\\
X1~X0~X2))~(k10\_group\_6~X1~X0~X2)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~\\
(u1\_struct\_0~(k10\_group\_6~X1~X0~X2))){\unicdcdcdhd}((v1\_group\_6~X3~(k5\_group\_6~\\
X1~(k9\_group\_6~X1~X0~X2))~(k10\_group\_6~X1~X0~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~\\
X1~X0~X2)))~(u1\_struct\_0~(k10\_group\_6~X1~X0~X2)))))))){\unicdcdcdhd}((v3\_funct\_2~\\
X3~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~\\
(k10\_group\_6~X1~X0~X2))){\unicdcdcdhd}(r1\_funct\_2~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~(k10\_group\_6~X1~X0~X2))~X2~(k1\_partfun1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~\\
X2)))~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~\\
(k10\_group\_6~X1~X0~X2))~(k8\_group\_6~X1~(k9\_group\_6~X1~X0~X2))~X3)))))))\end{array}
\label{hyp:mgjdbdpfhgchpgfhahpfgd}
\end{equation}
\begin{theorem}\label{thm:ehhdjdpfhgchpgfhahpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_group\_6~\\
X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~\\
(k10\_group\_6~X1~X0~X2))){\unicdcdcdhd}((v1\_group\_6~X3~(k5\_group\_6~X1~(k9\_group\_6~\\
X1~X0~X2))~(k10\_group\_6~X1~X0~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~\\
(u1\_struct\_0~(k10\_group\_6~X1~X0~X2)))))))){\unicdcdcdhd}((v3\_funct\_2~X3~(u1\_struct\_0~\\
(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~(k10\_group\_6~\\
X1~X0~X2))){\unicdcdcdhd}(r1\_funct\_2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~(k10\_group\_6~X1~X0~X2))~X2~(k1\_partfun1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~\\
(k5\_group\_6~X1~(k9\_group\_6~X1~X0~X2)))~(u1\_struct\_0~(k10\_group\_6~\\
X1~X0~X2))~(k8\_group\_6~X1~(k9\_group\_6~X1~X0~X2))~X3))))))\end{array}$$
\end{theorem}
\end{document}
