\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{t21\_group\_7 (TMdadDKL9RaCggAFpz3zZBWgkN7Yz3DmUMg)}
\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 $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_group\_7 : {{\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}((v1\_relat\_1~(k10\_finseq\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_finseq\_1~X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((v1\_partfun1~(k10\_finseq\_1~\\
X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}((v1\_group\_7~(k10\_finseq\_1~X0~\\
X1)){\unicdcdcdhd}((v2\_group\_7~(k10\_finseq\_1~X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}\\
(v3\_group\_7~(k10\_finseq\_1~X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)))))))))\end{array}
\label{hyp:ehcdadpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))){\unicdbdjdcd}((v1\_relat\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_finseq\_1~\\
X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}((v1\_funct\_1~(k10\_finseq\_1~X0~\\
X1)){\unicdcdcdhd}((v1\_partfun1~(k10\_finseq\_1~X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}\\
((v1\_group\_7~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}(v4\_group\_7~(k10\_finseq\_1~\\
X0~X1)~(k2\_tarski~np\_\_1~np\_\_2))))))))\end{array}
\label{hyp:ehbdjdpfhgchpgfhahpfhd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfhgchpgfhahpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))))){\unicdbdjdcd}((v1\_relat\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_finseq\_1~\\
X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}((v1\_funct\_1~(k10\_finseq\_1~X0~\\
X1)){\unicdcdcdhd}((v1\_partfun1~(k10\_finseq\_1~X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}\\
((v1\_group\_7~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}((v2\_group\_7~(k10\_finseq\_1~\\
X0~X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}((v3\_group\_7~(k10\_finseq\_1~X0~\\
X1)~(k2\_tarski~np\_\_1~np\_\_2)){\unicdcdcdhd}(v4\_group\_7~(k10\_finseq\_1~X0~X1)~\\
(k2\_tarski~np\_\_1~np\_\_2))))))))))\end{array}$$
\end{theorem}
\end{document}
