\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{t50\_abcmiz\_a (TMYNhUCPD5XcwVwygYaFvUZrAQA4ojAQNA8)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ k34\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k56\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k65\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~\\
(k34\_abcmiz\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
(k56\_abcmiz\_1~X0~X3~(k56\_abcmiz\_1~X0~X2~X1)=k56\_abcmiz\_1~X0~(k65\_abcmiz\_1~\\
X0~X2~X3)~X1))))\end{array}
\label{hyp:ehbdedjdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~\\
X0){\unicdcdcdhd}((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_abcmiz\_1~\\
X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_abcmiz\_1~(k34\_abcmiz\_1~X0))))))){\unicdbdjdcd}((v1\_funct\_1~(k65\_abcmiz\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k65\_abcmiz\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_abcmiz\_1~(k34\_abcmiz\_1~X0)))))\end{array}
\label{hyp:egehpflggdfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))){\unicdbdjdcd}((r1\_abcmiz\_a~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_abcmiz\_1~\\
X0))))){\unicdcdcdhd}(X1=k56\_abcmiz\_1~X0~X3~X2)))))\end{array}
\label{hyp:egcdbdpfbgcgdgngjgkhpfbg}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}(((r1\_abcmiz\_a~X0~X1~\\
X2){\unicdcdcdhd}(r1\_abcmiz\_a~X0~X2~X3)){\unicdbdjdcd}(r1\_abcmiz\_a~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
