\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{t133\_abcmiz\_1 (TMdj9ATFqGU7iZEhvyernwsj3ZRRRp1YydB)}
\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 $ v1\_funct\_1 : {{\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 $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ k34\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k56\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k35\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ m4\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k55\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k36\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k30\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k32\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k33\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}\\
((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_abcmiz\_1~X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpfngbdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((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)))))){\unicdbdjdcd}\\
(m4\_abcmiz\_1~(k55\_abcmiz\_1~X0~X1)~X0~(k28\_abcmiz\_1~X0))\end{array}
\label{hyp:egehpflgfdfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_abcmiz\_1){\unicdcdcdhd}((v1\_instalg1~\\
X1){\unicdcdcdhd}((v1\_abcmiz\_1~X1){\unicdcdcdhd}((v3\_abcmiz\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))))){\unicdbdjdcd}\\
(m1\_abcmiz\_1~(k35\_abcmiz\_1~X0~X1)~X1~(k14\_abcmiz\_1~X1))\end{array}
\label{hyp:egehpflgddfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k14\_abcmiz\_1~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdedpfbgcgdgngjgkhpfbd}
\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_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}(k56\_abcmiz\_1~X0~X1~X2=k3\_funct\_2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k55\_abcmiz\_1~\\
X0~X1)~X2)))\end{array}
\label{hyp:eggdbdpfbgcgdgngjgkhpfbd}
\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m4\_abcmiz\_1~X2~X0~(k28\_abcmiz\_1~X0)){\unicdbdjdcd}((X2=k55\_abcmiz\_1~\\
X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k2\_abcmiz\_1){\unicdbdjdcd}(((X3 \in k1\_relset\_1~\\
k2\_abcmiz\_1~X1){\unicdbdjdcd}(k3\_funct\_2~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~\\
X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~\\
X0~(k28\_abcmiz\_1~X0))))~X2~(k35\_abcmiz\_1~X3~X0)=k1\_funct\_1~X1~X3)){\unicdcdcdhd}\\
((\preoh X3 \in k1\_relset\_1~k2\_abcmiz\_1~X1){\unicdbdjdcd}(k3\_funct\_2~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~(k35\_abcmiz\_1~X3~X0)=\\
k35\_abcmiz\_1~X3~X0)))){\unicdcdcdhd}(({\unicdcdadad} X3 .  ((v2\_abcmiz\_1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_trees\_4~X4~(k3\_card\_3~(\\
u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_trees\_4~X5~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~\\
X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~X0)){\unicdbdjdcd}(((k3\_finseq\_1~X4=\\
k3\_finseq\_1~(k1\_msualg\_1~X0~X3)){\unicdcdcdhd}(X5=k11\_lang1~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X4~X2)){\unicdbdjdcd}(k3\_funct\_2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~(k36\_abcmiz\_1~\\
X0~X3~X4)=k36\_abcmiz\_1~X0~X3~X5))))){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_abcmiz\_1~\\
X3~X0~(k13\_abcmiz\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~(k30\_abcmiz\_1~X0~(k32\_abcmiz\_1~\\
X0)~X3)=k30\_abcmiz\_1~X0~(k32\_abcmiz\_1~X0)~(k3\_funct\_2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~X3))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_abcmiz\_1~X3~X0~(k13\_abcmiz\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_abcmiz\_1~X4~X0~(k12\_abcmiz\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~X2~(k31\_abcmiz\_1~\\
X0~(k33\_abcmiz\_1~X0)~X3~X4)=k31\_abcmiz\_1~X0~(k33\_abcmiz\_1~X0)~(\\
k3\_funct\_2~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))~X2~X3)~(k3\_funct\_2~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~\\
X0~(k28\_abcmiz\_1~X0))))~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~\\
X0~(k28\_abcmiz\_1~X0))))~X2~X4))))))))))\end{array}
\label{hyp:eggdadpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddddpfbgcgdgngjgkhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_abcmiz\_1~(k34\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_abcmiz\_1){\unicdbdjdcd}((X2 \in k1\_relset\_1~k2\_abcmiz\_1~\\
X1){\unicdbdjdcd}(k56\_abcmiz\_1~X0~X1~(k35\_abcmiz\_1~X2~X0)=k1\_funct\_1~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
