\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{t3\_abcmiz\_a (TMNKCNJvo9Vn99oKLMTURfvzH2QpncKk6kv)}
\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 $ v5\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ k35\_abcmiz\_1 : {{\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 $ k34\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k36\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ 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}(\preoh ({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k2\_abcmiz\_1){\unicdbdjdcd}(X1{\unicdcdgdad}k35\_abcmiz\_1~X2~X0)){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
((v2\_abcmiz\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_trees\_4~X3~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))~(k34\_abcmiz\_1~X0)){\unicdbdjdcd}(\preoh (k3\_finseq\_1~X3=k3\_finseq\_1~(k1\_msualg\_1~\\
X0~X2)){\unicdcdcdhd}(X1=k36\_abcmiz\_1~X0~X2~X3)))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m1\_abcmiz\_1~\\
X2~X0~(k13\_abcmiz\_1~X0)){\unicdbdjdcd}(X1{\unicdcdgdad}k30\_abcmiz\_1~X0~(k32\_abcmiz\_1~X0)~\\
X2)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_abcmiz\_1~X3~X0~(k12\_abcmiz\_1~X0)){\unicdbdjdcd}(X1{\unicdcdgdad}k31\_abcmiz\_1~X0~(k33\_abcmiz\_1~\\
X0)~X2~X3)))))))\end{array}
\label{hyp:ehfdddpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_4~X2~X0~X1){\unicdbdjded}(m1\_finseq\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfehchfgfgdhpfed}
\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}(k33\_abcmiz\_1~X0=k16\_abcmiz\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddddpfbgcgdgngjgkhpfbd}
\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}(k32\_abcmiz\_1~X0=k15\_abcmiz\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddcdpfbgcgdgngjgkhpfbd}
\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}\\
(\preoh v5\_abcmiz\_1~(k35\_abcmiz\_1~X0~X1)~X1~(k28\_abcmiz\_1~X1))\end{array}
\label{hyp:ggdgbdgdpfbgcgdgngjgkhpfbd}
\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}((\preoh v1\_xboole\_0~(k34\_abcmiz\_1~X0)){\unicdcdcdhd}\\
(v3\_trees\_3~(k34\_abcmiz\_1~X0)))\end{array}
\label{hyp:ggdgbdfdpfbgcgdgngjgkhpfbd}
\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}((m1\_abcmiz\_1~X1~\\
X0~(k13\_abcmiz\_1~X0)){\unicdcdcdhd}(m1\_abcmiz\_1~X2~X0~(k12\_abcmiz\_1~X0)))){\unicdbdjdcd}\\
(v5\_abcmiz\_1~(k31\_abcmiz\_1~X0~(k16\_abcmiz\_1~X0)~X1~X2)~X0~(k28\_abcmiz\_1~\\
X0))\end{array}
\label{hyp:ggdgbdedpfbgcgdgngjgkhpfbd}
\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}(m1\_abcmiz\_1~X1~X0~(k13\_abcmiz\_1~\\
X0))){\unicdbdjdcd}(v5\_abcmiz\_1~(k30\_abcmiz\_1~X0~(k15\_abcmiz\_1~X0)~X1)~X0~(\\
k28\_abcmiz\_1~X0))\end{array}
\label{hyp:ggdgbdddpfbgcgdgngjgkhpfbd}
\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}(((v2\_abcmiz\_1~X1~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdcdcdhd}(m1\_finseq\_1~X2~(k34\_abcmiz\_1~\\
X0)))){\unicdbdjdcd}((v5\_abcmiz\_1~(k36\_abcmiz\_1~X0~X1~X2)~X0~(k28\_abcmiz\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k36\_abcmiz\_1~X0~X1~X2)~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpflgddgdpfbgcgdgngjgkhpfbd}
\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}(m1\_subset\_1~(k34\_abcmiz\_1~X0)~(k1\_zfmisc\_1~\\
(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpflgddedpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}((v5\_abcmiz\_1~\\
X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_abcmiz\_1){\unicdbdjdcd}\\
(X1{\unicdcdgdad}k35\_abcmiz\_1~X2~X0))))\end{array}$$
\end{theorem}
\end{document}
