\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{t41\_qc\_lang2 (TMdud3CgsYfTAKCy2HhCRV2M6YxJEmgCEBD)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_qc\_lang2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}((\preoh v2\_qc\_lang1~(k12\_qc\_lang1~X0)~\\
X0){\unicdcdcdhd}((\preoh v3\_qc\_lang1~(k12\_qc\_lang1~X0)~X0){\unicdcdcdhd}((\preoh v4\_qc\_lang1~(k12\_qc\_lang1~\\
X0)~X0){\unicdcdcdhd}((\preoh v5\_qc\_lang1~(k12\_qc\_lang1~X0)~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k9\_qc\_lang1~X0)){\unicdbdjdcd}((\preoh (v2\_qc\_lang1~X1~X0){\unicdcdcdhd}(v3\_qc\_lang1~X1~X0)){\unicdcdcdhd}\\
((\preoh (v2\_qc\_lang1~X1~X0){\unicdcdcdhd}(v4\_qc\_lang1~X1~X0)){\unicdcdcdhd}((\preoh (v2\_qc\_lang1~\\
X1~X0){\unicdcdcdhd}(v5\_qc\_lang1~X1~X0)){\unicdcdcdhd}((\preoh (v3\_qc\_lang1~X1~X0){\unicdcdcdhd}(v4\_qc\_lang1~\\
X1~X0)){\unicdcdcdhd}((\preoh (v3\_qc\_lang1~X1~X0){\unicdcdcdhd}(v5\_qc\_lang1~X1~X0)){\unicdcdcdhd}(\preoh (v4\_qc\_lang1~\\
X1~X0){\unicdcdcdhd}(v5\_qc\_lang1~X1~X0))))))))))))\end{array}
\label{hyp:ehcdadpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k12\_qc\_lang1~X0)~(\\
k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgbdcdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}((v5\_qc\_lang1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k9\_qc\_lang1~\\
X0)){\unicdcdcdhd}(X1=k15\_qc\_lang1~X0~X2~X3)))))\end{array}
\label{hyp:egcdbdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}((v4\_qc\_lang1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k9\_qc\_lang1~X0)){\unicdcdcdhd}(X1=k14\_qc\_lang1~\\
X0~X2~X3)))))\end{array}
\label{hyp:egcdadpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}((r1\_qc\_lang2~\\
X0~X1~X2){\unicdbdjded}(\preoh (X2{\unicdcdgdad}k13\_qc\_lang1~X0~X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k9\_qc\_lang1~X0)){\unicdbdjdcd}((X2{\unicdcdgdad}k14\_qc\_lang1~X0~X1~X3){\unicdcdcdhd}(X2{\unicdcdgdad}k14\_qc\_lang1~\\
X0~X3~X1))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)){\unicdbdjdcd}(X2{\unicdcdgdad}k15\_qc\_lang1~X0~X3~X1)))))))\end{array}
\label{hyp:egbdjdpfbhdgpfmgbgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}((v3\_qc\_lang1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~\\
X0)){\unicdcdcdhd}(X1=k13\_qc\_lang1~X0~X2))))\end{array}
\label{hyp:egbdjdpfbhdgpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfbhdgpfmgbgoghgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}(\preoh r1\_qc\_lang2~X0~X1~(k12\_qc\_lang1~X0)))\end{array}$$
\end{theorem}
\end{document}
