\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{t51\_qc\_lang2 (TMMWqxoh6m4wB6ExKtNYPoy2AmhxyoDMwRy)}
\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k22\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}(\preoh (X1{\unicdcdgdad}k12\_qc\_lang1~X0){\unicdcdcdhd}((\preoh v2\_qc\_lang1~X1~X0){\unicdcdcdhd}((\preoh v3\_qc\_lang1~\\
X1~X0){\unicdcdcdhd}((\preoh v4\_qc\_lang1~X1~X0){\unicdcdcdhd}(\preoh v5\_qc\_lang1~X1~X0))))))\end{array}
\label{hyp:ehjdpfbhdgpfmgbgoghgbd}
\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}((v5\_qc\_lang1~\\
X1~X0){\unicdbdjdcd}((r1\_qc\_lang2~X0~X2~X1){\unicdbdjded}(X2=k22\_qc\_lang1~X0~X1)))))\end{array}
\label{hyp:ehfdadpfbhdgpfmgbgoghgcd}
\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}((v4\_qc\_lang1~\\
X1~X0){\unicdbdjdcd}((r1\_qc\_lang2~X0~X2~X1){\unicdbdjded}((X2=k19\_qc\_lang1~X0~X1){\unicdcdcdid}(X2=k20\_qc\_lang1~\\
X0~X1))))))\end{array}
\label{hyp:ehedjdpfbhdgpfmgbgoghgcd}
\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}((v3\_qc\_lang1~\\
X1~X0){\unicdbdjdcd}((r1\_qc\_lang2~X0~X2~X1){\unicdbdjded}(X2=k18\_qc\_lang1~X0~X1)))))\end{array}
\label{hyp:ehedidpfbhdgpfmgbgoghgcd}
\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}(\preoh (v2\_qc\_lang1~\\
X1~X0){\unicdcdcdhd}(r1\_qc\_lang2~X0~X2~X1))))\end{array}
\label{hyp:ehedhdpfbhdgpfmgbgoghgcd}
\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}(\preoh r1\_qc\_lang2~X0~X1~(k12\_qc\_lang1~X0)))\end{array}
\label{hyp:ehedbdpfbhdgpfmgbgoghgcd}
\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}(\preoh (v5\_qc\_lang1~X1~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~(k11\_qc\_lang1~\\
X0~X1))~(k3\_finseq\_1~(k11\_qc\_lang1~X0~(k22\_qc\_lang1~X0~X1))))))\end{array}
\label{hyp:ehbdgdpfbhdgpfmgbgoghgbd}
\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){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~(k11\_qc\_lang1~\\
X0~X1))~(k3\_finseq\_1~(k11\_qc\_lang1~X0~(k19\_qc\_lang1~X0~X1)))){\unicdcdcdhd}\\
(\preoh r1\_xxreal\_0~(k3\_finseq\_1~(k11\_qc\_lang1~X0~X1))~(k3\_finseq\_1~\\
(k11\_qc\_lang1~X0~(k20\_qc\_lang1~X0~X1)))))))\end{array}
\label{hyp:ehbdfdpfbhdgpfmgbgoghgbd}
\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}(\preoh (v3\_qc\_lang1~X1~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~(k11\_qc\_lang1~\\
X0~X1))~(k3\_finseq\_1~(k11\_qc\_lang1~X0~(k18\_qc\_lang1~X0~X1))))))\end{array}
\label{hyp:ehbdedpfbhdgpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfbhdgpfmgbgoghgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}(\preoh (r1\_qc\_lang2~\\
X0~X1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~(k11\_qc\_lang1~X0~X2))~(k3\_finseq\_1~\\
(k11\_qc\_lang1~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
