\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}
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\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{t11\_qc\_lang3 (TMLPgyqPMpgGgqXGguLxAiNhLbknDGXnqgV)}
\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 $ v5\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k24\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k18\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ k1\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X3 : \\
\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X4 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X7 .  \\
{\unicdcdadad} X8 .  (({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k9\_qc\_lang1~X8)){\unicdbdjdcd}({\unicdcdadad} X10 .  \\
(m1\_subset\_1~X10~X7){\unicdbdjdcd}((X10=X6~X9){\unicdbdjded}({\unicdcdaddd} X11 .  ((v1\_funct\_1~\\
X11){\unicdcdcdhd}((v1\_funct\_2~X11~(k9\_qc\_lang1~X8)~X7){\unicdcdcdhd}(m1\_subset\_1~X11~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_qc\_lang1~X8)~X7))))){\unicdcdcdhd}((X10=k3\_funct\_2~\\
(k9\_qc\_lang1~X8)~X7~X11~X9){\unicdcdcdhd}({\unicdcdadad} X12 .  (m1\_subset\_1~X12~(k9\_qc\_lang1~\\
X8)){\unicdbdjdcd}({\unicdcdadad} X13 .  (m1\_subset\_1~X13~X7){\unicdbdjdcd}({\unicdcdadad} X14 .  (m1\_subset\_1~\\
X14~X7){\unicdbdjdcd}(((X12=k12\_qc\_lang1~X8){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~X8)~\\
X7~X11~X12=X5)){\unicdcdcdhd}(((v2\_qc\_lang1~X12~X8){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~\\
X8)~X7~X11~X12=X4~X12)){\unicdcdcdhd}((((v3\_qc\_lang1~X12~X8){\unicdcdcdhd}(X13=k3\_funct\_2~\\
(k9\_qc\_lang1~X8)~X7~X11~(k18\_qc\_lang1~X8~X12))){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~\\
X8)~X7~X11~X12=X3~X13)){\unicdcdcdhd}((((v4\_qc\_lang1~X12~X8){\unicdcdcdhd}((X13=k3\_funct\_2~\\
(k9\_qc\_lang1~X8)~X7~X11~(k19\_qc\_lang1~X8~X12)){\unicdcdcdhd}(X14=k3\_funct\_2~\\
(k9\_qc\_lang1~X8)~X7~X11~(k20\_qc\_lang1~X8~X12)))){\unicdbdjdcd}(k3\_funct\_2~(\\
k9\_qc\_lang1~X8)~X7~X11~X12=X2~X13~X14)){\unicdcdcdhd}(((v5\_qc\_lang1~X12~X8){\unicdcdcdhd}\\
(X13=k3\_funct\_2~(k9\_qc\_lang1~X8)~X7~X11~(k22\_qc\_lang1~X8~X12))){\unicdbdjdcd}\\
(k3\_funct\_2~(k9\_qc\_lang1~X8)~X7~X11~X12=X1~X12~X13)))))))))))))){\unicdcdcdhd}\\
(v5\_qc\_lang1~X0~X8)){\unicdbdjdcd}(X6~X0=X1~X0~(X6~(k22\_qc\_lang1~X8~X0)))\end{array}
\label{hyp:dhhdpfbhdgpfmgbgoghgdd}
\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~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}\\
((X2=k24\_qc\_lang1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0))))))){\unicdcdcdhd}((X2=k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0))~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}(((X4=k12\_qc\_lang1~\\
X0){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~\\
X3~X4=k1\_subset\_1~(k3\_qc\_lang1~X0))){\unicdcdcdhd}(((v2\_qc\_lang1~X4~X0){\unicdbdjdcd}(\\
k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~X3~\\
X4=k23\_qc\_lang1~X0~(k17\_qc\_lang1~X0~X4))){\unicdcdcdhd}((((v3\_qc\_lang1~X4~\\
X0){\unicdcdcdhd}(X5=k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0))~X3~(k18\_qc\_lang1~X0~X4))){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~\\
(k3\_qc\_lang1~X0))~X3~X4=X5)){\unicdcdcdhd}((((v4\_qc\_lang1~X4~X0){\unicdcdcdhd}((X5=k3\_funct\_2~\\
(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~X3~(k19\_qc\_lang1~\\
X0~X4)){\unicdcdcdhd}(X6=k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0))~X3~(k20\_qc\_lang1~X0~X4)))){\unicdbdjdcd}(k3\_funct\_2~(k9\_qc\_lang1~X0)~(\\
k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~X3~X4=k4\_subset\_1~(k3\_qc\_lang1~\\
X0)~X5~X6)){\unicdcdcdhd}(((v5\_qc\_lang1~X4~X0){\unicdcdcdhd}(X5=k3\_funct\_2~(k9\_qc\_lang1~\\
X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~X3~(k22\_qc\_lang1~X0~X4))){\unicdbdjdcd}(\\
k3\_funct\_2~(k9\_qc\_lang1~X0)~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))~X3~\\
X4=k7\_subset\_1~(k3\_qc\_lang1~X0)~X5~(k1\_tarski~(k21\_qc\_lang1~X0~\\
X4))))))))))))))))\end{array}
\label{hyp:mgedpfbhdgpfmgbgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k24\_qc\_lang1~X0~X1)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0)))\end{array}
\label{hyp:egehpflgcdedpfbhdgpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbhdgpfmgbgoghgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}((v5\_qc\_lang1~X1~X0){\unicdbdjdcd}(k24\_qc\_lang1~X0~X1=k7\_subset\_1~(k3\_qc\_lang1~\\
X0)~(k24\_qc\_lang1~X0~(k22\_qc\_lang1~X0~X1))~(k1\_tarski~(k21\_qc\_lang1~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
