\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{t12\_substut1 (TMUjCFmy5t394ygWCtTpWkbNqRBfdqvNSd8)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_substut1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k20\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k25\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k24\_substut1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  (m1\_qc\_lang1~X1){\unicdbdjdcd}((({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k6\_qc\_lang1~\\
X1)~(k8\_qc\_lang1~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v3\_card\_1~X4~X2){\unicdcdcdhd}(m2\_finseq\_1~\\
X4~(k2\_qc\_lang1~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_substut1~\\
X1)){\unicdbdjdcd}(X0~(k17\_substut1~X1~X3~X4~X5)))))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k16\_substut1~X1)){\unicdbdjdcd}((v2\_substut1~X2~X1){\unicdbdjdcd}(X0~X2))){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k16\_substut1~X1)){\unicdbdjdcd}((X0~X2){\unicdbdjdcd}(X0~(k20\_substut1~\\
X1~X2)))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k16\_substut1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k16\_substut1~X1)){\unicdbdjdcd}(((k19\_substut1~X1~X2=k19\_substut1~\\
X1~X3){\unicdcdcdhd}((X0~X2){\unicdcdcdhd}(X0~X3))){\unicdbdjdcd}(X0~(k21\_substut1~X1~X2~X3))))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k2\_qc\_lang1~X1)~(k3\_qc\_lang1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k16\_substut1~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_substut1~\\
X4~X1~(k25\_substut1~X1~X3~X2)){\unicdbdjdcd}(((v3\_substut1~(k25\_substut1~X1~\\
X3~X2)~X1){\unicdcdcdhd}(X0~X3)){\unicdbdjdcd}(X0~(k24\_substut1~X1~(k25\_substut1~X1~X3~X2)~\\
X4)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k16\_substut1~X1)){\unicdbdjdcd}\\
(X0~X2)))\end{array}
\label{hyp:dhbdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_qc\_lang1~\\
X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k8\_qc\_lang1~X1~X0))\end{array}
\label{hyp:ggdghdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k6\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdggdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_qc\_lang1~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~X2~(k8\_qc\_lang1~\\
X0~X1)){\unicdcdcdhd}(((v3\_card\_1~X3~X1){\unicdcdcdhd}(m1\_finseq\_1~X3~(k2\_qc\_lang1~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_substut1~X0)))))){\unicdbdjdcd}(v4\_substut1~(k17\_substut1~\\
X0~X2~X3~X4)~X0)\end{array}
\label{hyp:ggdgfdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k2\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgcdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(m1\_subset\_1~(k8\_qc\_lang1~X0~X1)~(k1\_zfmisc\_1~(k6\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgidpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_qc\_lang1~X0)~(k1\_zfmisc\_1~\\
(k2\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k16\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k3\_qc\_lang1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k25\_substut1~X0~X1~X2)~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~\\
X0)))\end{array}
\label{hyp:egehpflgcdfdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k2\_zfmisc\_1~(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdcdcdhd}(m1\_substut1~\\
X2~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k24\_substut1~X0~X1~X2)~(k16\_substut1~\\
X0))\end{array}
\label{hyp:egehpflgcdedpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k16\_substut1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k16\_substut1~X0)))){\unicdbdjdcd}(\\
m1\_subset\_1~(k21\_substut1~X0~X1~X2)~(k16\_substut1~X0))\end{array}
\label{hyp:egehpflgcdbdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k16\_substut1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k20\_substut1~X0~X1)~(k16\_substut1~X0))\end{array}
\label{hyp:egehpflgcdadpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((v7\_substut1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~\\
(k16\_substut1~X0)~(k3\_qc\_lang1~X0))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_substut1~\\
X3~X0~X2){\unicdcdcdhd}((X1=k24\_substut1~X0~X2~X3){\unicdcdcdhd}(v3\_substut1~X2~X0))))))\end{array}
\label{hyp:egcdidpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((v6\_substut1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k16\_substut1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k16\_substut1~X0)){\unicdcdcdhd}((X1=k21\_substut1~\\
X0~X2~X3){\unicdcdcdhd}(k19\_substut1~X0~X2=k19\_substut1~X0~X3))))))\end{array}
\label{hyp:egcdhdpfdhfhcgdhehfhehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}((v5\_substut1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k16\_substut1~\\
X0)){\unicdcdcdhd}(X1=k20\_substut1~X0~X2))))\end{array}
\label{hyp:egcdgdpfdhfhcgdhehfhehbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfdhfhcgdhehfhehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k16\_substut1~\\
X0)){\unicdbdjdcd}(\preoh (\preoh v2\_substut1~X1~X0){\unicdcdcdhd}((\preoh v4\_substut1~X1~X0){\unicdcdcdhd}((\preoh v5\_substut1~\\
X1~X0){\unicdcdcdhd}((\preoh v6\_substut1~X1~X0){\unicdcdcdhd}(\preoh v7\_substut1~X1~X0))))))\end{array}$$
\end{theorem}
\end{document}
