\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t12\_turing\_1 (TMPYfM1Wm8TUM5XKoWo97dmm3afAb7juybz)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ l1\_turing\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u5\_turing\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_turing\_1 : {{\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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k8\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_turing\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_turing\_1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~\\
k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(k9\_turing\_1~X2~(k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~\\
k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~\\
X2~X3)~X0)=k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~k4\_numbers~(\\
k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~X2~X3)~\\
X0)){\unicdbdjdcd}(k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~X2~X3)~X1=k8\_nat\_1~\\
(k3\_zfmisc\_1~(u2\_turing\_1~X2)~k4\_numbers~(k9\_funct\_2~k4\_numbers~\\
(u1\_turing\_1~X2)))~(k10\_turing\_1~X2~X3)~X0)))))\end{array}
\label{hyp:ehbdbdpfehfhchjgoghgpfbd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(m1\_subset\_1~(k8\_nat\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_turing\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k3\_zfmisc\_1~\\
(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~\\
X0))))){\unicdbdjdcd}((v1\_funct\_1~(k10\_turing\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k10\_turing\_1~\\
X0~X1)~k5\_numbers~(k3\_zfmisc\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~(k10\_turing\_1~X0~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k3\_zfmisc\_1~(u2\_turing\_1~\\
X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))))))))\end{array}
\label{hyp:egehpflgbdadpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_turing\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_zfmisc\_1~\\
(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~\\
X0)))){\unicdbdjdcd}(((k1\_mcart\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0))~X1{\unicdcdgdad}u5\_turing\_1~X0){\unicdbdjdcd}(k9\_turing\_1~\\
X0~X1=k3\_xtuple\_0~(k1\_mcart\_1~(u2\_turing\_1~X0)~(u1\_turing\_1~X0)~\\
(k8\_domain\_1~k1\_numbers~(k1\_real\_1~np\_\_1)~k6\_numbers~np\_\_1)~(\\
k8\_turing\_1~X0~X1))~(k2\_xcmplx\_0~(k7\_turing\_1~X0~X1)~(k6\_turing\_1~\\
X0~(k8\_turing\_1~X0~X1)))~(k5\_turing\_1~X0~(k3\_mcart\_1~(u2\_turing\_1~\\
X0)~k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X0))~X1)~(k7\_turing\_1~\\
X0~X1)~(k2\_mcart\_1~(u2\_turing\_1~X0)~(u1\_turing\_1~X0)~(k8\_domain\_1~\\
k1\_numbers~(k1\_real\_1~np\_\_1)~k6\_numbers~np\_\_1)~(k8\_turing\_1~X0~\\
X1))))){\unicdcdcdhd}((k1\_mcart\_1~(u2\_turing\_1~X0)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X0))~X1=u5\_turing\_1~X0){\unicdbdjdcd}(k9\_turing\_1~\\
X0~X1=X1))))\end{array}
\label{hyp:eggdpfehfhchjgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\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:ehbdcdpfehfhchjgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_turing\_1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~\\
k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(k1\_mcart\_1~(u2\_turing\_1~X2)~k4\_numbers~(k9\_funct\_2~k4\_numbers~\\
(u1\_turing\_1~X2))~(k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~k4\_numbers~\\
(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~X2~X3)~\\
X0)=u5\_turing\_1~X2)){\unicdbdjdcd}(k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~\\
k4\_numbers~(k9\_funct\_2~k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~\\
X2~X3)~X1=k8\_nat\_1~(k3\_zfmisc\_1~(u2\_turing\_1~X2)~k4\_numbers~(k9\_funct\_2~\\
k4\_numbers~(u1\_turing\_1~X2)))~(k10\_turing\_1~X2~X3)~X0)))))\end{array}$$
\end{theorem}
\end{document}
