\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{t32\_yellow14 (TMHCRUyExPYBZVMupfoXJ5j7hsbUNJ7MnQC)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_yellow14 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel18 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X1 \in X0){\unicdbdjdcd}(k1\_funct\_1~(k2\_funcop\_1~\\
X0~X2)~X1=X2)\end{array}
\label{hyp:ehhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_waybel\_3~X2){\unicdcdcdhd}(v1\_waybel18~X2)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k3\_waybel18~X0~X2))){\unicdbdjdcd}\\
(k5\_card\_3~X1~(k2\_pre\_topc~(k3\_waybel18~X0~X2)~(k6\_domain\_1~(u1\_struct\_0~\\
(k3\_waybel18~X0~X2))~X3))=k2\_pre\_topc~(k4\_waybel18~X0~X2~X1)~(k6\_domain\_1~\\
(u1\_struct\_0~(k4\_waybel18~X0~X2~X1))~(k5\_waybel18~X0~X2~X3~X1))))))\end{array}
\label{hyp:ehddbdpfjhfgmgmgpghhbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_funcop\_1}~{X0}}~{X1}}={{{k2\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}((v4\_waybel\_3~X1){\unicdcdcdhd}(v1\_waybel18~X1)))))){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_struct\_0~(k3\_waybel18~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(k5\_waybel18~X0~X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v4\_waybel\_3~X1){\unicdcdcdhd}(v1\_waybel18~X1)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}\\
(k4\_waybel18~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdcdcdhd}(\\
(m1\_subset\_1~X2~(u1\_struct\_0~(k3\_waybel18~X0~(k7\_funcop\_1~X0~X1)))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}(k2\_yellow14~X0~X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfjhfgmgmgpghhbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_pre\_topc~X1){\unicdbdjdcd}(v1\_waybel18~(k2\_funcop\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgjdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_struct\_0~X1)){\unicdbdjdcd}\\
(v4\_waybel\_3~(k2\_funcop\_1~X0~X1))\end{array}
\label{hyp:ggdgidpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k2\_funcop\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~\\
(k2\_funcop\_1~X0~X1)~X0){\unicdcdcdhd}((v1\_funct\_1~(k2\_funcop\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(k2\_funcop\_1~X0~X1)~X0)))\end{array}
\label{hyp:ggdgcdadpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{v4\_relat\_1}~{({{{k2\_funcop\_1}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ggdgbdhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_funcop\_1~X0~X1=k2\_zfmisc\_1~X0~(k1\_tarski~\\
X1)\end{array}
\label{hyp:egcdpfggfhogdgpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfjhfgmgmgpghhbded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k3\_waybel18~\\
X0~(k7\_funcop\_1~X0~X2)))){\unicdbdjdcd}(k5\_card\_3~X1~(k2\_pre\_topc~(k3\_waybel18~\\
X0~(k7\_funcop\_1~X0~X2))~(k6\_domain\_1~(u1\_struct\_0~(k3\_waybel18~\\
X0~(k7\_funcop\_1~X0~X2)))~X3))=k2\_pre\_topc~X2~(k6\_domain\_1~(u1\_struct\_0~\\
X2)~(k2\_yellow14~X0~X2~X3~X1))))))\end{array}$$
\end{theorem}
\end{document}
