\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{t31\_e\_siec (TMKCKBX6zprozn9tw6oa4pawJ86UC4GzCad)}
\maketitle
Let $ v2\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_e\_siec : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_xboole\_0~X0~X1=k5\_xboole\_0~X0~(k4\_xboole\_0~\\
X1~X0)\end{array}
\label{hyp:ehjdidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X2~X1)){\unicdbdjdcd}(r1\_tarski~(k2\_xboole\_0~X0~X2)~X1)\end{array}
\label{hyp:ehidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((r1\_tarski~(k13\_e\_siec~X0)~(k2\_zfmisc\_1~(k12\_e\_siec~X0)~(k12\_e\_siec~\\
X0))){\unicdcdcdhd}(r1\_tarski~(k14\_e\_siec~X0)~(k2\_zfmisc\_1~(k12\_e\_siec~X0)~\\
(k12\_e\_siec~X0))))\end{array}
\label{hyp:ehcdbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k4\_relat\_1~(k2\_xboole\_0~X0~X1)=k2\_xboole\_0~\\
(k4\_relat\_1~X0)~(k4\_relat\_1~X1)){\unicdcdcdhd}((k4\_relat\_1~(k3\_xboole\_0~X0~\\
X1)=k3\_xboole\_0~(k4\_relat\_1~X0)~(k4\_relat\_1~X1)){\unicdcdcdhd}(k4\_relat\_1~\\
(k6\_subset\_1~X0~X1)=k6\_subset\_1~(k4\_relat\_1~X0)~(k4\_relat\_1~X1)))\end{array}
\label{hyp:ehbdedpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{r1\_tarski}~{({{k4\_relat\_1}~{X0}})}}~{({{{k2\_zfmisc\_1}~{X0}}~{X0}})}}}\label{hyp:ehbdddpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~\\
(k4\_xboole\_0~X0~X2)~X1)\end{array}
\label{hyp:ehbdadjdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_e\_siec~X0){\unicdbdjdcd}((v2\_e\_siec~X0){\unicdbdjded}((r1\_tarski~(u1\_e\_siec~\\
X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}((r1\_tarski~\\
(u2\_e\_siec~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))){\unicdcdcdhd}\\
((k3\_relat\_1~(u1\_e\_siec~X0)~(u1\_e\_siec~X0)=u1\_e\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~\\
(u1\_e\_siec~X0)~(u2\_e\_siec~X0)=u1\_e\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~(u2\_e\_siec~\\
X0)~(u2\_e\_siec~X0)=u2\_e\_siec~X0){\unicdcdcdhd}(k3\_relat\_1~(u2\_e\_siec~X0)~(\\
u1\_e\_siec~X0)=u2\_e\_siec~X0)))))))\end{array}
\label{hyp:egbdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k17\_e\_siec~X0=k2\_xboole\_0~(k4\_xboole\_0~(k2\_xboole\_0~(u1\_e\_siec~\\
X0)~(u2\_e\_siec~X0))~(k4\_relat\_1~(u1\_struct\_0~X0)))~(k4\_relat\_1~\\
(k4\_xboole\_0~(u1\_struct\_0~X0)~(k10\_xtuple\_0~(u1\_e\_siec~X0)))))\end{array}
\label{hyp:egbdjdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
(k12\_e\_siec~X0=u1\_struct\_0~X0)\end{array}
\label{hyp:egbdedpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddbdpffgpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_e\_siec~X0){\unicdcdcdhd}((v3\_e\_siec~X0){\unicdcdcdhd}(l1\_e\_siec~X0))){\unicdbdjdcd}\\
((r1\_tarski~(k17\_e\_siec~X0)~(k2\_zfmisc\_1~(k12\_e\_siec~X0)~(k12\_e\_siec~\\
X0))){\unicdcdcdhd}(r1\_tarski~(k14\_e\_siec~X0)~(k2\_zfmisc\_1~(k12\_e\_siec~X0)~\\
(k12\_e\_siec~X0))))\end{array}$$
\end{theorem}
\end{document}
