\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=}
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\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{t62\_gfacirc1 (TMYKkWEaxaUwifwNaW8U9ARxR7zZTF7Ztgq)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_gfacirc1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k23\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k24\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboolean : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xboolean : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\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 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k3\_xboolean~\\
(k10\_xboolean~X0~X1)=k10\_xboolean~(k3\_xboolean~X0)~X1))\end{array}
\label{hyp:ehhdedpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k4\_gfacirc1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k6\_margrel1){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}(((X4=k1\_funct\_1~X3~\\
X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~X3~X2))){\unicdbdjdcd}((k1\_twoscomp~\\
(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~(k5\_facirc\_1~(k22\_gfacirc1~\\
X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~(k24\_gfacirc1~X0~X1~X2)=\\
k2\_binarith~(k2\_binarith~X4~(k9\_margrel1~X5))~(k9\_margrel1~X6)){\unicdcdcdhd}\\
((k1\_funct\_1~(k5\_facirc\_1~(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k4\_gfacirc1)=\\
k2\_binarith~X4~(k9\_margrel1~X5)){\unicdcdcdhd}((k1\_funct\_1~(k5\_facirc\_1~(\\
k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X0=X4){\unicdcdcdhd}(\\
(k1\_funct\_1~(k5\_facirc\_1~(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~\\
X0~X1~X2)~X3~np\_\_2)~X1=X5){\unicdcdcdhd}(k1\_funct\_1~(k5\_facirc\_1~(k22\_gfacirc1~\\
X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~X2=X6))))))))))\end{array}
\label{hyp:ehgdbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}(k9\_margrel1~X0=k3\_xboolean~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(k2\_binarith~X0~X1=k10\_xboolean~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}(m1\_subset\_1~(k9\_margrel1~\\
X0)~k6\_margrel1)\end{array}
\label{hyp:egehpflgjdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(m1\_subset\_1~(k2\_binarith~X0~X1)~k6\_margrel1)\end{array}
\label{hyp:egehpflgcdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xboolean~X0){\unicdcdcdhd}(v1\_xboolean~X1)){\unicdbdjdcd}(\\
k10\_xboolean~X0~X1=k10\_xboolean~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdadpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k6\_margrel1}})}{\unicdbdjdcd}{({{v1\_xboolean}~{X0}})}}}\label{hyp:dgdgcdpfngbgchhgchfgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k4\_gfacirc1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k6\_margrel1){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}(((X4=k1\_funct\_1~X3~\\
X0){\unicdcdcdhd}((X5=k1\_funct\_1~X3~X1){\unicdcdcdhd}(X6=k1\_funct\_1~X3~X2))){\unicdbdjdcd}(k1\_twoscomp~\\
(k22\_gfacirc1~X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~(k5\_facirc\_1~(k22\_gfacirc1~\\
X0~X1~X2)~(k23\_gfacirc1~X0~X1~X2)~X3~np\_\_2)~(k24\_gfacirc1~X0~X1~X2)=\\
k9\_margrel1~(k2\_binarith~(k2\_binarith~X4~(k9\_margrel1~X5))~X6)))))))\end{array}$$
\end{theorem}
\end{document}
