\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{t26\_yellow\_6 (TMVBbVk56Em3tHKnDpCmH3g7NeuySVyx7j9)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_orders\_2 : {{\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 $ v6\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_yellow\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_yellow\_6~\\
X2~X0~X1){\unicdbdjdcd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
(v1\_partfun1~X2~X0)))))\end{array}
\label{hyp:egehpfngddpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_0~X1~X0){\unicdbdjdcd}\\
(l1\_orders\_2~X1))\end{array}
\label{hyp:egehpfmgbdpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v7\_waybel\_0~X1){\unicdcdcdhd}\\
(l1\_waybel\_0~X1~X0)))){\unicdcdcdhd}(m3\_yellow\_6~X2~(u1\_struct\_0~X1)~X0))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k8\_yellow\_6~X0~X1~X2)){\unicdcdcdhd}((v4\_orders\_2~(k8\_yellow\_6~\\
X0~X1~X2)){\unicdcdcdhd}((v6\_waybel\_0~(k8\_yellow\_6~X0~X1~X2)~X0){\unicdcdcdhd}((v7\_waybel\_0~\\
(k8\_yellow\_6~X0~X1~X2)){\unicdcdcdhd}(l1\_waybel\_0~(k8\_yellow\_6~X0~X1~X2)~X0)))))\end{array}
\label{hyp:egehpflgidpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_yellow\_1~X1))))){\unicdbdjdcd}(\\
(v1\_orders\_2~(k5\_yellow\_1~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k5\_yellow\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}(\\
(v1\_orders\_2~(k3\_yellow\_3~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k3\_yellow\_3~\\
X0~X1)))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}((v1\_orders\_2~(g1\_orders\_2~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(g1\_orders\_2~\\
X0~X1)))\end{array}
\label{hyp:egehpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_yellow\_1~X1))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=k5\_yellow\_1~\\
X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k4\_card\_3~(k12\_pralg\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X2)){\unicdbdjdcd}((X3 \in k4\_card\_3~(k12\_pralg\_1~X0~X1)){\unicdbdjdcd}((r1\_orders\_2~\\
X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~X5)){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~X6)){\unicdcdcdhd}((X5=X3){\unicdcdcdhd}((X6=X4){\unicdcdcdhd}({\unicdcdadad} X7 .  \\
\preoh (X7 \in X0){\unicdcdcdhd}({\unicdcdadad} X8 .  (l1\_orders\_2~X8){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~X8)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_struct\_0~\\
X8)){\unicdbdjdcd}(\preoh (X8=k1\_funct\_1~X1~X7){\unicdcdcdhd}((X9=k1\_funct\_1~X5~X7){\unicdcdcdhd}((X10=k1\_funct\_1~\\
X6~X7){\unicdcdcdhd}(r1\_orders\_2~X8~X9~X10)))))))))))))))))))\end{array}
\label{hyp:egedpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=k3\_yellow\_3~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
(u1\_orders\_2~X2=k2\_yellow\_3~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_orders\_2~X0)~(u1\_orders\_2~\\
X1))))))\end{array}
\label{hyp:egcdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v7\_waybel\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~\\
X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_yellow\_6~X2~(u1\_struct\_0~X1)~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v4\_orders\_2~X3){\unicdcdcdhd}((v6\_waybel\_0~X3~X0){\unicdcdcdhd}(\\
(v7\_waybel\_0~X3){\unicdcdcdhd}(l1\_waybel\_0~X3~X0))))){\unicdbdjdcd}((X3=k8\_yellow\_6~X0~\\
X1~X2){\unicdbdjded}((g1\_orders\_2~(u1\_struct\_0~X3)~(u1\_orders\_2~X3)=k3\_yellow\_3~\\
X1~(k5\_yellow\_1~(u1\_struct\_0~X1)~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~\\
X5)){\unicdbdjdcd}(((X4 \in u1\_struct\_0~X1){\unicdcdcdhd}(X5 \in u1\_struct\_0~(k5\_yellow\_1~(u1\_struct\_0~\\
X1)~X2))){\unicdbdjdcd}(k1\_binop\_1~(u1\_waybel\_0~X0~X3)~X4~X5=k1\_funct\_1~(u1\_waybel\_0~\\
X0~(k7\_yellow\_6~(u1\_struct\_0~X1)~X0~X2~X4))~(k1\_funct\_1~X5~X4))))))))))\end{array}
\label{hyp:egbdddpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_yellow\_6~\\
X2~X0~X1){\unicdbdjdcd}(v1\_yellow\_1~X2))\end{array}
\label{hyp:dgdgbdpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~X0){\unicdbdjdcd}(X0=g1\_orders\_2~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfjhfgmgmgpghhpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v7\_waybel\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~\\
X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_yellow\_6~X2~(u1\_struct\_0~X1)~X0){\unicdbdjdcd}(u1\_struct\_0~\\
(k8\_yellow\_6~X0~X1~X2)=k2\_zfmisc\_1~(u1\_struct\_0~X1)~(k4\_card\_3~\\
(k12\_pralg\_1~(u1\_struct\_0~X1)~X2)))))\end{array}$$
\end{theorem}
\end{document}
