\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{t4\_yellow20 (TMbhizeh5QgexYZqDRdCmhZMQvs4Kc2GUvC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k13\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k12\_functor0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k11\_functor0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v12\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~X2~X0~X1){\unicdcdcdhd}(\\
l2\_functor0~X2~X0~X1)){\unicdbdjdcd}(k13\_functor0~X0~X0~X1~(k12\_functor0~X0)~\\
X2=g2\_functor0~X0~X1~(u1\_functor0~X0~X1~X2)~(u2\_functor0~X0~X1~X2))))\end{array}
\label{hyp:ehfdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}\\
(k13\_functor0~X0~X1~X1~X2~(k11\_functor0~X1)=g2\_functor0~X0~X1~(u1\_functor0~\\
X0~X1~X2)~(u2\_functor0~X0~X1~X2))))\end{array}
\label{hyp:ehedpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjdcd}((v21\_functor0~\\
(k15\_functor0~X0~X1~X2)~X1~X0){\unicdcdcdhd}(v8\_functor0~(k15\_functor0~X0~X1~\\
X2)~X1~X0)))))\end{array}
\label{hyp:ehddfdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l1\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(l1\_altcat\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v1\_altcat\_2~X3){\unicdcdcdhd}(l1\_altcat\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v8\_functor0~X4~X0~X1){\unicdcdcdhd}(l2\_functor0~X4~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\\
v8\_functor0~X5~X1~X2){\unicdcdcdhd}(l2\_functor0~X5~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  (l2\_functor0~\\
X6~X2~X3){\unicdbdjdcd}(k13\_functor0~X0~X1~X3~X4~(k13\_functor0~X1~X2~X3~X5~X6)=k13\_functor0~\\
X0~X2~X3~(k13\_functor0~X0~X1~X2~X4~X5)~X6)))))))\end{array}
\label{hyp:ehddcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}((v1\_altcat\_2~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}((v1\_altcat\_2~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjdcd}(k13\_functor0~\\
X0~X1~X0~X2~(k15\_functor0~X0~X1~X2)=k12\_functor0~X0))))\end{array}
\label{hyp:ehbdjdpfggfhogdgehpgchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}(k12\_functor0~X0=k11\_functor0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}(l2\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}(l2\_functor0~X2~\\
X0~X1))){\unicdbdjdcd}((v9\_functor0~(k15\_functor0~X0~X1~X2)~X1~X0){\unicdcdcdhd}(l2\_functor0~\\
(k15\_functor0~X0~X1~X2)~X1~X0))\end{array}
\label{hyp:egehpflgbdfdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}((v8\_functor0~X2~X0~X1){\unicdcdcdhd}(v12\_functor0~X2~X0~X1)))\end{array}
\label{hyp:dgdgbdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v12\_altcat\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_altcat\_2~X0)))\end{array}
\label{hyp:dgdgbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}((l1\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1))){\unicdbdjdcd}((v9\_functor0~X2~X0~X1){\unicdbdjdcd}(X2=g2\_functor0~\\
X0~X1~(u1\_functor0~X0~X1~X2)~(u2\_functor0~X0~X1~X2)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghjdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehedpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~X2~X0~X1){\unicdbdjdcd}\\
((v21\_functor0~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_functor0~X3~X1~X0){\unicdbdjdcd}((\\
k13\_functor0~X1~X0~X1~X3~X2=k12\_functor0~X1){\unicdbdjdcd}(g2\_functor0~X1~X0~\\
(u1\_functor0~X1~X0~X3)~(u2\_functor0~X1~X0~X3)=k15\_functor0~X0~X1~\\
X2))))))\end{array}$$
\end{theorem}
\end{document}
