\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}
\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{t13\_functor1 (TMFxE7YzYv96ZLx7BtkLmZpNwiqd7Hu32LJ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k14\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v9\_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}((v1\_altcat\_2~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_altcat\_2~X2~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_altcat\_2~X3~X1)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k10\_functor0~X0~X2=k13\_functor0~X3~X1~X0~(k10\_functor0~X1~X3)~(\\
k10\_functor0~X0~X1))))))\end{array}
\label{hyp:ehedpfggfhogdgehpgchbd}
\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 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0))){\unicdbdjdcd}((v8\_functor0~(k10\_functor0~\\
X0~X1)~X1~X0){\unicdcdcdhd}(v9\_functor0~(k10\_functor0~X0~X1)~X1~X0))\end{array}
\label{hyp:ggdgbdcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\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 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}\\
(l1\_altcat\_1~X1))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(\\
l1\_altcat\_1~X2))){\unicdcdcdhd}(((v8\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~X3~X0~\\
X1)){\unicdcdcdhd}(l2\_functor0~X4~X1~X2))))){\unicdbdjdcd}((v9\_functor0~(k13\_functor0~\\
X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}(l2\_functor0~(k13\_functor0~X0~X1~X2~X3~X4)~X0~\\
X2))\end{array}
\label{hyp:egehpflgbdddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_altcat\_1~X0){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}\\
((v9\_functor0~(k10\_functor0~X0~X1)~X1~X0){\unicdcdcdhd}(l2\_functor0~(k10\_functor0~\\
X0~X1)~X1~X0))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_altcat\_2~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_altcat\_2~X2~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  (l2\_functor0~X3~X0~X1){\unicdbdjdcd}(k14\_functor0~X0~X1~X2~X3=k13\_functor0~\\
X2~X0~X1~(k10\_functor0~X0~X2)~X3))))\end{array}
\label{hyp:egddhdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfggfhogdgehpgchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_altcat\_2~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(m1\_altcat\_2~\\
X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_altcat\_2~X3~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}(m1\_altcat\_2~X4~X2)){\unicdbdjdcd}((X3=X4){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (l2\_functor0~X5~X0~X1){\unicdbdjdcd}(k14\_functor0~X0~X1~X3~X5=k14\_functor0~\\
X2~X1~X4~(k14\_functor0~X0~X1~X2~X5))))))))\end{array}$$
\end{theorem}
\end{document}
