\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t8\_functor2 (TMWAKAYsHanmveAXZRqMSeYG39JfRk4Bad3)}
\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 $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ 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}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_functor0~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_functor0~\\
X4~X0~X1){\unicdbdjdcd}(((r1\_functor2~X0~X1~X2~X3){\unicdcdcdhd}(r1\_functor2~X0~X1~X3~X4)){\unicdbdjdcd}\\
(r1\_functor2~X0~X1~X2~X4))))))\end{array}
\label{hyp:ehcdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\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 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
X4~X0~X1)){\unicdbdjdcd}(((r1\_functor2~X0~X1~X2~X3){\unicdcdcdhd}(r1\_functor2~X0~X1~X3~X4)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_functor2~X5~X0~X1~X2~X3){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X6~X7{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(k1\_altcat\_1~X0~X6~X7)){\unicdbdjdcd}(k5\_altcat\_1~X1~(k3\_functor0~X0~X1~X2~\\
X6)~(k3\_functor0~X0~X1~X2~X7)~(k3\_functor0~X0~X1~X3~X7)~(k6\_functor0~\\
X0~X1~X2~X6~X7~X8)~(k2\_functor2~X0~X1~X2~X3~X5~X7)=k5\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X6)~(k3\_functor0~X0~X1~X3~X6)~(k3\_functor0~X0~X1~X3~X7)~(k2\_functor2~\\
X0~X1~X2~X3~X5~X6)~(k6\_functor0~X0~X1~X3~X6~X7~X8)))))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_functor2~X6~X0~X1~X3~X4){\unicdbdjdcd}(({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X7~X8{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k1\_altcat\_1~\\
X0~X7~X8)){\unicdbdjdcd}(k5\_altcat\_1~X1~(k3\_functor0~X0~X1~X3~X7)~(k3\_functor0~\\
X0~X1~X3~X8)~(k3\_functor0~X0~X1~X4~X8)~(k6\_functor0~X0~X1~X3~X7~X8~X9)~\\
(k2\_functor2~X0~X1~X3~X4~X6~X8)=k5\_altcat\_1~X1~(k3\_functor0~X0~X1~\\
X3~X7)~(k3\_functor0~X0~X1~X4~X7)~(k3\_functor0~X0~X1~X4~X8)~(k2\_functor2~\\
X0~X1~X3~X4~X6~X7)~(k6\_functor0~X0~X1~X4~X7~X8~X9)))))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X7~X8{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~(k1\_altcat\_1~X0~X7~X8)){\unicdbdjdcd}(k5\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X7)~(k3\_functor0~X0~X1~X2~X8)~(k3\_functor0~X0~X1~X4~X8)~(k6\_functor0~\\
X0~X1~X2~X7~X8~X9)~(k2\_functor2~X0~X1~X2~X4~(k3\_functor2~X0~X1~X2~X3~X4~\\
X5~X6)~X8)=k5\_altcat\_1~X1~(k3\_functor0~X0~X1~X2~X7)~(k3\_functor0~\\
X0~X1~X4~X7)~(k3\_functor0~X0~X1~X4~X8)~(k2\_functor2~X0~X1~X2~X4~(k3\_functor2~\\
X0~X1~X2~X3~X4~X5~X6)~X7)~(k6\_functor0~X0~X1~X4~X7~X8~X9)))))))))))))))\end{array}
\label{hyp:mgbdfdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (((\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}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~\\
X0~X1){\unicdcdcdhd}((m2\_functor0~X3~X0~X1){\unicdcdcdhd}((m2\_functor0~X4~X0~X1){\unicdcdcdhd}((m1\_functor2~\\
X5~X0~X1~X2~X3){\unicdcdcdhd}(m1\_functor2~X6~X0~X1~X3~X4))))))){\unicdbdjdcd}(m1\_functor2~(\\
k3\_functor2~X0~X1~X2~X3~X4~X5~X6)~X0~X1~X2~X4)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchcd}
\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 .  ((v15\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~\\
X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1)){\unicdbdjdcd}((r2\_functor2~X0~X1~X2~X3){\unicdbdjded}((r1\_functor2~\\
X0~X1~X2~X3){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_functor2~X4~X0~X1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X5~X6{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_altcat\_1~X0~X5~X6)){\unicdbdjdcd}(k5\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X5)~(k3\_functor0~X0~X1~X2~X6)~(k3\_functor0~X0~X1~X3~X6)~(k6\_functor0~\\
X0~X1~X2~X5~X6~X7)~(k2\_functor2~X0~X1~X2~X3~X4~X6)=k5\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X5)~(k3\_functor0~X0~X1~X3~X5)~(k3\_functor0~X0~X1~X3~X6)~(k2\_functor2~\\
X0~X1~X2~X3~X4~X5)~(k6\_functor0~X0~X1~X3~X5~X6~X7))))))))))))\end{array}
\label{hyp:eggdpfggfhogdgehpgchcd}
\end{equation}
\begin{theorem}\label{thm:ehidpfggfhogdgehpgchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
X4~X0~X1)){\unicdbdjdcd}(((r2\_functor2~X0~X1~X2~X3){\unicdcdcdhd}(r2\_functor2~X0~X1~X3~X4)){\unicdbdjdcd}\\
(r2\_functor2~X0~X1~X2~X4))))))\end{array}$$
\end{theorem}
\end{document}
