\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{t105\_group\_9 (TMHMJ5z7j85atdE7ULZe7V2utK2dMvfoYXa)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_finseq\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~(k6\_group\_9~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~X2){\unicdcdcdhd}((k1\_nat\_1~X4~np\_\_1 \in \\
k4\_finseq\_1~X2){\unicdcdcdhd}((k1\_funct\_1~X2~X4=k1\_funct\_1~X2~(k1\_nat\_1~X4~\\
np\_\_1)){\unicdcdcdhd}(X3=k2\_finseq\_3~X4~X2)))){\unicdbdjdcd}(v8\_group\_9~X3~X0~X1)))))\end{array}
\label{hyp:ehjdedpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X1){\unicdbdjdcd}(m2\_finseq\_1~(k2\_finseq\_3~X0~X2)~\\
X1)))\end{array}
\label{hyp:ehbdadfdpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~X2){\unicdcdcdhd}\\
((k1\_nat\_1~X4~np\_\_1 \in k4\_finseq\_1~X2){\unicdcdcdhd}((k1\_funct\_1~X2~X4=k1\_funct\_1~\\
X2~(k1\_nat\_1~X4~np\_\_1)){\unicdcdcdhd}(X3=k2\_finseq\_3~X4~X2)))){\unicdbdjdcd}(k20\_group\_9~\\
X0~X1~X3=k2\_finseq\_3~X4~(k20\_group\_9~X0~X1~X2))))))\end{array}
\label{hyp:ehbdadedpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((X3 \in k4\_finseq\_1~(k20\_group\_9~\\
X0~X1~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((v2\_group\_1~X4){\unicdcdcdhd}(\\
(v3\_group\_1~X4){\unicdcdcdhd}((v3\_group\_9~X4~X0){\unicdcdcdhd}(l1\_group\_9~X4~X0))))){\unicdbdjdcd}(\\
(X4=k1\_funct\_1~(k20\_group\_9~X0~X1~X2)~X3){\unicdbdjdcd}(v7\_struct\_0~X4)))){\unicdbdjdcd}\\
((X3 \in k4\_finseq\_1~X2){\unicdcdcdhd}((k1\_nat\_1~X3~np\_\_1 \in k4\_finseq\_1~X2){\unicdcdcdhd}(k1\_funct\_1~\\
X2~X3=k1\_funct\_1~X2~(k1\_nat\_1~X3~np\_\_1)))))))\end{array}
\label{hyp:ehbdadddpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
\preoh v1\_xboole\_0~(k6\_group\_9~X0~X1))\end{array}
\label{hyp:ggdgddpfhgchpgfhahpfjd}
\end{equation}
\begin{theorem}\label{thm:ehbdadfdpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~\\
X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(((X3=k20\_group\_9~X0~X1~X2){\unicdcdcdhd}\\
((X4 \in k4\_finseq\_1~X3){\unicdcdcdhd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}((v2\_group\_1~\\
X5){\unicdcdcdhd}((v3\_group\_1~X5){\unicdcdcdhd}((v3\_group\_9~X5~X0){\unicdcdcdhd}(l1\_group\_9~X5~X0))))){\unicdbdjdcd}\\
((X5=k1\_funct\_1~X3~X4){\unicdbdjdcd}(v7\_struct\_0~X5))))){\unicdbdjdcd}(((v8\_group\_9~(\\
k2\_finseq\_3~X4~X2)~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~(k2\_finseq\_3~X4~X2)~(k6\_group\_9~\\
X0~X1))){\unicdcdcdhd}({\unicdcdadad} X5 .  ((v8\_group\_9~X5~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X5~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}((X5=k2\_finseq\_3~X4~X2){\unicdbdjdcd}(k20\_group\_9~X0~X1~X5=k2\_finseq\_3~\\
X4~X3))))))))\end{array}$$
\end{theorem}
\end{document}
