\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{t35\_autalg\_1 (TMZ3w8evA87UWii8PDLuVp6U1sizArnhM6L)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_autalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_autalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_autalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v15\_algstr\_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 $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~(k3\_autalg\_1~X0))~(u1\_struct\_0~\\
(k7\_autalg\_1~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)))){\unicdcdcdhd}((v1\_group\_6~\\
X1~(k3\_autalg\_1~X0)~(k7\_autalg\_1~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_autalg\_1~X0))~(u1\_struct\_0~(k7\_autalg\_1~(k6\_msualg\_1~X0)~\\
(k9\_msualg\_1~X0))))))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (X2 \in k1\_autalg\_1~X0){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X2=k16\_funcop\_1~k6\_numbers~X2)){\unicdbdjdcd}(v3\_funct\_2~X1~\\
(u1\_struct\_0~(k3\_autalg\_1~X0))~(u1\_struct\_0~(k7\_autalg\_1~(k6\_msualg\_1~\\
X0)~(k9\_msualg\_1~X0))))))\end{array}
\label{hyp:ehddedpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((k9\_xtuple\_0~X1=k1\_autalg\_1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(X2 \in k1\_autalg\_1~X0){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k16\_funcop\_1~k6\_numbers~\\
X2))){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~(k3\_autalg\_1~\\
X0))~(u1\_struct\_0~(k7\_autalg\_1~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0)))){\unicdcdcdhd}((v1\_group\_6~X1~(k3\_autalg\_1~X0)~(k7\_autalg\_1~(k6\_msualg\_1~\\
X0)~(k9\_msualg\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_autalg\_1~X0))~(u1\_struct\_0~(k7\_autalg\_1~(k6\_msualg\_1~\\
X0)~(k9\_msualg\_1~X0)))))))))))\end{array}
\label{hyp:ehddddpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
v1\_funct\_1~X2)){\unicdcdcdhd}((k9\_xtuple\_0~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in X1){\unicdbdjdcd}(\\
k1\_funct\_1~X2~X3=X0~X3)))\end{array}
\label{hyp:dhddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdcdcdhd}((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v15\_algstr\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))))){\unicdbdjdcd}((r2\_group\_6~X0~X1){\unicdbdjded}(r1\_group\_6~X0~\\
X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k7\_autalg\_1~X0~X1)){\unicdcdcdhd}((v15\_algstr\_0~(k7\_autalg\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_group\_1~(k7\_autalg\_1~X0~X1)){\unicdcdcdhd}(v3\_group\_1~(k7\_autalg\_1~\\
X0~X1)))))\end{array}
\label{hyp:ggdgfdpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v4\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:ggdgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v13\_struct\_0~\\
(k6\_msualg\_1~X0)~np\_\_1){\unicdcdcdhd}((v1\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v5\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:ggdgcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_autalg\_1~X0)){\unicdcdcdhd}((v15\_algstr\_0~(k3\_autalg\_1~X0)){\unicdcdcdhd}((v2\_group\_1~\\
(k3\_autalg\_1~X0)){\unicdcdcdhd}(v3\_group\_1~(k3\_autalg\_1~X0)))))\end{array}
\label{hyp:ggdgbdpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l3\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:egehpflgjdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k7\_autalg\_1~X0~X1)){\unicdcdcdhd}((v2\_group\_1~(k7\_autalg\_1~\\
X0~X1)){\unicdcdcdhd}((v3\_group\_1~(k7\_autalg\_1~X0~X1)){\unicdcdcdhd}(l3\_algstr\_0~(k7\_autalg\_1~\\
X0~X1)))))\end{array}
\label{hyp:egehpflghdpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k6\_msualg\_1~X0)){\unicdcdcdhd}((v5\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l1\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_autalg\_1~X0)){\unicdcdcdhd}((v2\_group\_1~(k3\_autalg\_1~X0)){\unicdcdcdhd}((v3\_group\_1~\\
(k3\_autalg\_1~X0)){\unicdcdcdhd}(l3\_algstr\_0~(k3\_autalg\_1~X0)))))\end{array}
\label{hyp:egehpflgddpfbgfhehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}((r1\_group\_6~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_group\_6~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdcdcdhd}(v3\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egbdbdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v13\_struct\_0~X0~np\_\_1){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(v7\_struct\_0~X0)))\end{array}
\label{hyp:dgdgbdbdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfbgfhehbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(r2\_group\_6~(k3\_autalg\_1~\\
X0)~(k7\_autalg\_1~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
