\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{t1\_mod\_2 (TMYVveA1DBZm5y427eZiLuWAY6DX97rEjPM)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\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\_mod\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_algstr\_0 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_funct\_5 : {\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ v7\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_algstr\_0)){\unicdbdjdcd}(X0=\\
k1\_xboole\_0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_algstr\_0)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k3\_algstr\_0)){\unicdbdjdcd}(k3\_rlvect\_1~\\
k3\_algstr\_0~X0~X1=k1\_xboole\_0))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k3\_algstr\_0)){\unicdbdjdcd}(k4\_algstr\_0~k3\_algstr\_0~X0=k1\_xboole\_0)){\unicdcdcdhd}\\
(k4\_struct\_0~k3\_algstr\_0=k1\_xboole\_0)))\end{array}
\label{hyp:ehedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_funct\_5}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g2\_algstr\_0~X0~X1~X2=g2\_algstr\_0~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((l1\_struct\_0~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~\\
X1))))){\unicdcdcdhd}((m1\_subset\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~X1)~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_vectsp\_1~X0~X1~\\
X2~X3~X4=g1\_vectsp\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}\\
((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v13\_struct\_0}~{k3\_algstr\_0}}~{np\_\_1}})}{\unicdcdcdhd}{({{v8\_algstr\_0}~{k3\_algstr\_0}})}}\label{hyp:ggdgjdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_vectsp\_1~X1~X0){\unicdbdjdcd}\\
(l2\_algstr\_0~X1))\end{array}
\label{hyp:egehpfmgbdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k9\_funct\_5){\unicdcdcdhd}((v1\_funct\_2~k9\_funct\_5~(k2\_zfmisc\_1~\\
np\_\_1~np\_\_1)~np\_\_1){\unicdcdcdhd}(m1\_subset\_1~k9\_funct\_5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_1~np\_\_1)~np\_\_1))))\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_funct\_5}}~{np\_\_1}}\label{hyp:egehpflgfdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k4\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{l2\_algstr\_0}~{k3\_algstr\_0}}\label{hyp:egehpflgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k1\_mod\_2~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k1\_mod\_2~X0)){\unicdcdcdhd}\\
((v7\_vectsp\_1~(k1\_mod\_2~X0)~X0){\unicdcdcdhd}((v8\_vectsp\_1~(k1\_mod\_2~X0)~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~(k1\_mod\_2~X0)~X0){\unicdcdcdhd}((v10\_vectsp\_1~(k1\_mod\_2~X0)~\\
X0){\unicdcdcdhd}((v11\_vectsp\_1~(k1\_mod\_2~X0)~X0){\unicdcdcdhd}((v2\_rlvect\_1~(k1\_mod\_2~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k1\_mod\_2~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k1\_mod\_2~X0)){\unicdcdcdhd}\\
(l1\_vectsp\_1~(k1\_mod\_2~X0)~X0)))))))))))\end{array}
\label{hyp:egehpflgbdpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k10\_funct\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k10\_funct\_3~X0~X1)~(k2\_zfmisc\_1~X0~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k10\_funct\_3~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X1))))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_algstr\_0}={{{{g2\_algstr\_0}~{np\_\_1}}~{k9\_funct\_5}}~{k5\_funct\_5}}}\label{hyp:egjdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
(k1\_mod\_2~X0=g1\_vectsp\_1~X0~np\_\_1~k9\_funct\_5~k5\_funct\_5~(k10\_funct\_3~\\
(u1\_struct\_0~X0)~np\_\_1))\end{array}
\label{hyp:egbdpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}((v8\_algstr\_0~X0){\unicdbdjdcd}(X0=g2\_algstr\_0~\\
(u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghidpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)){\unicdbdjdcd}\\
((v7\_vectsp\_1~X1~X0){\unicdbdjdcd}(X1=g1\_vectsp\_1~X0~(u1\_struct\_0~X1)~(u1\_algstr\_0~\\
X1)~(u2\_struct\_0~X1)~(u1\_vectsp\_1~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghhdpfghfgdgehdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfngpgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k1\_mod\_2~X0))){\unicdbdjdcd}(X1=\\
k4\_struct\_0~(k1\_mod\_2~X0)))\end{array}$$
\end{theorem}
\end{document}
