\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{t17\_mod\_2 (TMGmnF66Q1gt4SkTpPSoZVVfU2L4uiJ51e7)}
\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 $ v2\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\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}((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 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v13\_algstr\_0~X3){\unicdcdcdhd}((v8\_vectsp\_1~\\
X3~X0){\unicdcdcdhd}((v9\_vectsp\_1~X3~X0){\unicdcdcdhd}((v10\_vectsp\_1~X3~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
X3~X0){\unicdcdcdhd}((v2\_rlvect\_1~X3){\unicdcdcdhd}((v3\_rlvect\_1~X3){\unicdcdcdhd}((v4\_rlvect\_1~X3){\unicdcdcdhd}\\
(l1\_vectsp\_1~X3~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}\\
((v13\_algstr\_0~X4){\unicdcdcdhd}((v8\_vectsp\_1~X4~X0){\unicdcdcdhd}((v9\_vectsp\_1~X4~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X4~X0){\unicdcdcdhd}((v11\_vectsp\_1~X4~X0){\unicdcdcdhd}((v2\_rlvect\_1~X4){\unicdcdcdhd}\\
((v3\_rlvect\_1~X4){\unicdcdcdhd}((v4\_rlvect\_1~X4){\unicdcdcdhd}(l1\_vectsp\_1~X4~X0)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v2\_mod\_2~X5~X0){\unicdcdcdhd}(m1\_mod\_2~X5~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v2\_mod\_2~X6~X0){\unicdcdcdhd}(m1\_mod\_2~X6~X0~X2~X3)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v2\_mod\_2~\\
X7~X0){\unicdcdcdhd}(m1\_mod\_2~X7~X0~X3~X4)){\unicdbdjdcd}(k8\_mod\_2~X0~X7~(k8\_mod\_2~X0~X6~X5)=\\
k8\_mod\_2~X0~(k8\_mod\_2~X0~X7~X6)~X5))))))))\end{array}
\label{hyp:ehbdgdpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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))))))))){\unicdcdcdhd}\\
(l1\_mod\_2~X1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_mod\_2~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k3\_mod\_2~X0~X1)){\unicdcdcdhd}((v8\_vectsp\_1~(k3\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v9\_vectsp\_1~\\
(k3\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v10\_vectsp\_1~(k3\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
(k3\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v2\_rlvect\_1~(k3\_mod\_2~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k3\_mod\_2~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k3\_mod\_2~X0~X1)){\unicdcdcdhd}(l1\_vectsp\_1~\\
(k3\_mod\_2~X0~X1)~X0))))))))))\end{array}
\label{hyp:egehpflgddpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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))))))))){\unicdcdcdhd}\\
(l1\_mod\_2~X1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_mod\_2~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k2\_mod\_2~X0~X1)){\unicdcdcdhd}((v8\_vectsp\_1~(k2\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v9\_vectsp\_1~\\
(k2\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v10\_vectsp\_1~(k2\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
(k2\_mod\_2~X0~X1)~X0){\unicdcdcdhd}((v2\_rlvect\_1~(k2\_mod\_2~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k2\_mod\_2~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k2\_mod\_2~X0~X1)){\unicdcdcdhd}(l1\_vectsp\_1~\\
(k2\_mod\_2~X0~X1)~X0))))))))))\end{array}
\label{hyp:egehpflgcdpfngpgegpfcd}
\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}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v3\_mod\_2~X3~X0){\unicdcdcdhd}(l1\_mod\_2~X3~X0)){\unicdbdjdcd}((m1\_mod\_2~X3~\\
X0~X1~X2){\unicdbdjded}((k2\_mod\_2~X0~X3=X1){\unicdcdcdhd}(k3\_mod\_2~X0~X3=X2))))))\end{array}
\label{hyp:egidpfngpgegpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfngpgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_mod\_2~X1~X0){\unicdcdcdhd}((v3\_mod\_2~X1~X0){\unicdcdcdhd}(l1\_mod\_2~X1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v2\_mod\_2~X2~X0){\unicdcdcdhd}((v3\_mod\_2~X2~X0){\unicdcdcdhd}(l1\_mod\_2~X2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v2\_mod\_2~X3~X0){\unicdcdcdhd}((v3\_mod\_2~X3~X0){\unicdcdcdhd}(l1\_mod\_2~X3~X0))){\unicdbdjdcd}\\
(((k2\_mod\_2~X0~X3=k3\_mod\_2~X0~X2){\unicdcdcdhd}(k2\_mod\_2~X0~X2=k3\_mod\_2~X0~X1)){\unicdbdjdcd}\\
(k8\_mod\_2~X0~X3~(k8\_mod\_2~X0~X2~X1)=k8\_mod\_2~X0~(k8\_mod\_2~X0~X3~X2)~\\
X1)))))\end{array}$$
\end{theorem}
\end{document}
