\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\_anproj\_2 (TMcBTMjEzALRMJjmBvQyf5GCZeTSU2MLYKb)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\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\_numbers : {\iota}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v9\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_anproj\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_anproj\_1 : {{\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}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh r2\_anproj\_1~X0~X1~X2~X3){\unicdbdjdcd}((\preoh v9\_struct\_0~\\
X1~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X2~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X3~X0){\unicdcdcdhd}((\preoh r1\_anproj\_1~\\
X0~X1~X2){\unicdcdcdhd}((\preoh r1\_anproj\_1~X0~X2~X3){\unicdcdcdhd}(\preoh r1\_anproj\_1~X0~X3~X1))))))))))\end{array}
\label{hyp:ehbdcdpfbgogahchpgkgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_anproj\_1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}((k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~\\
(k1\_rlvect\_1~X0~X1~X4)~(k1\_rlvect\_1~X0~X2~X5))~(k1\_rlvect\_1~X0~X3~\\
X6)=k4\_struct\_0~X0){\unicdcdcdhd}(\preoh (X4=k6\_numbers){\unicdcdcdhd}((X5=k6\_numbers){\unicdcdcdhd}(\\
X6=k6\_numbers)))))))))))\end{array}
\label{hyp:egcdpfbgogahchpgkgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfbgogahchpgkgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~k1\_numbers){\unicdbdjdcd}((k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~\\
X0~X1~X4)~(k1\_rlvect\_1~X0~X2~X5))~(k1\_rlvect\_1~X0~X3~X6)=k4\_struct\_0~\\
X0){\unicdbdjdcd}((X4=k6\_numbers){\unicdcdcdhd}((X5=k6\_numbers){\unicdcdcdhd}(X6=k6\_numbers))))))){\unicdbdjdcd}\\
((\preoh v9\_struct\_0~X1~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X2~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X3~\\
X0){\unicdcdcdhd}((\preoh r2\_anproj\_1~X0~X1~X2~X3){\unicdcdcdhd}(\preoh r1\_anproj\_1~X0~X1~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
