\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{t115\_group\_2 (TMcxcAALrcUH2QZ89S9LmRrzrJKy4E9b8u7)}
\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 $ l3\_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 $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\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 .  (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}((k6\_algstr\_0~X0~X1~X2=X3){\unicdbdjded}\\
(X2=k6\_algstr\_0~X0~(k2\_group\_1~X0~X1)~X3)))))\end{array}
\label{hyp:ehbdddpfhgchpgfhahpfbd}
\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 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_group\_2~X3~X0){\unicdbdjdcd}((k13\_group\_2~X0~X3~X1=k13\_group\_2~X0~X3~X2){\unicdbdjded}\\
(r1\_struct\_0~X3~(k6\_algstr\_0~X0~(k2\_group\_1~X0~X2)~X1))))))\end{array}
\label{hyp:ehbdbdedpfhgchpgfhahpfcd}
\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 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_group\_2~X2~X0){\unicdbdjdcd}((X1 \in k13\_group\_2~X0~X2~X1){\unicdcdcdhd}\\
(X1 \in k14\_group\_2~X0~X2~X1))))\end{array}
\label{hyp:ehbdadidpfhgchpgfhahpfcd}
\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}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_group\_2~X3~X1){\unicdbdjdcd}((X0 \in k13\_group\_2~\\
X1~X3~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdcdcdhd}((X0=\\
k6\_algstr\_0~X1~X2~X4){\unicdcdcdhd}(r1\_struct\_0~X3~X4))))))\end{array}
\label{hyp:ehbdadddpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_xboole\_0}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{r1\_xboole\_0}~{X1}}~{X0}})}}}}\label{hyp:dhjhngngfgehchjhpfchbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l3\_algstr\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_algstr\_0~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflggdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdbdfdpfhgchpgfhahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_group\_2~X3~X0){\unicdbdjdcd}((k13\_group\_2~X0~X3~X1=k13\_group\_2~X0~X3~X2){\unicdbdjded}\\
(\preoh r1\_xboole\_0~(k13\_group\_2~X0~X3~X1)~(k13\_group\_2~X0~X3~X2))))))\end{array}$$
\end{theorem}
\end{document}
