\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{t78\_group\_11 (TMQqaNwhpacvVXn6EGNWFX8JU4rs7m1FpSe)}
\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 $ v1\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_group\_11 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_group\_11 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 .  ((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_group\_3~X2~X0){\unicdcdcdhd}(m1\_group\_2~X2~X0)){\unicdbdjdcd}(\\
\preoh (m1\_group\_2~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~\\
X3~X0){\unicdcdcdhd}(m1\_group\_2~X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}(\\
(v1\_group\_3~X4~X0){\unicdcdcdhd}(m1\_group\_2~X4~X0))){\unicdbdjdcd}(\preoh (u1\_struct\_0~X3=k4\_group\_11~\\
X0~X1~X2){\unicdcdcdhd}((u1\_struct\_0~X4=k3\_group\_11~X0~X1~X2){\unicdcdcdhd}(r1\_tarski~(k4\_group\_11~\\
X0~X1~X4)~(k4\_group\_11~X0~X1~X3)))))))))\end{array}
\label{hyp:ehhdgdpfhgchpgfhahpfbdbd}
\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\_group\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_2~X2~X0){\unicdbdjdcd}(r1\_tarski~(k3\_group\_11~X0~X2~X1)~(k4\_group\_11~\\
X0~X2~X1))))\end{array}
\label{hyp:ehfdfdpfhgchpgfhahpfbdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdidpfhgchpgfhahpfbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_group\_3~X2~X0){\unicdcdcdhd}(m1\_group\_2~X2~X0)){\unicdbdjdcd}(\\
\preoh (m1\_group\_2~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~\\
X3~X0){\unicdcdcdhd}(m1\_group\_2~X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}(\\
(v1\_group\_3~X4~X0){\unicdcdcdhd}(m1\_group\_2~X4~X0))){\unicdbdjdcd}(\preoh (u1\_struct\_0~X3=k4\_group\_11~\\
X0~X1~X2){\unicdcdcdhd}((u1\_struct\_0~X4=k3\_group\_11~X0~X1~X2){\unicdcdcdhd}(r1\_tarski~(k3\_group\_11~\\
X0~X1~X4)~(k4\_group\_11~X0~X1~X3)))))))))\end{array}$$
\end{theorem}
\end{document}
