\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\_group\_7 (TMW1mjTfkd689VwcrA3u5wzmz8jR7Kr1mFW)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\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 $ k2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((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){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_algstr\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_algstr\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u2\_algstr\_0~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}((\\
v15\_algstr\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}(l3\_algstr\_0~(k2\_group\_7~X0~\\
X1)))\end{array}
\label{hyp:egehpflgcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v15\_algstr\_0~X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdbdjdcd}((X2=k2\_group\_7~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=k4\_card\_3~(k12\_pralg\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k4\_card\_3~(k12\_pralg\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k4\_card\_3~(k12\_pralg\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
\preoh (X5 \in X0){\unicdcdcdhd}({\unicdcdadad} X6 .  ((\preoh v2\_struct\_0~X6){\unicdcdcdhd}(l3\_algstr\_0~X6)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  ((v1\_relat\_1~X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdbdjdcd}(\preoh (X6=k1\_funct\_1~\\
X1~X5){\unicdcdcdhd}((X7=k1\_binop\_1~(u2\_algstr\_0~X2)~X3~X4){\unicdcdcdhd}(k1\_funct\_1~X7~\\
X5=k1\_binop\_1~(u2\_algstr\_0~X6)~(k1\_funct\_1~X3~X5)~(k1\_funct\_1~\\
X4~X5))))))))))))\end{array}
\label{hyp:egcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (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}(k6\_algstr\_0~\\
X0~X1~X2=k5\_binop\_1~(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)~X1~X2)))\end{array}
\label{hyp:egbdidpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfhgchpgfhahpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~\\
X5){\unicdcdcdhd}((v4\_relat\_1~X5~X0){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_partfun1~X5~X0){\unicdcdcdhd}\\
(v1\_group\_7~X5))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((\preoh v2\_struct\_0~X6){\unicdcdcdhd}(l3\_algstr\_0~\\
X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~(k2\_group\_7~X0~\\
X5))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~(k2\_group\_7~X0~\\
X5))){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X6)){\unicdbdjdcd}({\unicdcdadad} X10 .  \\
(m1\_subset\_1~X10~(u1\_struct\_0~X6)){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}((X6=k1\_funct\_1~\\
X5~X1){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}((X4=k6\_algstr\_0~(k2\_group\_7~X0~X5)~\\
X7~X8){\unicdcdcdhd}((k1\_funct\_1~X2~X1=X9){\unicdcdcdhd}(k1\_funct\_1~X3~X1=X10))))))){\unicdbdjdcd}(\\
k6\_algstr\_0~X6~X9~X10=k1\_funct\_1~X4~X1))))))))))\end{array}$$
\end{theorem}
\end{document}
