\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{t120\_gfacirc1 (TMJYnYFEcGa8Z1CFXYzciA6wZnnrvn1KTtA)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k46\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_twoscomp : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((k4\_tarski~(k10\_finseq\_1~X0~\\
X1)~X3 \in u1\_struct\_0~(k8\_facirc\_1~X0~X1~X2~X3)){\unicdcdcdhd}(k4\_tarski~(k10\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~X3)~X2)~X3 \in u1\_struct\_0~(k8\_facirc\_1~\\
X0~X1~X2~X3)))\end{array}
\label{hyp:ehgdbdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0 \in u1\_struct\_0~(k8\_facirc\_1~\\
X0~X1~X2~X3)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k8\_facirc\_1~X0~X1~X2~X3)){\unicdcdcdhd}(X2 \in u1\_struct\_0~\\
(k8\_facirc\_1~X0~X1~X2~X3))))\end{array}
\label{hyp:ehgdadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k14\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k14\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k14\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdedpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k46\_gfacirc1~X0~X1~X2=k8\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egedgdpfhgggbgdgjgchdgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdadpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k46\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((X2 \in u1\_struct\_0~\\
(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp \in \\
u1\_struct\_0~(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}(k4\_tarski~(k10\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp)~X2)~k14\_twoscomp \in \\
u1\_struct\_0~(k46\_gfacirc1~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
