\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{t132\_gfacirc1 (TMZwmgFQHor65LDsupvYkju5stQBQJNb1tA)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k49\_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 $ k4\_twoscomp : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k29\_twoscomp : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k46\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k43\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ 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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2 \in u1\_struct\_0~(k2\_circcomb~X0~X1)){\unicdcdcdhd}(\\
X2 \in u1\_struct\_0~(k2\_circcomb~X1~X0)))))\end{array}
\label{hyp:ehcdadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdcdadpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k43\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((X2 \in u1\_struct\_0~\\
(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X0~X1)~k4\_twoscomp \in \\
u1\_struct\_0~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k4\_twoscomp \in u1\_struct\_0~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~\\
(k10\_finseq\_1~X2~X0)~k4\_twoscomp \in u1\_struct\_0~(k43\_gfacirc1~X0~\\
X1~X2)){\unicdcdcdhd}(k4\_tarski~(k11\_finseq\_1~(k4\_tarski~(k10\_finseq\_1~X0~\\
X1)~k4\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X1~X2)~k4\_twoscomp)~\\
(k4\_tarski~(k10\_finseq\_1~X2~X0)~k4\_twoscomp))~k29\_twoscomp \in u1\_struct\_0~\\
(k43\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:ehbdbdbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k46\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k46\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k46\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k46\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgedgdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k43\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k43\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k43\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k43\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgedddpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k49\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k46\_gfacirc1~X0~X1~X2)~(k43\_gfacirc1~X0~X1~X2)\end{array}
\label{hyp:egedjdpfhgggbgdgjgchdgbd}
\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:ehbdddcdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k49\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((X2 \in u1\_struct\_0~\\
(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp \in \\
u1\_struct\_0~(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~k14\_twoscomp)~X2)~k14\_twoscomp \in \\
u1\_struct\_0~(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k4\_twoscomp \in u1\_struct\_0~(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((k4\_tarski~\\
(k10\_finseq\_1~X1~X2)~k4\_twoscomp \in u1\_struct\_0~(k49\_gfacirc1~X0~\\
X1~X2)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X2~X0)~k4\_twoscomp \in u1\_struct\_0~\\
(k49\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}(k4\_tarski~(k11\_finseq\_1~(k4\_tarski~\\
(k10\_finseq\_1~X0~X1)~k4\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X1~\\
X2)~k4\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X2~X0)~k4\_twoscomp))~\\
k29\_twoscomp \in u1\_struct\_0~(k49\_gfacirc1~X0~X1~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
