\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{t35\_facirc\_1 (TMZHS4Zhw8W53iFbds9LGZr35Si5G9NaJ4f)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\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 $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}((v1\_circcomb~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (X1 \in u4\_struct\_0~X0){\unicdbdjdcd}(k1\_funct\_1~(u2\_msualg\_1~\\
X0)~X1=X1)))\end{array}
\label{hyp:ehededpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}((v5\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~\\
X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}((v4\_circcomb~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~X0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~\\
(k6\_circuit2~X0~X1~X2)~(k2\_msualg\_1~X0~X3)=k1\_funct\_1~(k2\_xtuple\_0~\\
X3)~(k3\_relat\_1~(k1\_msualg\_1~X0~X3)~X2))))))\end{array}
\label{hyp:ehddedpfggbgdgjgchdgpfbd}
\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 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_msualg\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_msualg\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u2\_msualg\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_msualg\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_msualg\_1~X0)~(u4\_struct\_0~X0)~(k3\_finseq\_2~(\\
u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(u1\_msualg\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u4\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpffhbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v2\_circcomb~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
X1 \in u4\_struct\_0~X0){\unicdbdjdcd}(X1=k4\_tarski~(k1\_funct\_1~(u1\_msualg\_1~X0)~\\
X1)~(k2\_xtuple\_0~X1))))\end{array}
\label{hyp:egidpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k2\_msualg\_1~\\
X0~X1=k3\_funct\_2~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)~(u2\_msualg\_1~\\
X0)~X1))\end{array}
\label{hyp:egcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k1\_msualg\_1~\\
X0~X1=k3\_funct\_2~(u4\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))~\\
(u1\_msualg\_1~X0)~X1))\end{array}
\label{hyp:egbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_circcomb~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_msafree2~X0)))\end{array}
\label{hyp:dgdgcdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_circcomb~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v5\_circcomb~X0)))\end{array}
\label{hyp:dgdgbdpfdgjgchdgdgpgngcg}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~\\
X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}((v3\_circcomb~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}((v4\_circcomb~\\
X1~X0){\unicdcdcdhd}((v6\_circcomb~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((k4\_tarski~X3~X4 \in u4\_struct\_0~\\
X0){\unicdbdjdcd}(k1\_funct\_1~(k6\_circuit2~X0~X1~X2)~(k4\_tarski~X3~X4)=k1\_funct\_1~\\
X4~(k3\_relat\_1~X3~X2)))))))\end{array}$$
\end{theorem}
\end{document}
