\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{t13\_circuit1 (TMT5uP9zLHtcWzEReAi44LXg8R395XXxh46)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_msafree2 : {{\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 $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_circuit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_tarski : {{\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 $ v6\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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\_msafree2~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}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~(k5\_msafree2~X0~X1))~X2)){\unicdbdjdcd}(\preoh (X2 \in k7\_subset\_1~\\
(u1\_struct\_0~X0)~(k3\_msafree2~X0)~(k1\_msafree2~X0)){\unicdcdcdhd}((k5\_card\_1~\\
X3=k4\_circuit1~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_finseq\_1~X4){\unicdcdcdhd}(v6\_trees\_3~X4)))){\unicdbdjdcd}(X3{\unicdcdgdad}k4\_trees\_4~(k4\_tarski~\\
(k4\_msafree2~X0~X2)~(u1\_struct\_0~X0))~X4)))))))\end{array}
\label{hyp:ehbdcdpfdgjgchdgfhjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
((v2\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k4\_msafree2~X0~X1)~(u4\_struct\_0~X0))\end{array}
\label{hyp:egehpflgedpfngdhbgggchfgfgcd}
\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 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((v6\_trees\_3~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v3\_trees\_2~X2))){\unicdbdjdcd}((X2=k4\_trees\_4~X0~X1){\unicdbdjded}(({\unicdcdaddd} X3 .  (\\
(v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finseq\_1~X3){\unicdcdcdhd}(v6\_trees\_3~\\
X3)))){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(k9\_xtuple\_0~X2=k11\_trees\_3~(k2\_funct\_6~X3)))){\unicdcdcdhd}\\
((k1\_funct\_1~X2~k1\_xboole\_0=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
k5\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~X3){\unicdbdjdcd}(k5\_trees\_2~\\
X2~(k12\_finseq\_1~k5\_numbers~X3)=k1\_funct\_1~X1~(k2\_nat\_1~X3~np\_\_1)))))))))\end{array}
\label{hyp:egedpfehchfgfgdhpfed}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_msafree2~X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdcdcdhd}\\
(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_funct\_1~(u3\_msualg\_1~X0~(k5\_msafree2~X0~X1))~X2)){\unicdbdjdcd}(v3\_trees\_2~\\
X3))\end{array}
\label{hyp:dgdgcdpfdgjgchdgfhjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_msafree2~X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdcdcdhd}\\
(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_funct\_1~(u3\_msualg\_1~X0~(k5\_msafree2~X0~X1))~X2)){\unicdbdjdcd}((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(v1\_finset\_1~X3)))))\end{array}
\label{hyp:dgdgbdpfdgjgchdgfhjgehbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfdgjgchdgfhjgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~\\
X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_funct\_1~(u3\_msualg\_1~X0~(k5\_msafree2~X0~X1))~X2)){\unicdbdjdcd}(\preoh (X2 \in k7\_subset\_1~\\
(u1\_struct\_0~X0)~(k3\_msafree2~X0)~(k1\_msafree2~X0)){\unicdcdcdhd}((k5\_card\_1~\\
X3=k4\_circuit1~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}(k1\_funct\_1~X3~k1\_xboole\_0{\unicdcdgdad}k4\_tarski~X4~(u1\_struct\_0~X0))))))))\end{array}$$
\end{theorem}
\end{document}
