\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{t54\_facirc\_1 (TMS8HBV8QRLxD2QnsaQhkYy1GaC2Xy2z1mq)}
\maketitle
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\_\_3 : {\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 $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(v1\_finset\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(k4\_finseq\_2~np\_\_3~X3)~X3){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_3~X3)~X3))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_card\_3~\\
(u3\_msualg\_1~(k5\_circcomb~X4~(k11\_finseq\_1~X0~X1~X2))~(k7\_circcomb~\\
np\_\_3~X3~X4~(k11\_finseq\_1~X0~X1~X2))))){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~\\
(k5\_circcomb~X4~(k11\_finseq\_1~X0~X1~X2))~(k7\_circcomb~np\_\_3~X3~X4~\\
(k11\_finseq\_1~X0~X1~X2))~X5)~(k4\_tarski~(k11\_finseq\_1~X0~X1~X2)~X4)=\\
k1\_funct\_1~X4~(k11\_finseq\_1~(k1\_funct\_1~X5~X0)~(k1\_funct\_1~X5~X1)~\\
(k1\_funct\_1~X5~X2))){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~\\
X4~(k11\_finseq\_1~X0~X1~X2))~(k7\_circcomb~np\_\_3~X3~X4~(k11\_finseq\_1~\\
X0~X1~X2))~X5)~X0=k1\_funct\_1~X5~X0){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(\\
k5\_circcomb~X4~(k11\_finseq\_1~X0~X1~X2))~(k7\_circcomb~np\_\_3~X3~X4~\\
(k11\_finseq\_1~X0~X1~X2))~X5)~X1=k1\_funct\_1~X5~X1){\unicdcdcdhd}(k1\_funct\_1~(\\
k6\_circuit2~(k5\_circcomb~X4~(k11\_finseq\_1~X0~X1~X2))~(k7\_circcomb~\\
np\_\_3~X3~X4~(k11\_finseq\_1~X0~X1~X2))~X5)~X2=k1\_funct\_1~X5~X2))))))\end{array}
\label{hyp:ehfdcdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k6\_margrel1}}}}\label{hyp:ggdgcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_finset\_1}~{({{{k2\_tarski}~{X0}}~{X1}})}}}}\label{hyp:ggdgcdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_margrel1}={{{k2\_tarski}~{k6\_numbers}}~{np\_\_1}}}\label{hyp:egbdbdpfngbgchhgchfgmgbd}
\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\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}(k7\_facirc\_1~X0~X1~X2~X3=k7\_circcomb~\\
np\_\_3~k6\_margrel1~X3~(k11\_finseq\_1~X0~X1~X2))\end{array}
\label{hyp:egbdbdpfggbgdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfggbgdgjgchdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(\\
k4\_card\_3~(u3\_msualg\_1~(k5\_circcomb~X3~(k11\_finseq\_1~X0~X1~X2))~\\
(k7\_facirc\_1~X0~X1~X2~X3)))){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~\\
X3~(k11\_finseq\_1~X0~X1~X2))~(k7\_facirc\_1~X0~X1~X2~X3)~X4)~(k4\_tarski~\\
(k11\_finseq\_1~X0~X1~X2)~X3)=k1\_funct\_1~X3~(k11\_finseq\_1~(k1\_funct\_1~\\
X4~X0)~(k1\_funct\_1~X4~X1)~(k1\_funct\_1~X4~X2))){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~\\
(k5\_circcomb~X3~(k11\_finseq\_1~X0~X1~X2))~(k7\_facirc\_1~X0~X1~X2~X3)~\\
X4)~X0=k1\_funct\_1~X4~X0){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~\\
X3~(k11\_finseq\_1~X0~X1~X2))~(k7\_facirc\_1~X0~X1~X2~X3)~X4)~X1=k1\_funct\_1~\\
X4~X1){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~X3~(k11\_finseq\_1~\\
X0~X1~X2))~(k7\_facirc\_1~X0~X1~X2~X3)~X4)~X2=k1\_funct\_1~X4~X2)))))\end{array}$$
\end{theorem}
\end{document}
