\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{t29\_gfacirc1 (TMc6hjharDjTynrDPV4heMyKSzRgpL4DMhn)}
\maketitle
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 $ 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 $ k10\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ 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.
Let $ k10\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
{\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X3{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X1~X2)~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k4\_card\_3~(u3\_msualg\_1~(k8\_facirc\_1~\\
X1~X2~X3~X0)~(k10\_facirc\_1~X1~X2~X3~X0)))){\unicdbdjdcd}((k1\_twoscomp~(k8\_facirc\_1~\\
X1~X2~X3~X0)~(k10\_facirc\_1~X1~X2~X3~X0)~(k6\_circuit2~(k8\_facirc\_1~\\
X1~X2~X3~X0)~(k10\_facirc\_1~X1~X2~X3~X0)~X4)~(k9\_facirc\_1~X1~X2~X3~X0)=\\
k1\_funct\_1~X0~(k10\_finseq\_1~(k1\_funct\_1~X4~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~X0))~(k1\_funct\_1~X4~X3))){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k8\_facirc\_1~\\
X1~X2~X3~X0)~(k10\_facirc\_1~X1~X2~X3~X0)~X4)~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~X0)=k1\_funct\_1~X0~(k10\_finseq\_1~(k1\_funct\_1~X4~X1)~(k1\_funct\_1~\\
X4~X2))){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~(k8\_facirc\_1~X1~X2~X3~X0)~(k10\_facirc\_1~\\
X1~X2~X3~X0)~X4)~X1=k1\_funct\_1~X4~X1){\unicdcdcdhd}((k1\_funct\_1~(k6\_circuit2~\\
(k8\_facirc\_1~X1~X2~X3~X0)~(k10\_facirc\_1~X1~X2~X3~X0)~X4)~X2=k1\_funct\_1~\\
X4~X2){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~(k8\_facirc\_1~X1~X2~X3~X0)~(k10\_facirc\_1~\\
X1~X2~X3~X0)~X4)~X3=k1\_funct\_1~X4~X3)))))))\end{array}
\label{hyp:mgbdgdpfhgggbgdgjgchdgbd}
\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 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}((X0=k14\_twoscomp){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_margrel1){\unicdbdjdcd}(k1\_funct\_1~X0~(k10\_finseq\_1~X1~X2)=k2\_binarith~\\
X1~X2))))\end{array}
\label{hyp:egbdddpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k12\_gfacirc1~X0~X1~X2=k9\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdcdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k11\_gfacirc1~X0~X1~X2=k10\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k10\_gfacirc1~X0~X1~X2=k8\_facirc\_1~\\
X0~X1~X2~k14\_twoscomp\end{array}
\label{hyp:egbdadpfhgggbgdgjgchdgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k14\_twoscomp){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(\\
u3\_msualg\_1~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~k6\_margrel1){\unicdbdjdcd}(((X4=k1\_funct\_1~X3~(k4\_tarski~\\
(k10\_finseq\_1~X0~X1)~k14\_twoscomp)){\unicdcdcdhd}(X7=k1\_funct\_1~X3~X2)){\unicdbdjdcd}(\\
k1\_twoscomp~(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)~(k6\_circuit2~\\
(k10\_gfacirc1~X0~X1~X2)~(k11\_gfacirc1~X0~X1~X2)~X3)~(k12\_gfacirc1~\\
X0~X1~X2)=k2\_binarith~X4~X7)))))))\end{array}$$
\end{theorem}
\end{document}
