\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\_abcmiz\_a (TMRRaEEJejrn8vZegoaCqGnsKhzadLMdATN)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k34\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k36\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ 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\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v6\_trees\_3 : {{\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 $ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_4~X2~X0~X1){\unicdbdjded}(m1\_finseq\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k34\_abcmiz\_1~X0)){\unicdcdcdhd}\\
(v3\_trees\_3~(k34\_abcmiz\_1~X0)))\end{array}
\label{hyp:ggdgbdfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\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}((v1\_relat\_1~(k4\_trees\_4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k4\_trees\_4~\\
X0~X1)){\unicdcdcdhd}(v3\_trees\_2~(k4\_trees\_4~X0~X1))))\end{array}
\label{hyp:egehpflgedpfehchfgfgdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~\\
X0){\unicdcdcdhd}((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(((v2\_abcmiz\_1~X1~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdcdcdhd}(m1\_finseq\_1~X2~(k34\_abcmiz\_1~\\
X0)))){\unicdbdjdcd}((v5\_abcmiz\_1~(k36\_abcmiz\_1~X0~X1~X2)~X0~(k28\_abcmiz\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k36\_abcmiz\_1~X0~X1~X2)~(k3\_card\_3~(u3\_msualg\_1~\\
X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpflgddgdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k34\_abcmiz\_1~X0)~(k1\_zfmisc\_1~\\
(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpflgddedpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}(((v5\_abcmiz\_1~\\
X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjdcd}(k10\_abcmiz\_a~X0~X1=k1\_xtuple\_0~(k1\_funct\_1~\\
X1~k1\_xboole\_0))){\unicdcdcdhd}((\preoh v5\_abcmiz\_1~X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjdcd}(k10\_abcmiz\_a~\\
X0~X1=k1\_xboole\_0))))\end{array}
\label{hyp:egjdpfbgcgdgngjgkhpfbg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_4~X2~(k3\_card\_3~(\\
u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~\\
X0)){\unicdbdjdcd}((k3\_finseq\_1~X2=k3\_finseq\_1~(k1\_msualg\_1~X0~X1)){\unicdbdjdcd}(k36\_abcmiz\_1~\\
X0~X1~X2=k4\_trees\_4~(k4\_tarski~X1~(u1\_struct\_0~X0))~X2))))\end{array}
\label{hyp:egddfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_trees\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_finseq\_1~X1~X0){\unicdbdjdcd}(v6\_trees\_3~X1))\end{array}
\label{hyp:dgdgbdhdpfehchfgfgdhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_4~X2~(k3\_card\_3~(\\
u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~\\
X0)){\unicdbdjdcd}((k3\_finseq\_1~X2=k3\_finseq\_1~(k1\_msualg\_1~X0~X1)){\unicdbdjdcd}(k10\_abcmiz\_a~\\
X0~(k36\_abcmiz\_1~X0~X1~X2)=X1))))\end{array}$$
\end{theorem}
\end{document}
