\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{t64\_modelc\_2 (TMM4CzUawnebSkGFahmW1PZXPx56s8pFEm3)}
\maketitle
Let $ v1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k25\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k43\_modelc\_2 : {\iota}$ be given.
Let $ r7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k30\_modelc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k42\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r6\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_robbins1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k15\_modelc\_2 : {\iota}$ be given.
Let $ u1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k47\_modelc\_2 : {\iota}$ be given.
Let $ k46\_modelc\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k30\_modelc\_1~(k25\_modelc\_2~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k25\_modelc\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(u1\_struct\_0~(k42\_modelc\_2~X0~X1))){\unicdbdjdcd}((r6\_modelc\_2~\\
X0~X1~X2~(k3\_robbins1~(k42\_modelc\_2~X0~X1)~X3)){\unicdbdjded}(\preoh r6\_modelc\_2~X0~\\
X1~X2~X3)))))\end{array}
\label{hyp:ehfdhdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_modelc\_2~X1){\unicdcdcdhd}(l1\_modelc\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k15\_modelc\_2~\\
(u1\_modelc\_2~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k15\_modelc\_2~(u1\_modelc\_2~X1)))))){\unicdbdjdcd}(k21\_modelc\_2~X1~X2~(k3\_modelc\_2~\\
X0)=k3\_robbins1~X1~(k21\_modelc\_2~X1~X2~X0))))\end{array}
\label{hyp:ehfdadpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
v1\_modelc\_2~(k3\_modelc\_2~X0))\end{array}
\label{hyp:ggdgcdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k30\_modelc\_1~(k25\_modelc\_2~X0)))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k42\_modelc\_2~X0~X1)){\unicdcdcdhd}((v9\_modelc\_2~(k42\_modelc\_2~\\
X0~X1)){\unicdcdcdhd}(v10\_modelc\_2~(k42\_modelc\_2~X0~X1))))\end{array}
\label{hyp:ggdgbdbdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k47\_modelc\_2){\unicdcdcdhd}((v1\_funct\_2~k47\_modelc\_2~k15\_modelc\_2~\\
(u1\_modelc\_2~(k42\_modelc\_2~k43\_modelc\_2~k46\_modelc\_2))){\unicdcdcdhd}(m1\_subset\_1~\\
k47\_modelc\_2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k15\_modelc\_2~(u1\_modelc\_2~\\
(k42\_modelc\_2~k43\_modelc\_2~k46\_modelc\_2))))))\end{array}
\label{hyp:egehpflgedhdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~k46\_modelc\_2){\unicdcdcdhd}(m1\_subset\_1~k46\_modelc\_2~(k1\_zfmisc\_1~\\
(k30\_modelc\_1~(k25\_modelc\_2~k43\_modelc\_2))))\end{array}
\label{hyp:egehpflgedgdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k43\_modelc\_2}}}}\label{hyp:egehpflgedddpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k30\_modelc\_1~(k25\_modelc\_2~X0)))))){\unicdbdjdcd}\\
(l1\_modelc\_2~(k42\_modelc\_2~X0~X1))\end{array}
\label{hyp:egehpflgedcdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k5\_numbers){\unicdbdjdcd}(m2\_finseq\_1~(k3\_modelc\_2~\\
X0)~k5\_numbers)\end{array}
\label{hyp:egehpflgddpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_modelc\_2~\\
X0){\unicdcdcdhd}(l1\_modelc\_2~X0))){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k15\_modelc\_2~\\
(u1\_modelc\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k15\_modelc\_2~(u1\_modelc\_2~X0)))))){\unicdcdcdhd}((v1\_modelc\_2~X2){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~k5\_numbers)))){\unicdbdjdcd}(m1\_subset\_1~(k21\_modelc\_2~X0~X1~X2)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgcdbdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((r7\_modelc\_2~\\
X0~X1){\unicdbdjded}(r6\_modelc\_2~k43\_modelc\_2~k46\_modelc\_2~X0~(k21\_modelc\_2~\\
(k42\_modelc\_2~k43\_modelc\_2~k46\_modelc\_2)~k47\_modelc\_2~X1))))\end{array}
\label{hyp:eggdddpfngpgegfgmgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfngpgegfgmgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}((r7\_modelc\_2~\\
X1~(k3\_modelc\_2~X0)){\unicdbdjded}(\preoh r7\_modelc\_2~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
