\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{t3\_matrix13 (TMPcyQe64ymwZxUQEUz8EJWuHpSMDAW412V)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_matrix\_1~X2~X1~X0~X0){\unicdbdjdcd}((k3\_finseq\_1~X2=X0){\unicdcdcdhd}((k1\_matrix\_1~\\
X2=X0){\unicdcdcdhd}(k2\_matrix\_1~X2=k2\_zfmisc\_1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~\\
X0))))))\end{array}
\label{hyp:ehcdedpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_matrix\_1~X2~X1~X0~X0))){\unicdbdjdcd}(k5\_matrix\_1~X0~X1~X2=k4\_matrix\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~X0~X1~X2){\unicdbdjdcd}\\
((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))))\end{array}
\label{hyp:egehpfngbdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_matrix\_1~X2~X1~X0~X0))){\unicdbdjdcd}(m1\_matrix\_1~(k5\_matrix\_1~X0~X1~\\
X2)~X1~X0~X0)\end{array}
\label{hyp:egehpflgfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}\\
((v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdcdcdhd}(m1\_matrix\_1~X2~(u1\_struct\_0~X1)~\\
X0~X0))){\unicdbdjdcd}(m2\_finseq\_1~(k13\_matrix\_3~X0~X1~X2)~(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpflgbdddpfngbgehchjgihpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}((X2=k4\_matrix\_1~X0~X1){\unicdbdjded}\\
((k3\_finseq\_1~X2=k1\_matrix\_1~X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((k4\_tarski~X3~X4 \in k2\_matrix\_1~\\
X2){\unicdbdjded}(k4\_tarski~X4~X3 \in k2\_matrix\_1~X1)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((k4\_tarski~X4~X3 \in k2\_matrix\_1~\\
X1){\unicdbdjdcd}(k3\_matrix\_1~X0~X2~X3~X4=k3\_matrix\_1~X0~X1~X4~X3)))))))))\end{array}
\label{hyp:eggdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}((X3=\\
k13\_matrix\_3~X0~X1~X2){\unicdbdjded}((k3\_finseq\_1~X3=X0){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}((X4 \in k2\_finseq\_1~X0){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k3\_matrix\_1~(u1\_struct\_0~\\
X1)~X2~X4~X4))))))))\end{array}
\label{hyp:egbdadpfngbgehchjgihpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddpfngbgehchjgihbddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(k13\_matrix\_3~X0~X1~X2=k13\_matrix\_3~X0~X1~(k5\_matrix\_1~\\
X0~(u1\_struct\_0~X1)~X2))))\end{array}$$
\end{theorem}
\end{document}
