\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{t28\_grnilp\_1 (TMMv8mr3LyQYrUu28XW7ogDZ8Me7YjuaC8s)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_grnilp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k7\_group\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_group\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_grnilp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_group\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}(((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))))){\unicdbdjded}(k10\_group\_5~X0=X0))\end{array}
\label{hyp:ehidcdpfhgchpgfhahpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v15\_algstr\_0~X2){\unicdcdcdhd}((v1\_group\_3~X2~X0){\unicdcdcdhd}(m1\_group\_2~X2~X0))){\unicdbdjdcd}\\
((m1\_group\_6~X2~X0~X1){\unicdbdjdcd}(m1\_group\_2~(k5\_group\_6~X1~(k1\_group\_6~\\
X0~X1~X2))~(k5\_group\_6~X0~X2)))))\end{array}
\label{hyp:ehcdidpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_6~X2~X0~X1){\unicdbdjded}(m1\_group\_2~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}((v1\_group\_3~X1~X0){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_group\_6~X0~X1)){\unicdcdcdhd}(v15\_algstr\_0~(k5\_group\_6~\\
X0~X1)))\end{array}
\label{hyp:ggdgfdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(m1\_group\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_6~X2~X0~X1){\unicdbdjdcd}(m1\_group\_2~X2~X0))\end{array}
\label{hyp:egehpfngbdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v15\_algstr\_0~(k10\_group\_5~X0)){\unicdcdcdhd}(\\
m1\_group\_2~(k10\_group\_5~X0)~X0))\end{array}
\label{hyp:egehpflgbdadpfhgchpgfhahpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_grnilp\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m2\_finseq\_1~\\
X1~(k2\_grnilp\_1~X0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~k6\_numbers){\unicdcdcdhd}\\
((k1\_funct\_1~X1~np\_\_1=k7\_group\_2~X0){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~\\
X1)=k6\_group\_2~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(((X2 \in k4\_finseq\_1~X1){\unicdcdcdhd}(k2\_xcmplx\_0~X2~np\_\_1 \in k4\_finseq\_1~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~X3~X0){\unicdcdcdhd}(m1\_group\_2~\\
X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}((v1\_group\_3~X4~X0){\unicdcdcdhd}\\
(m1\_group\_2~X4~X0))){\unicdbdjdcd}(((X3=k1\_funct\_1~X1~X2){\unicdcdcdhd}(X4=k1\_funct\_1~\\
X1~(k2\_xcmplx\_0~X2~np\_\_1))){\unicdbdjdcd}((m1\_group\_6~X4~X0~X3){\unicdcdcdhd}(m1\_group\_6~\\
(k5\_group\_6~X3~(k1\_group\_6~X0~X3~X4))~(k5\_group\_6~X0~X4)~(k10\_group\_5~\\
(k5\_group\_6~X0~X4))))))))))))))\end{array}
\label{hyp:egcdpfhgchogjgmgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfhgchogjgmgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}(({\unicdcdaddd} X1 .  (m2\_finseq\_1~X1~(k2\_grnilp\_1~\\
X0)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~\\
X1~np\_\_1=k7\_group\_2~X0){\unicdcdcdhd}((k1\_funct\_1~X1~(k3\_finseq\_1~X1)=k6\_group\_2~\\
X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((X2 \in \\
k4\_finseq\_1~X1){\unicdcdcdhd}(k2\_xcmplx\_0~X2~np\_\_1 \in k4\_finseq\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v15\_algstr\_0~X3){\unicdcdcdhd}((v1\_group\_3~X3~X0){\unicdcdcdhd}(m1\_group\_2~X3~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}((v1\_group\_3~X4~X0){\unicdcdcdhd}(m1\_group\_2~\\
X4~X0))){\unicdbdjdcd}(((X3=k1\_funct\_1~X1~X2){\unicdcdcdhd}(X4=k1\_funct\_1~X1~(k2\_xcmplx\_0~\\
X2~np\_\_1))){\unicdbdjdcd}((m1\_group\_6~X4~X0~X3){\unicdcdcdhd}((\preoh v2\_struct\_0~(k5\_group\_6~\\
X0~X4)){\unicdcdcdhd}((v2\_group\_1~(k5\_group\_6~X0~X4)){\unicdcdcdhd}((v3\_group\_1~(k5\_group\_6~\\
X0~X4)){\unicdcdcdhd}((v5\_group\_1~(k5\_group\_6~X0~X4)){\unicdcdcdhd}(l3\_algstr\_0~(k5\_group\_6~\\
X0~X4)))))))))))))))){\unicdbdjdcd}(v1\_grnilp\_1~X0))\end{array}$$
\end{theorem}
\end{document}
