\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\_osalg\_1 (TMFCrx2iAooSC2T3A1VcKEJZmsdPGMsW3Y7)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_osalg\_1 : {{\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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r6\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r5\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r3\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v7\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v8\_osalg\_1~X0){\unicdcdcdhd}((v10\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~\\
(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}(((r1\_osalg\_1~\\
X0~X1~X2){\unicdcdcdhd}((r2\_osalg\_1~X0~X3~(k1\_msualg\_1~X0~X1)){\unicdcdcdhd}(r2\_osalg\_1~X0~\\
X3~(k1\_msualg\_1~X0~X2)))){\unicdbdjdcd}(k2\_osalg\_1~X0~X1~X3=k2\_osalg\_1~X0~X2~\\
X3)))))\end{array}
\label{hyp:ehddedpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_osalg\_1~X0~X1~X2){\unicdbdjded}(k8\_osalg\_1~X0~X1=k8\_osalg\_1~X0~X2))))\end{array}
\label{hyp:ehddbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v8\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdbdjdcd}\\
((v10\_osalg\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(\preoh (r2\_osalg\_1~X0~X2~(k1\_msualg\_1~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u4\_struct\_0~X0)){\unicdbdjdcd}(\preoh r5\_osalg\_1~X0~X1~X3~X2))))))\end{array}
\label{hyp:ehbdbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~(u1\_struct\_0~X0)~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r3\_osalg\_1~X0~X1~X2~X3){\unicdbdjded}((r1\_osalg\_1~X0~X1~\\
X2){\unicdcdcdhd}((r2\_osalg\_1~X0~X3~(k1\_msualg\_1~X0~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u4\_struct\_0~X0)){\unicdbdjdcd}(((r1\_osalg\_1~X0~X1~X4){\unicdcdcdhd}(r2\_osalg\_1~X0~X3~\\
(k1\_msualg\_1~X0~X4))){\unicdbdjdcd}(r2\_osalg\_1~X0~(k1\_msualg\_1~X0~X2)~(k1\_msualg\_1~\\
X0~X4))))))))))\end{array}
\label{hyp:egjdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}((v8\_osalg\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(v7\_osalg\_1~X1~\\
X0)))\end{array}
\label{hyp:egidpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}((v7\_osalg\_1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u4\_struct\_0~X0)){\unicdbdjdcd}(((r1\_osalg\_1~X0~X1~X2){\unicdcdcdhd}(r2\_osalg\_1~X0~(k1\_msualg\_1~\\
X0~X1)~(k1\_msualg\_1~X0~X2))){\unicdbdjdcd}(r3\_orders\_2~X0~(k2\_msualg\_1~X0~X1)~\\
(k2\_msualg\_1~X0~X2))))))\end{array}
\label{hyp:eghdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((r6\_osalg\_1~X0~X1~X2){\unicdbdjded}((r1\_osalg\_1~X0~X1~X2){\unicdcdcdhd}((r2\_osalg\_1~\\
X0~(k1\_msualg\_1~X0~X1)~(k1\_msualg\_1~X0~X2)){\unicdcdcdhd}(r3\_orders\_2~X0~(k2\_msualg\_1~\\
X0~X1)~(k2\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:egcdadpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v8\_osalg\_1~X0){\unicdcdcdhd}((v10\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((r2\_osalg\_1~X0~X2~(k1\_msualg\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u4\_struct\_0~X0)){\unicdbdjdcd}((X3=k2\_osalg\_1~X0~X1~X2){\unicdbdjded}(r3\_osalg\_1~X0~\\
X1~X3~X2))))))\end{array}
\label{hyp:egbdedpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~(u1\_struct\_0~X0)~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r5\_osalg\_1~X0~X1~X2~X3){\unicdbdjded}((r3\_osalg\_1~X0~X1~\\
X2~X3){\unicdcdcdhd}(r4\_osalg\_1~X0~X1~X2~X3))))))\end{array}
\label{hyp:egbdbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~(u1\_struct\_0~X0)~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r4\_osalg\_1~X0~X1~X2~X3){\unicdbdjded}((r1\_osalg\_1~X0~X1~\\
X2){\unicdcdcdhd}((r2\_osalg\_1~X0~X3~(k1\_msualg\_1~X0~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u4\_struct\_0~X0)){\unicdbdjdcd}(((r1\_osalg\_1~X0~X1~X4){\unicdcdcdhd}(r2\_osalg\_1~X0~X3~\\
(k1\_msualg\_1~X0~X4))){\unicdbdjdcd}(r3\_orders\_2~X0~(k2\_msualg\_1~X0~X2)~(k2\_msualg\_1~\\
X0~X4))))))))))\end{array}
\label{hyp:egbdadpfpgdhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfpgdhbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v8\_osalg\_1~X0){\unicdcdcdhd}((v10\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((r2\_osalg\_1~X0~X2~(k1\_msualg\_1~X0~X1)){\unicdbdjdcd}(r6\_osalg\_1~X0~(k2\_osalg\_1~\\
X0~X1~X2)~X1))))\end{array}$$
\end{theorem}
\end{document}
