Ajustando uma árvore enorme em uma página

Question 1

Bem, você poderia fazer isso, mas seus leitores não vão agradecer por isso! Seria melhor repensar a forma como você está apresentando as informações (ou imprimir em A3).

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}

\begin{document}
\begin{tikzpicture}
\Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
\end{tikzpicture}


\rotatebox{90}{%
\resizebox{\textheight}{!}{%
 \begin{tikzpicture}[baseline=(current bounding box.center)]
\Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
\end{tikzpicture} {\Huge$\Rightarrow$}
 \begin{tikzpicture} [baseline=(current bounding box.center),  scale=.5]
    \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] : t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
\draw[semithick, dashed, ->] (le)..controls +(south west:5) and +(south:5) .. (ue);
\draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
\begin{scope}[xshift=-0.5cm,yshift=-10cm]
      \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] : t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
\draw[semithick, dashed, ->] (le)..controls +(south west:2) and +(south:2) .. (ue);
\draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \end{scope}
    \end{tikzpicture}}}
\end{document}

Se você quiser a primeira árvore na mesma página, você pode tentar isso, mas, novamente, seus leitores não acharão fácil:

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}

\begin{document}
\rotatebox{90}{%
  \begin{minipage}{\textheight}
  \begin{tikzpicture}
    \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
  \end{tikzpicture}

  \resizebox{\textheight}{!}{%
    \begin{tikzpicture}[baseline=(current bounding box.center)]
      \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
    \end{tikzpicture} {\Huge$\Rightarrow$}
    \begin{tikzpicture} [baseline=(current bounding box.center),  scale=.5]
      \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] : t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
      \draw[semithick, dashed, ->] (le)..controls +(south west:5) and +(south:5) .. (ue);
      \draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \begin{scope}[xshift=-0.5cm,yshift=-10cm]
        \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] : t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
        \draw[semithick, dashed, ->] (le)..controls +(south west:2) and +(south:2) .. (ue);
        \draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \end{scope}
    \end{tikzpicture}}
\end{minipage}}
\end{document}

Adicione \centeringse \minipagequiser que as árvores sejam centralizadas:

Presumo que a escala diferente tenha algum significado, por isso mantive a escala relativa constante dentro da caixa girada. No entanto, os resultados obviamente parecem um pouco estranhos....

Answer

Bem, você poderia fazer isso, mas seus leitores não vão agradecer por isso! Seria melhor repensar a forma como você está apresentando as informações (ou imprimir em A3).

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}

\begin{document}
\begin{tikzpicture}
\Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
\end{tikzpicture}


\rotatebox{90}{%
\resizebox{\textheight}{!}{%
 \begin{tikzpicture}[baseline=(current bounding box.center)]
\Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
\end{tikzpicture} {\Huge$\Rightarrow$}
 \begin{tikzpicture} [baseline=(current bounding box.center),  scale=.5]
    \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] : t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
\draw[semithick, dashed, ->] (le)..controls +(south west:5) and +(south:5) .. (ue);
\draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
\begin{scope}[xshift=-0.5cm,yshift=-10cm]
      \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] : t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
\draw[semithick, dashed, ->] (le)..controls +(south west:2) and +(south:2) .. (ue);
\draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \end{scope}
    \end{tikzpicture}}}
\end{document}

Se você quiser a primeira árvore na mesma página, você pode tentar isso, mas, novamente, seus leitores não acharão fácil:

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}

\begin{document}
\rotatebox{90}{%
  \begin{minipage}{\textheight}
  \begin{tikzpicture}
    \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
  \end{tikzpicture}

  \resizebox{\textheight}{!}{%
    \begin{tikzpicture}[baseline=(current bounding box.center)]
      \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
    \end{tikzpicture} {\Huge$\Rightarrow$}
    \begin{tikzpicture} [baseline=(current bounding box.center),  scale=.5]
      \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] : t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
      \draw[semithick, dashed, ->] (le)..controls +(south west:5) and +(south:5) .. (ue);
      \draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \begin{scope}[xshift=-0.5cm,yshift=-10cm]
        \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]: (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] : (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] : t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]: (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]: (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man: \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m): (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m): (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y): (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
        \draw[semithick, dashed, ->] (le)..controls +(south west:2) and +(south:2) .. (ue);
        \draw[semithick, dashed, ->] (me)..controls +(south west:7) and +(south:7) .. (ne);
      \end{scope}
    \end{tikzpicture}}
\end{minipage}}
\end{document}

Adicione \centeringse \minipagequiser que as árvores sejam centralizadas:

Presumo que a escala diferente tenha algum significado, por isso mantive a escala relativa constante dentro da caixa girada. No entanto, os resultados obviamente parecem um pouco estranhos....

Question 2

Concordo com o cfr que você pode querer repensar a quantidade de informações que está colocando em uma página, principalmente se você realmente precisa da árvore no topo, que é duplicada antes da seta.

Aqui estão as alterações que fiz para economizar espaço. Eles são todos independentes um do outro, então você pode ajustá-los para atender às suas necessidades, mas acho que você descobrirá que a quebra de linha faz a maior diferença.

Quebra de linha nos nós da árvore.Em suas árvores semânticas, quebrei as linhas nos dois pontos. Para permitir a quebra de linha nos nós, você precisará do arquivo every tree node/.style={align=center,anchor=north}. Também ajustei level distancepara evitar que os galhos ficassem muito planos ou invertidos depois que as linhas fossem quebradas.
Margens.Reduzi todas as margens para 2,5 cm usando a geometryembalagem.
Dimensionamento.Eu usei \scaleboxum comando fornecido por graphicx, que é carregado por tikz. Descobri que funciona melhor que a scaleopção em tikz.

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}
\usepackage[margin=2.5cm]{geometry}

\begin{document}

  \scalebox{.7}{
  \begin{tikzpicture}
    \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
  \end{tikzpicture}
  }

  \rotatebox{90}{%
    \scalebox{.6}{
    \begin{tikzpicture}[baseline=(current bounding box.center)]
      \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
    \end{tikzpicture} {\Huge$\Rightarrow$}
    }
    \scalebox{.6}{
    \begin{tikzpicture} [baseline=(current bounding box.center), every tree node/.style={align=center,anchor=north}, level distance = 9ex]
      \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]:}\\\formula{(t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]:}\\ \formula{(\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] :}\\ \formula{(e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$:\\ \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] :}\\\formula{t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]:}\\ \formula{(\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]:}\\\formula{(e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man:\\ \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m):}\\\formula{(t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m):}\\\formula{ (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y):}\\\formula{ (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
      \draw[semithick, dashed, ->] (le.south west)..controls +(south west:4) and +(south:5) .. (ue);
      \draw[semithick, dashed, ->] (me.south west)..controls +(-10,-3) and +(south:7) .. (ne);
      \begin{scope}[xshift=-0.5cm,yshift=-12cm]
        \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]:}\\\formula{ (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]:}\\\formula{ (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] :}\\\formula{ (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$:\\\formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] :}\\\formula{ t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]:}\\\formula{ (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]:}\\\formula{ (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man:\\\formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m):}\\\formula{ (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m):}\\\formula{ (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y):}\\\formula{ (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
        \draw[semithick, dashed, ->] (le.west)..controls +(west:1) and +(south:1) .. (ue);
        \draw[semithick, dashed, ->] (me.south west)..controls +(-12,-3) and +(south:8) .. (ne);
      \end{scope}
    \end{tikzpicture}}}

\end{document}

Answer

Concordo com o cfr que você pode querer repensar a quantidade de informações que está colocando em uma página, principalmente se você realmente precisa da árvore no topo, que é duplicada antes da seta.

Aqui estão as alterações que fiz para economizar espaço. Eles são todos independentes um do outro, então você pode ajustá-los para atender às suas necessidades, mas acho que você descobrirá que a quebra de linha faz a maior diferença.

Quebra de linha nos nós da árvore.Em suas árvores semânticas, quebrei as linhas nos dois pontos. Para permitir a quebra de linha nos nós, você precisará do arquivo every tree node/.style={align=center,anchor=north}. Também ajustei level distancepara evitar que os galhos ficassem muito planos ou invertidos depois que as linhas fossem quebradas.
Margens.Reduzi todas as margens para 2,5 cm usando a geometryembalagem.
Dimensionamento.Eu usei \scaleboxum comando fornecido por graphicx, que é carregado por tikz. Descobri que funciona melhor que a scaleopção em tikz.

\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\newcommand\formula[1]{\ensuremath{#1}}
\usepackage{ulem}
\usepackage[margin=2.5cm]{geometry}

\begin{document}

  \scalebox{.7}{
  \begin{tikzpicture}
    \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
  \end{tikzpicture}
  }

  \rotatebox{90}{%
    \scalebox{.6}{
    \begin{tikzpicture}[baseline=(current bounding box.center)]
      \Tree [.S  [.DP [.D some ] [.N woman ] ] [.VP  [.V hugs ] [.DP [.D every ] [.N man ] ]]]
    \end{tikzpicture} {\Huge$\Rightarrow$}
    }
    \scalebox{.6}{
    \begin{tikzpicture} [baseline=(current bounding box.center), every tree node/.style={align=center,anchor=north}, level distance = 9ex]
      \Tree [.{\formula{\exists y [woman' (y) \land [\forall x [man' (x) \rightarrow hug'(y, x)]]:}\\\formula{(t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \exists y [woman' (y) \land Q(x)]:}\\ \formula{(\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists y [woman' (y) \land Q(x)] :}\\ \formula{(e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$:\\ \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\forall x [man' (x) \rightarrow saw'(j, x)] :}\\\formula{t_{1} }} [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]:}\\ \formula{(\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall (x) [P(x) \rightarrow Q(x)]:}\\\formula{(e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man:\\ \formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m):}\\\formula{(t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (me) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m):}\\\formula{ (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y):}\\\formula{ (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (le) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
      \draw[semithick, dashed, ->] (le.south west)..controls +(south west:4) and +(south:5) .. (ue);
      \draw[semithick, dashed, ->] (me.south west)..controls +(-10,-3) and +(south:7) .. (ne);
      \begin{scope}[xshift=-0.5cm,yshift=-12cm]
        \Tree [.{\formula{\forall x [man' (x) \rightarrow[\exists y [woman' (y) \rightarrow hug'(y, x)]]:}\\\formula{ (t} \hspace{0.1cm}}  [.{\formula{\lambda Q. \forall x [man' (x) \rightarrow Q(x)]:}\\\formula{ (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \forall x [P(x) \rightarrow Q(x)] :}\\\formula{ (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda z. woman(z)$:\\\formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [.  \node (ne) {e$_{2}$}; ] [.{\formula{\exists x [woman' (y) \land saw'(j, y)] :}\\\formula{ t_{1} }} [.{\formula{\lambda Q. \exists (y) [woman'(y) \land Q(y)]:}\\\formula{ (\forall X(e_{3} \rightarrow X) \rightarrow X))} \hspace{0.1cm}} [. { \formula{\lambda P. \lambda Q. \exists (y) [P(y) \land Q(y)]:}\\\formula{ (e_{4} \rightarrow t_{1})\rightarrow (\forall X(e_{3} \rightarrow X) \rightarrow X))}}   ] [.{$\lambda$ x. x is a man:\\\formula{(e_{4} \rightarrow t_{1})}}   ] ] [.{\formula{\lambda m. saw(k,m):}\\\formula{(e_{3} \rightarrow t_{1})} } [. \node (ue) {e$_{3}$}; ] [.{\formula{saw(k,m):}\\\formula{ (t_{1}) \hspace{0.1cm}  }} [.\node [circle,draw] (le) {k : e$_{2}$} ;] [.{\formula{\lambda x. saw(x,m):}\\\formula{ (e_{2}  \rightarrow t_{1}) \hspace{0.1cm}  }} [. {\formula{\lambda y\lambda x. saw(x,y):}\\\formula{ (e_{3} \rightarrow (e_{2}  \rightarrow  t_{1})} } ] [. \node [circle,draw] (me) {m : e$_{3}$} ; ]  ]  ] ] ] ] ] ] ]
        \draw[semithick, dashed, ->] (le.west)..controls +(west:1) and +(south:1) .. (ue);
        \draw[semithick, dashed, ->] (me.south west)..controls +(-12,-3) and +(south:8) .. (ne);
      \end{scope}
    \end{tikzpicture}}}

\end{document}

Ajustando uma árvore enorme em uma página

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