Centering the "prooftrees.sty" trees

Question

Is it possible to overlap the center of the node containing the first premiss of proof trees like the ones in the MWE with the vertical center of the page?

Here is the MWE:

\documentclass[openany,oneside,a4paper,11pt]{memoir}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[linguistics]{forest}
\usepackage[tableaux]{prooftrees}

    \begin{document}

    \begin{center}
        \begin{tableau}
            {}
            [\forall x(Fx \rightarrow Bx),just={premiss}
            [Fa,just={premiss}
            [\lnot Ba, just={negated the conclusion}
            [Fa \rightarrow Ba, just={1 $ \forall $}
            [\lnot Fa, just={4 $ \rightarrow $}, close]
            [Ba, close]
            ]
            ]
            ]
            ]
        \end{tableau}
    \end{center}

    \begin{center}
        \begin{tableau}% Adepted from Peter Smith's "LATEX for logicians: Setting tableaux using prooftrees.sty"
            {
                line no sep= 1.5cm,
                just sep= 1.5cm,
                for tree={s sep'=10mm},
                just refs right, % Set where crossreferences go
            }
            [((P \land Q) \rightarrow R), just={Premiss}, name=Prem
            [\neg(P \rightarrow (Q \rightarrow R)), just={Negated conclusion}, name=NegConc
            [P, just={From: NegConc}
            [\neg(Q \rightarrow R), just={From: NegConc},name=Alice
            [Q, just={From: Alice}
            [\neg R, s sep=30mm, just={From: Alice}
            [\neg(P \land Q), just={Alternatives from: Prem},name=Bertie
            [\neg P, close, just={Alternatives from: Bertie}
            ]
            [\neg Q, close
            ]
            ]
            [R, close]
            ]
            ]
            ]
            ]
            ]
            ]
        \end{tableau}
    \end{center}

    \end{document}

Answer 1

For the record, I recommend not doing this for both technical and aesthetic reasons.

Caveat emptor.

The tableau is just a box. Whatever you do in the box is, basically, irrelevant to how that box is treated as a whole. So, the only way I can think to do this (without using absolute positioning) is using brute force and ignorance.

centre first premise makes the box bigger by enough to shift the tree such that the centre of the first premise aligns with the point halfway between the left and right margins, provided that the box is placed at the left margin.

The upshot of this is that you must eliminate the center environment and add \noindent if the tableau starts a new paragraph.

Your second tableau is too wide for the text block already. Centring the fist premise as described makes the problem much worse.

showframe is used to illustrate the layout and the problem.

Again I do not recommend trying this at home. Should not be taken internally. Keep out of reach of small children, cats and parakeets. Provided as is. If it breaks, you get to keep all the itsy-bitsy little pieces.

\documentclass[openany,oneside,a4paper,11pt]{memoir}
\usepackage{amssymb}
\usepackage{amsmath,showframe}
\usepackage[linguistics]{forest}
\usepackage[tableaux]{prooftrees}

\begin{document}
\forestset{
  declare dimen register={centring dim},
  centring dim'=0pt,
  centre first premise/.style={
    before drawing tree={
      for nodewalk={
        fake=r,
        1,
        while nodewalk valid={n}{n}
      }{
        tempdima/.process={OOw2+d{max x}{min x}{(##1-##2)/2}  },
      },
      tempdimb/.min={>OOw2+d{x}{min x}{##1+##2}}{tree},
      tikz+={
        \path (current bounding box.west) -- ++({-.5\textwidth-\forestregister{tempdimb}},0);
      }
    },
  },
}

\noindent
\begin{tableau}
  {centre first premise}
  [\forall x(Fx \rightarrow Bx),just={premiss}
  [Fa,just={premiss}
  [\lnot Ba, just={negated conclusion}
  [Fa \rightarrow Ba, just={1 $ \forall $}
  [\lnot Fa, just={4 $ \rightarrow $}, close]
  [Ba, close]
  ]
  ]
  ]
  ]
\end{tableau}

\noindent
\begin{tableau}% Adepted from Peter Smith's "LATEX for logicians: Setting tableaux using prooftrees.sty"
  {
    line no sep= 1.5cm,
    just sep= 1.5cm,
    for tree={s sep'=10mm},
    just refs right, % Set where crossreferences go
    centre first premise,
  }
  [((P \land Q) \rightarrow R), just={Premiss}, name=Prem
  [\neg(P \rightarrow (Q \rightarrow R)), just={Negated conclusion}, name=NegConc
  [P, just={From: NegConc}
  [\neg(Q \rightarrow R), just={From: NegConc},name=Alice
  [Q, just={From: Alice}
  [\neg R, s sep=30mm, just={From: Alice}
  [\neg(P \land Q), just={Alternatives from: Prem},name=Bertie
  [\neg P, close, just={Alternatives from: Bertie}
  ]
  [\neg Q, close
  ]
  ]
  [R, close]
  ]
  ]
  ]
  ]
  ]
  ]
\end{tableau}

\end{document}