Is it possible to draw resolution proof tree in beamer

The tree can be easily done using TikZ:

\documentclass{article} \usepackage{tikz} \usetikzlibrary{calc,fit,trees} \begin{document} \begin{tikzpicture}[ grow'=up, level 1/.style={sibling distance=14em}, level 2/.style={sibling distance=6em}] \node (f) {False} child { node (1l) {$p(a)$} child {node (2ll) {$\neg p(a)$}} child {node (2lr) {$p(a)\vee p(b)$}} } child {node (1r) {$\neg p(a)$} child {node (2rl) {$p(X)\vee r(X)$}} child {node (2rr) {$\neg r(b)$}} }; \end{tikzpicture} \end{document} 

The only thing that might not be trivial is to draw the closed paths surrounding some groups of formulas; one possible approach here would be to use Jake's answer to padded boundary of convex hull:

\documentclass{article} \usepackage{tikz} \usetikzlibrary{calc,fit,trees} \newcommand{\convexpath}[2]{ [ create hullnodes/.code={ \global\edef\namelist{#1} \foreach [count=\counter] \nodename in \namelist { \global\edef\numberofnodes{\counter} \node at (\nodename) [draw=none,name=hullnode\counter] {}; } \node at (hullnode\numberofnodes) [name=hullnode0,draw=none] {}; \pgfmathtruncatemacro\lastnumber{\numberofnodes+1} \node at (hullnode1) [name=hullnode\lastnumber,draw=none] {}; }, create hullnodes ] ($(hullnode1)!#2!-90:(hullnode0)$) \foreach [ evaluate=\currentnode as \previousnode using \currentnode-1, evaluate=\currentnode as \nextnode using \currentnode+1 ] \currentnode in {1,...,\numberofnodes} { -- ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode)$) let \p1 = ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode) - (hullnode\currentnode)$), \n1 = {atan2(\x1,\y1)}, \p2 = ($(hullnode\currentnode)!#2!90:(hullnode\nextnode) - (hullnode\currentnode)$), \n2 = {atan2(\x2,\y2)}, \n{delta} = {-Mod(\n1-\n2,360)} in {arc [start angle=\n1, delta angle=\n{delta}, radius=#2]} } -- cycle } \begin{document} \begin{tikzpicture}[ grow'=up, level 1/.style={sibling distance=14em}, level 2/.style={sibling distance=6em}] \node (f) {False} child { node (1l) {$p(a)$} child {node (2ll) {$\neg p(a)$}} child {node (2lr) {$p(a)\vee p(b)$}} } child {node (1r) {$\neg p(a)$} child {node (2rl) {$p(X)\vee r(X)$}} child {node (2rr) {$\neg r(b)$}} }; \draw[cyan!70!black] \convexpath{f,1l.west,1r.east}{13pt}; \draw[red!70!black] \convexpath{1r,2rl.west,2rr.east}{12pt}; \end{tikzpicture} \end{document} 

You have access to many resources related to TikZ:

• The pgf manual.
• The minimal introduction to TikZ.
• The examples gallery at TeXample.net
• The numerous examples on this site.