Symbolic manipulations, which can be achieved by computer algebra systems such as Maple [Abell & Braselton 94], Mathematica [Wolfram 99] and Gap [Gap 00].
Example construction, e.g. building Cayley tables, which can be achieved by model generators like MACE [McCune 94], Finder [Slaney 92] and Kimba [Konrad & Wolfram 99].
Inventing concepts, which can be achieved by machine learning programs such as Progol [Muggleton 95], RIPPER [Cohen 95] and C4.5 [Quinlan 93].
Making conjectures, which can be achieved with specialised techniques such as those employed by Graffiti [Fajtlowicz 88], the PSLQ algorithm [Bailey 98] and the AGX program [Caporossi & Hansen 99].
Proving theorems, which can be achieved by a plethora of automated theorem provers, including: Otter [McCune 90], A-Clam [Richardson et al. 98], Spass [Weidenbach 99] and Vampire [Voronkov 95].
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