Geodesic
Solution lifting method for handling Meta-variables in the TH$\exists$OREM$\forall$ system
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VII, Tome 293 (2002), pp. 94-117

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We approach the problem of finding witnessing terms in proofs by the method of meta-variables. We describe an efficient method for handling meta-variables in natural style proofs and its implementation in the TH$\exists$OREM$\forall$ system. The method is based on a special technique for finding meta-substitutions when the proof search is performed in an AND/OR deduction tree. The implementation does not depend on the search strategy and allows easy integration with various special provers as well as with special unification/solving engines. We demonstrate the use of this method in the context of a special forward/backward inference strategy for producing proofs in elementary analysis. 
@article{ZNSL_2002_293_a4,
     author = {B. Yu. Konev and T. Jebelean},
     title = {Solution lifting method for handling {Meta-variables} in the {TH}$\exists${OREM}$\forall$ system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--117},
     publisher = {mathdoc},
     volume = {293},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_293_a4/}
}
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B. Yu. Konev; T. Jebelean. Solution lifting method for handling Meta-variables in the TH$\exists$OREM$\forall$ system. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VII, Tome 293 (2002), pp. 94-117. http://geodesic.mathdoc.fr/item/ZNSL_2002_293_a4/