Geodesic
On biconjunctive reduction classes
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 170-174

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A predicate formula is biconjunctive if it is of the form $$ P\biggl(\bigvee_{i=1}^l\{j=1}^{\delta_i}F_{ij}\biggr) $$ where $P$ is prefix, $\delta_i\leq2$ and $F_{ij}$ are atomic formulas possibly with negation. There are described 4 classes of biconjunctive formulas each having both undecidable problem of derivability in classical predicate calculus and undecidable problem of finite refutability. 
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     author = {V. P. Orevkov},
     title = {On biconjunctive reduction classes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {20},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a15/}
}
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V. P. Orevkov. On biconjunctive reduction classes. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 170-174. http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a15/