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fof(no_universal_set,conjecture,?[XV]:universal_set(XV)).
fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))).
fof(no_universal_set1,axiom,~~?[X0]:universal_set(X0)).
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fof(no_universal_set,conjecture,elem(fR,fR)<=>~elem(fR,fR)).
fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))).
fof(no_universal_set1,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))).
fof(no_universal_set2,axiom,universal_set(fV)).
fof(no_universal_set3,axiom,~~?[X0]:universal_set(X0)).
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fof(no_universal_set,conjecture,$false).
fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))).
fof(no_universal_set1,axiom,elem(fR,fR)<=>~elem(fR,fR)).
fof(no_universal_set2,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))).
fof(no_universal_set3,axiom,universal_set(fV)).
fof(no_universal_set4,axiom,~~?[X0]:universal_set(X0)).
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fof(no_universal_set,conjecture,$false).
fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))).
fof(no_universal_set1,axiom,$false).
fof(no_universal_set2,axiom,elem(fR,fR)<=>~elem(fR,fR)).
fof(no_universal_set3,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))).
fof(no_universal_set4,axiom,universal_set(fV)).
fof(no_universal_set5,axiom,~~?[X0]:universal_set(X0)).
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