fof(nouns,conjecture,fx=fx).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
fof(nouns1,axiom,bar(fy)).
fof(nouns2,axiom,bar(fx)).
------------------
fof(adj_nouns,conjecture,fx=fx).
fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
fof(adj_nouns1,axiom,bar(fy)&foo(fy)).
fof(adj_nouns2,axiom,bar(fx)&foo(fx)).
------------------
fof(nouns_suchthat,conjecture,fx=fx).
fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)).
fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
fof(nouns_suchthat1,axiom,bar(fy)).
fof(nouns_suchthat2,axiom,bar(fx)).
fof(nouns_suchthat3,axiom,foo(fx)&baz(fy)).
------------------
fof(noun_verb,conjecture,fx=fy<=>(bar(fx)&fx=fy)).
fof(nouns_suchthat,axiom,![Xx,Xy]:((foo(Xx)&baz(Xy)&bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)).
fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
------------------
fof(adjs,conjecture,foo(fx)&baz(fx)).
fof(noun_verb,axiom,![Xx,Xy]:(Xx=Xy<=>(bar(Xx)&Xx=Xy))).
fof(nouns_suchthat,axiom,![Xx,Xy]:((foo(Xx)&baz(Xy)&bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)).
fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
------------------
fof(are_nouns,conjecture,bar(fx)&foo(fx)&bar(fy)&foo(fy)).
fof(adjs,axiom,![Xx]:(foo(Xx)&baz(Xx))).
fof(noun_verb,axiom,![Xx,Xy]:(Xx=Xy<=>(bar(Xx)&Xx=Xy))).
fof(nouns_suchthat,axiom,![Xx,Xy]:((foo(Xx)&baz(Xy)&bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)).
fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)).
fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)).
fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)).
fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
fof(are_nouns1,axiom,bar(fy)&foo(fy)).
fof(are_nouns2,axiom,bar(fx)&foo(fx)).