% Mizar problem: t4_glib_009,glib_009,98,5 
fof(t4_glib_009, conjecture,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] : k6_relat_1(B, A)=k5_relat_1(A, k9_xtuple_0(k6_relat_1(B, A)))) ) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k6_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => v1_relat_1(k6_relat_1(A, B))) ) ).
fof(dt_k8_relat_1, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc9_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_relat_1(k6_relat_1(A, B)) & v1_funct_1(k6_relat_1(A, B))) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd7_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => k6_relat_1(A, k6_relat_1(A, B))=k6_relat_1(A, B)) ) ).
fof(t113_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => k6_relat_1(A, B)=k5_relat_1(B, k8_relat_1(B, A))) ) ) ).
fof(t1_mfold_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] : k9_xtuple_0(k6_relat_1(B, A))=k8_relat_1(A, B)) ) ) ).
