% Mizar problem: t5_glib_009,glib_009,108,5 
fof(t5_glib_009, conjecture,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  =>  (! [B] :  (k2_funct_1(k5_relat_1(A, B))=k6_relat_1(B, k2_funct_1(A)) & k2_funct_1(k6_relat_1(B, A))=k5_relat_1(k2_funct_1(A), B)) ) ) ) ).
fof(d5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v2_funct_1(A) => k2_funct_1(A)=k2_relat_1(A)) ) ) ).
fof(dt_k2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A))) ) ) ).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(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(fc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  =>  (v1_relat_1(k2_relat_1(A)) & v1_funct_1(k2_relat_1(A))) ) ) ).
fof(fc6_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  =>  (v1_relat_1(k2_funct_1(A)) &  (v1_funct_1(k2_funct_1(A)) & v2_funct_1(k2_funct_1(A))) ) ) ) ).
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(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(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(t2_glib_009, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (k2_relat_1(k5_relat_1(A, B))=k6_relat_1(B, k2_relat_1(A)) & k2_relat_1(k6_relat_1(B, A))=k5_relat_1(k2_relat_1(A), B)) ) ) ) ).
fof(t52_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v2_funct_1(B) => v2_funct_1(k5_relat_1(B, A))) ) ) ) ).
fof(t58_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v2_funct_1(B) => v2_funct_1(k6_relat_1(A, B))) ) ) ) ).
