% Mizar problem: t23_funcop_1,funcop_1,603,5 
fof(t23_funcop_1, conjecture,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (! [D] :  (! [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  =>  (k5_relat_1(A, D)=k5_relat_1(B, D) => k5_relat_1(k3_funcop_1(E, A, C), D)=k5_relat_1(k3_funcop_1(E, B, C), D)) ) ) ) ) ) ) ) ) ) ).
fof(d3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  => k3_funcop_1(A, B, C)=k3_relat_1(k13_funct_3(B, C), A)) ) ) ) ) ) ).
fof(dt_k13_funct_3, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k13_funct_3(A, B)) & v1_funct_1(k13_funct_3(A, B))) ) ) ).
fof(dt_k3_funcop_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc6_funcop_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  ( (v1_relat_1(B) & v1_funct_1(B))  &  (v1_relat_1(C) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k3_funcop_1(A, B, C)) & v1_funct_1(k3_funcop_1(A, B, C))) ) ) ).
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(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_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(t5_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] : k5_relat_1(k13_funct_3(A, B), C)=k13_funct_3(k5_relat_1(A, C), B)) ) ) ) ) ).
fof(t83_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (! [C] :  (v1_relat_1(C) => k5_relat_1(k3_relat_1(B, C), A)=k3_relat_1(k5_relat_1(B, A), C)) ) ) ) ) ).
