% Mizar problem: t6_funcop_1,funcop_1,270,5 
fof(t6_funcop_1, conjecture,  (! [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(A, k5_relat_1(B, C))) ) ) ) ) ).
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_k1_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A))) ) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
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(involutiveness_k1_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => k1_funcop_1(k1_funcop_1(A))=A) ) ).
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(t2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => k13_funct_3(A, B)=k1_funcop_1(k13_funct_3(B, A))) ) ) ) ).
fof(t3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] : k1_funcop_1(k5_relat_1(A, B))=k5_relat_1(k1_funcop_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)) ) ) ) ) ).
