% Mizar problem: t26_e_siec,e_siec,658,5 
fof(t26_e_siec, conjecture,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k2_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A)))), k2_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u2_e_siec(A))))))=k2_relat_1(k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A)))) & k3_relat_1(k2_relat_1(k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A)))), k2_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u1_e_siec(A))))))=k2_relat_1(k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_l1_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_u1_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => v1_relat_1(u1_e_siec(A))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_e_siec, axiom,  (! [A] :  (l1_e_siec(A) => v1_relat_1(u2_e_siec(A))) ) ).
fof(existence_l1_e_siec, axiom,  (? [A] : l1_e_siec(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(fc28_relat_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) & v5_relat_1(k4_relat_1(A), A)) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(rc2_e_siec, axiom,  (? [A] :  (l1_e_siec(A) & v2_e_siec(A)) ) ).
fof(rc3_e_siec, axiom,  (? [A] :  (l1_e_siec(A) & v3_e_siec(A)) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rd2_relat_1, axiom,  (! [A] : k10_xtuple_0(k4_relat_1(A))=A) ).
fof(rd3_relat_1, axiom,  (! [A] : k2_relat_1(k4_relat_1(A))=k4_relat_1(A)) ).
fof(t23_e_siec, axiom,  (! [A] :  ( (v2_e_siec(A) &  (v3_e_siec(A) & l1_e_siec(A)) )  =>  (k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u2_e_siec(A)))), k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))))=k4_xboole_0(u2_e_siec(A), k4_relat_1(u1_struct_0(A))) & k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(A), k10_xtuple_0(u1_e_siec(A)))), k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A))))=k4_xboole_0(u1_e_siec(A), k4_relat_1(u1_struct_0(A)))) ) ) ).
fof(t35_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) => k2_relat_1(k3_relat_1(A, B))=k3_relat_1(k2_relat_1(B), k2_relat_1(A))) ) ) ) ).
