% Mizar problem: l69_bvfunc14,bvfunc14,5521,5 
fof(l69_bvfunc14, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (! [H] :  (! [I] : k7_enumset1(A, B, C, D, E, F, G, H, I)=k2_xboole_0(k2_enumset1(A, B, C, D), k3_enumset1(E, F, G, H, I))) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d2_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (E=k2_enumset1(A, B, C, D) <=>  (! [F] :  (r2_hidden(F, E) <=>  ~ ( ( ~ (F=A)  &  ( ~ (F=B)  &  ( ~ (F=C)  &  ~ (F=D) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (F=k3_enumset1(A, B, C, D, E) <=>  (! [G] :  (r2_hidden(G, F) <=>  ~ ( ( ~ (G=A)  &  ( ~ (G=B)  &  ( ~ (G=C)  &  ( ~ (G=D)  &  ~ (G=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d7_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (! [H] :  (! [I] :  (! [J] :  (J=k7_enumset1(A, B, C, D, E, F, G, H, I) <=>  (! [K] :  (r2_hidden(K, J) <=>  ~ ( ( ~ (K=A)  &  ( ~ (K=B)  &  ( ~ (K=C)  &  ( ~ (K=D)  &  ( ~ (K=E)  &  ( ~ (K=F)  &  ( ~ (K=G)  &  ( ~ (K=H)  &  ~ (K=I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_enumset1, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k3_enumset1, axiom, $true).
fof(dt_k7_enumset1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc3_subset_1, axiom,  (! [A, B, C, D] :  ~ (v1_xboole_0(k2_enumset1(A, B, C, D))) ) ).
fof(fc4_subset_1, axiom,  (! [A, B, C, D, E] :  ~ (v1_xboole_0(k3_enumset1(A, B, C, D, E))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc8_subset_1, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ~ (v1_xboole_0(k7_enumset1(A, B, C, D, E, F, G, H, I))) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
