% Mizar problem: t12_relat_1,relat_1,323,33 
fof(t12_relat_1, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) => k10_xtuple_0(k2_xboole_0(A, B))=k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(B))) ) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(t27_xtuple_0, axiom,  (! [A] :  (! [B] : k10_xtuple_0(k2_xboole_0(A, B))=k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(B))) ) ).
