% Mizar problem: t31_xtuple_0,xtuple_0,743,5 
fof(t31_xtuple_0, conjecture,  (! [A] :  (! [B] : k11_xtuple_0(k2_xboole_0(A, B))=k2_xboole_0(k11_xtuple_0(A), k11_xtuple_0(B))) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d14_xtuple_0, axiom,  (! [A] : k11_xtuple_0(A)=k9_xtuple_0(k9_xtuple_0(A))) ).
fof(dt_k11_xtuple_0, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(t23_xtuple_0, axiom,  (! [A] :  (! [B] : k9_xtuple_0(k2_xboole_0(A, B))=k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B))) ) ).
