% Mizar problem: t35_xtuple_0,xtuple_0,782,5 
fof(t35_xtuple_0, conjecture,  (! [A] :  (! [B] : k12_xtuple_0(k2_xboole_0(A, B))=k2_xboole_0(k12_xtuple_0(A), k12_xtuple_0(B))) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d15_xtuple_0, axiom,  (! [A] : k12_xtuple_0(A)=k10_xtuple_0(k9_xtuple_0(A))) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_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))) ) ).
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))) ) ).
