% Mizar problem: t21_relat_1,relat_1,465,5 
fof(t21_relat_1, conjecture,  (! [A] :  (v1_relat_1(A) => k1_relat_1(A)=k1_relat_1(k2_relat_1(A))) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d6_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k1_relat_1(A)=k2_xboole_0(k9_xtuple_0(A), k10_xtuple_0(A))) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_relat_1, axiom, $true).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k9_xtuple_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(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(t20_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (k10_xtuple_0(A)=k9_xtuple_0(k2_relat_1(A)) & k9_xtuple_0(A)=k10_xtuple_0(k2_relat_1(A))) ) ) ).
