% Mizar problem: t18_relat_1,relat_1,369,5 
fof(t18_relat_1, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) => k1_relat_1(k2_xboole_0(A, B))=k2_xboole_0(k1_relat_1(A), k1_relat_1(B))) ) ) ) ).
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_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(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))) ) ).
fof(t4_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k2_xboole_0(k2_xboole_0(A, B), C)=k2_xboole_0(A, k2_xboole_0(B, C))) ) ) ).
