% Mizar problem: t154_relat_1,relat_1,2499,5 
fof(t154_relat_1, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) => k5_relat_1(A, k9_xtuple_0(B))=k5_relat_1(A, k9_xtuple_0(k5_relat_1(B, k9_xtuple_0(A))))) ) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(t61_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => k9_xtuple_0(k5_relat_1(B, A))=k3_xboole_0(k9_xtuple_0(B), A)) ) ) ).
fof(t71_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) => k5_relat_1(k5_relat_1(C, A), B)=k5_relat_1(C, k3_xboole_0(A, B))) ) ) ) ).
