% Mizar problem: l98_xboole_1,xboole_1,1215,5 
fof(l98_xboole_1, conjecture,  (! [A] :  (! [B] : k5_xboole_0(A, B)=k4_xboole_0(k2_xboole_0(A, B), k3_xboole_0(A, B))) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k5_xboole_0, axiom,  (! [A, B] : k5_xboole_0(A, B)=k5_xboole_0(B, A)) ).
fof(d6_xboole_0, axiom,  (! [A] :  (! [B] : k5_xboole_0(A, B)=k2_xboole_0(k4_xboole_0(A, B), k4_xboole_0(B, A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_xboole_0, axiom, $true).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(t42_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k4_xboole_0(k2_xboole_0(A, B), C)=k2_xboole_0(k4_xboole_0(A, C), k4_xboole_0(B, C))) ) ) ).
fof(t47_xboole_1, axiom,  (! [A] :  (! [B] : k4_xboole_0(A, k3_xboole_0(A, B))=k4_xboole_0(A, B)) ) ).
