% Mizar problem: t34_surrealr,surrealr,2505,43 
fof(t34_surrealr, conjecture,  (! [A] :  (! [B] :  (! [C] : k9_surrealr(A, k2_xboole_0(B, C))=k2_xboole_0(k9_surrealr(A, B), k9_surrealr(A, C))) ) ) ).
fof(fc8_surreal0, axiom,  (! [A, B] :  ( (v3_surreal0(A) & v3_surreal0(B))  => v3_surreal0(k2_xboole_0(A, B))) ) ).
fof(rc2_surreal0, axiom,  (? [A] : v3_surreal0(A)) ).
fof(dt_k7_surrealr, axiom, $true).
fof(fc7_surrealr, axiom,  (! [A, B] : v3_surreal0(k7_surrealr(A, B))) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(commutativity_k9_surrealr, axiom,  (! [A, B] : k9_surrealr(A, B)=k9_surrealr(B, A)) ).
fof(redefinition_k9_surrealr, axiom,  (! [A, B] : k9_surrealr(A, B)=k7_surrealr(A, B)) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k9_surrealr, axiom, $true).
fof(t33_surrealr, axiom,  (! [A] :  (! [B] :  (! [C] : k9_surrealr(k2_xboole_0(A, B), C)=k2_xboole_0(k9_surrealr(A, C), k9_surrealr(B, C))) ) ) ).
