% Mizar problem: l8_mmlquer2,mmlquer2,114,59 
fof(l8_mmlquer2, conjecture,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v5_ordinal1(B)) )  => k10_xtuple_0(k1_ordinal4(A, B))=k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(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(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_ordinal4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) & v1_funct_1(k1_ordinal4(A, B))) ) ) ) ).
fof(dt_k2_xboole_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(t2_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) )  => k10_xtuple_0(k1_ordinal4(A, B))=k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(B))) ) ) ) ).
