% Mizar problem: t12_ordinal3,ordinal3,102,11 
fof(t12_ordinal3,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k6_ordinal2(k1_tarski(A)) = A ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_ordinal1,cc2_ordinal1,d6_ordinal2,dt_k1_setfam_1,dt_k1_tarski,dt_k2_ordinal2,dt_k6_ordinal2,rc1_ordinal1,t11_setfam_1,t9_ordinal3]),
    [file(ordinal3,t12_ordinal3)]).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(d6_ordinal2,axiom,(
    ! [A] : k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A)) ),
    file(ordinal2,d6_ordinal2),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k2_ordinal2,axiom,(
    $true ),
    file(ordinal2,k2_ordinal2),
    []).

fof(dt_k6_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k6_ordinal2(A)) ),
    file(ordinal2,k6_ordinal2),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(t11_setfam_1,axiom,(
    ! [A] : k1_setfam_1(k1_tarski(A)) = A ),
    file(setfam_1,t11_setfam_1),
    []).

fof(t9_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k2_ordinal2(k1_tarski(A)) = k1_tarski(A) ) ),
    file(ordinal3,t9_ordinal3),
    []).