% Mizar problem: t35_card_2,card_2,798,26 
fof(t35_card_2,conjecture,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( v1_card_1(C)
             => k2_card_2(k2_card_2(A,B),C) = k2_card_2(A,k2_card_2(B,C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_card_1,cc1_ordinal1,cc2_ordinal1,commutativity_k2_card_2,d2_card_2,dt_k1_card_1,dt_k2_card_2,dt_k2_zfmisc_1,rc1_card_1,rc1_ordinal1,redefinition_r2_wellord2,reflexivity_r2_wellord2,symmetry_r2_wellord2,t12_card_2,t14_card_2]),
    [file(card_2,t35_card_2)]).

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

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(commutativity_k2_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => k2_card_2(A,B) = k2_card_2(B,A) ) ),
    file(card_2,k2_card_2),
    []).

fof(d2_card_2,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k2_card_2(A,B) = k1_card_1(k2_zfmisc_1(A,B)) ) ) ),
    file(card_2,d2_card_2),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k2_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k2_card_2(A,B)) ) ),
    file(card_2,k2_card_2),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

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

fof(redefinition_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(reflexivity_r2_wellord2,axiom,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    []).

fof(symmetry_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(t12_card_2,axiom,(
    ! [A,B,C] : 
      ( r2_wellord2(k2_zfmisc_1(k2_zfmisc_1(A,B),C),k2_zfmisc_1(A,k2_zfmisc_1(B,C)))
      & k1_card_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C)) = k1_card_1(k2_zfmisc_1(A,k2_zfmisc_1(B,C))) ) ),
    file(card_2,t12_card_2),
    []).

fof(t14_card_2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),B))
      & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(A,k1_card_1(B)))
      & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),k1_card_1(B)))
      & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),B))
      & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(A,k1_card_1(B)))
      & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),k1_card_1(B))) ) ),
    file(card_2,t14_card_2),
    []).