% Mizar problem: t43_card_2,card_2,914,23 
fof(t43_card_2,conjecture,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ! [C] : 
              ( v1_card_1(C)
             => k3_card_2(A,k2_card_2(B,C)) = k3_card_2(k3_card_2(A,B),C) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_card_1,cc1_ordinal1,cc2_ordinal1,commutativity_k2_card_2,d2_card_2,d3_card_2,d5_card_1,dt_k1_card_1,dt_k1_funct_2,dt_k2_card_2,dt_k2_zfmisc_1,dt_k3_card_2,l9_card_2,rc1_card_1,rc1_ordinal1,redefinition_r2_wellord2,reflexivity_r2_wellord2,symmetry_r2_wellord2,t22_wellord2,t67_funct_5,t70_funct_5]),
    [file(card_2,t43_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(d3_card_2,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)) ) ) ),
    file(card_2,d3_card_2),
    []).

fof(d5_card_1,axiom,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( B = k1_card_1(A)
      <=> r2_wellord2(A,B) ) ) ),
    file(card_1,d5_card_1),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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(dt_k3_card_2,axiom,(
    ! [A,B] : 
      ( ( v1_card_1(A)
        & v1_card_1(B) )
     => v1_card_1(k3_card_2(A,B)) ) ),
    file(card_2,k3_card_2),
    []).

fof(l9_card_2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))
      & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(B,A)) ) ),
    file(card_2,l9_card_2),
    []).

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(t22_wellord2,axiom,(
    ! [A,B,C] : 
      ( ( r2_wellord2(A,B)
        & r2_wellord2(B,C) )
     => r2_wellord2(A,C) ) ),
    file(wellord2,t22_wellord2),
    []).

fof(t67_funct_5,axiom,(
    ! [A,B,C,D] : 
      ( ( r2_wellord2(A,B)
        & r2_wellord2(C,D) )
     => ( r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D))
        & k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) ) ),
    file(funct_5,t67_funct_5),
    []).

fof(t70_funct_5,axiom,(
    ! [A,B,C] : 
      ( r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C)))
      & k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) ) ),
    file(funct_5,t70_funct_5),
    []).