% Mizar problem: t30_classes2,classes2,513,12 
fof(t30_classes2,conjecture,(
    ! [A,B] : 
      ( ( v2_classes1(A)
        & v1_ordinal1(A)
        & r2_hidden(B,A) )
     => r2_hidden(k6_classes1(B),A) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_classes2,cc1_ordinal1,cc1_partfun1,cc2_ordinal1,cc3_ordinal1,commutativity_k2_xboole_0,connectedness_r1_ordinal1,d10_xboole_0,d1_classes1,d1_ordinal1,d2_card_3,d2_classes1,d2_funct_2,d2_ordinal1,d2_ordinal2,d3_tarski,d4_card_3,d4_tarski,d5_card_1,d5_card_3,d5_funct_1,d8_card_3,d8_classes1,dt_k1_card_1,dt_k1_card_3,dt_k1_funct_1,dt_k1_funct_2,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ordinal2,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_card_3,dt_k3_tarski,dt_k4_card_3,dt_k4_classes1,dt_k6_card_3,dt_k6_classes1,dt_k6_relat_1,dt_k7_card_3,dt_m1_subset_1,existence_m1_subset_1,fc1_ordinal1,fc1_subset_1,fc2_ordinal1,fc2_partfun1,fc2_subset_1,fc3_ordinal1,fc4_ordinal1,idempotence_k2_xboole_0,rc1_card_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,redefinition_r1_ordinal1,redefinition_r2_wellord2,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r2_wellord2,s1_card_3__e28_26__classes2,s1_ordinal1__e5_26__classes2,s1_xboole_0__e13_26__classes2,s3_funct_1__e18_26__classes2,symmetry_r2_wellord2,t10_classes2,t12_classes2,t14_card_1,t1_boole,t1_classes2,t1_subset,t1_xboole_1,t21_card_1,t22_ordinal1,t23_classes2,t23_ordinal1,t26_ordinal1,t27_card_1,t28_card_1,t2_subset,t30_card_1,t31_ordinal1,t34_ordinal1,t35_funct_1,t3_subset,t42_classes1,t47_classes1,t4_subset,t54_card_3,t56_card_3,t5_subset,t6_boole,t6_classes2,t71_relat_1,t73_classes1,t74_classes1,t76_classes1,t7_boole,t7_ordinal1,t8_boole,t92_zfmisc_1,t9_ordinal2]),
    [file(classes2,t30_classes2)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    []).

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

fof(cc1_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    []).

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

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(connectedness_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_classes1,axiom,(
    ! [A] : 
      ( v1_classes1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r1_tarski(C,B) )
         => r2_hidden(C,A) ) ) ),
    file(classes1,d1_classes1),
    []).

fof(d1_ordinal1,axiom,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    []).

fof(d2_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( B = k1_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(card_3,d2_card_3),
    []).

fof(d2_classes1,axiom,(
    ! [A] : 
      ( v2_classes1(A)
    <=> ( v1_classes1(A)
        & ! [B] : 
            ( r2_hidden(B,A)
           => r2_hidden(k1_zfmisc_1(B),A) )
        & ! [B] : ~ ( r1_tarski(B,A)
            & ~ r2_tarski(B,A)
            & ~ r2_hidden(B,A) ) ) ) ),
    file(classes1,d2_classes1),
    []).

fof(d2_funct_2,axiom,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    []).

fof(d2_ordinal1,axiom,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    []).

fof(d2_ordinal2,axiom,(
    ! [A,B] : 
      ( B = k2_ordinal2(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ( r2_hidden(C,A)
            & v3_ordinal1(C) ) ) ) ),
    file(ordinal2,d2_ordinal2),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d4_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    []).

fof(d4_tarski,axiom,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    []).

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(d5_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d8_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k7_card_3(A) = k1_card_1(k4_card_3(A)) ) ),
    file(card_3,d8_card_3),
    []).

fof(d8_classes1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( B = k6_classes1(A)
      <=> ( r1_tarski(A,k4_classes1(B))
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_tarski(A,k4_classes1(C))
               => r1_ordinal1(B,C) ) ) ) ) ) ),
    file(classes1,d8_classes1),
    []).

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

fof(dt_k1_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_card_3(A))
        & v1_funct_1(k1_card_3(A))
        & v1_card_3(k1_card_3(A)) ) ) ),
    file(card_3,k1_card_3),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_k4_classes1,axiom,(
    $true ),
    file(classes1,k4_classes1),
    []).

fof(dt_k6_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k6_card_3(A)) ) ),
    file(card_3,k6_card_3),
    []).

fof(dt_k6_classes1,axiom,(
    ! [A] : v3_ordinal1(k6_classes1(A)) ),
    file(classes1,k6_classes1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k7_card_3(A)) ) ),
    file(card_3,k7_card_3),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc1_ordinal1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_partfun1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A))
      & v3_relat_2(k6_relat_1(A))
      & v4_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(partfun1,fc2_partfun1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    []).

fof(fc4_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

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

fof(reflexivity_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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

fof(s1_card_3__e28_26__classes2,axiom,(
    ! [A] : 
    ? [B] : 
      ( v1_relat_1(B)
      & v1_funct_1(B)
      & v1_card_3(B)
      & k1_relat_1(B) = A
      & ! [C] : 
          ( r2_hidden(C,A)
         => k1_funct_1(B,C) = k1_card_1(k1_zfmisc_1(C)) ) ) ),
    file(classes2,s1_card_3__e28_26__classes2),
    []).

fof(s1_ordinal1__e5_26__classes2,axiom,(
    ! [A] : 
      ( ? [B] : 
          ( v3_ordinal1(B)
          & ? [C] : 
              ( B = k6_classes1(C)
              & r2_hidden(C,A)
              & ~ r2_hidden(B,A) ) )
     => ? [B] : 
          ( v3_ordinal1(B)
          & ? [D] : 
              ( B = k6_classes1(D)
              & r2_hidden(D,A)
              & ~ r2_hidden(B,A) )
          & ! [E] : 
              ( v3_ordinal1(E)
             => ( ? [F] : 
                    ( E = k6_classes1(F)
                    & r2_hidden(F,A)
                    & ~ r2_hidden(E,A) )
               => r1_ordinal1(B,E) ) ) ) ) ),
    file(classes2,s1_ordinal1__e5_26__classes2),
    []).

fof(s1_xboole_0__e13_26__classes2,axiom,(
    ! [A,B] : 
    ? [C] : 
    ! [D] : 
      ( r2_hidden(D,C)
    <=> ( r2_hidden(D,k2_ordinal2(A))
        & ? [E] : 
            ( r2_hidden(E,B)
            & D = k6_classes1(E) ) ) ) ),
    file(classes2,s1_xboole_0__e13_26__classes2),
    []).

fof(s3_funct_1__e18_26__classes2,axiom,(
    ! [A] : 
    ? [B] : 
      ( v1_relat_1(B)
      & v1_funct_1(B)
      & k1_relat_1(B) = A
      & ! [C] : 
          ( r2_hidden(C,A)
         => k1_funct_1(B,C) = k6_classes1(C) ) ) ),
    file(classes2,s3_funct_1__e18_26__classes2),
    []).

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

fof(t10_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => k2_ordinal2(A) = k1_card_1(A) ) ),
    file(classes2,t10_classes2),
    []).

fof(t12_classes2,axiom,(
    ! [A,B] : 
      ( ( v2_classes1(A)
        & r2_hidden(B,A) )
     => r2_hidden(k1_card_1(B),A) ) ),
    file(classes2,t12_classes2),
    []).

fof(t14_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ! [B] : 
          ( v1_card_1(B)
         => ( r2_hidden(A,B)
          <=> ~ r1_tarski(B,A) ) ) ) ),
    file(card_1,t14_card_1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_classes2,axiom,(
    ! [A,B] : 
      ( ( v1_classes1(A)
        & r2_hidden(B,A) )
     => ( ~ r2_wellord2(B,A)
        & r2_hidden(k1_card_1(B),k1_card_1(A)) ) ) ),
    file(classes2,t1_classes2),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t21_card_1,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    []).

fof(t22_ordinal1,axiom,(
    ! [A] : 
      ( v1_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,C) )
               => r2_hidden(A,C) ) ) ) ) ),
    file(ordinal1,t22_ordinal1),
    []).

fof(t23_classes2,axiom,(
    ! [A,B] : 
      ( v2_classes1(A)
     => ( ( ~ ( r2_hidden(B,A)
              & v1_ordinal1(A) )
          & ~ ( r2_hidden(B,A)
              & r1_tarski(B,A) )
          & ~ ( r2_hidden(k1_card_1(B),k1_card_1(A))
              & r1_tarski(B,A) ) )
        | r1_tarski(k1_funct_2(B,A),A) ) ) ),
    file(classes2,t23_classes2),
    []).

fof(t23_ordinal1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    []).

fof(t26_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
            | r2_hidden(B,A) ) ) ) ),
    file(ordinal1,t26_ordinal1),
    []).

fof(t27_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    []).

fof(t28_card_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = B
          & r1_tarski(A,k2_relat_1(C)) ) ) ),
    file(card_1,t28_card_1),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t30_card_1,axiom,(
    ! [A] : r2_hidden(k1_card_1(A),k1_card_1(k1_zfmisc_1(A))) ),
    file(card_1,t30_card_1),
    []).

fof(t31_ordinal1,axiom,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,A)
         => ( v3_ordinal1(B)
            & r1_tarski(B,A) ) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,t31_ordinal1),
    []).

fof(t34_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,k1_ordinal1(B))
          <=> r1_ordinal1(A,B) ) ) ) ),
    file(ordinal1,t34_ordinal1),
    []).

fof(t35_funct_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t42_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r2_hidden(k4_classes1(A),k4_classes1(B)) ) ) ) ),
    file(classes1,t42_classes1),
    []).

fof(t47_classes1,axiom,(
    ! [A,B,C] : 
      ( v3_ordinal1(C)
     => ( ( r1_tarski(A,B)
          & r2_hidden(B,k4_classes1(C)) )
       => r2_hidden(A,k4_classes1(C)) ) ) ),
    file(classes1,t47_classes1),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t54_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))) ) ),
    file(card_3,t54_card_3),
    []).

fof(t56_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_hidden(k6_card_3(A),k7_card_3(B)) ) ) ) ),
    file(card_3,t56_card_3),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_classes2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v2_classes1(B)
            & r2_hidden(A,B) )
         => ( r2_hidden(k1_ordinal1(A),B)
            & r1_tarski(A,B) ) ) ) ),
    file(classes2,t6_classes2),
    []).

fof(t71_relat_1,axiom,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    []).

fof(t73_classes1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r1_tarski(A,k4_classes1(B))
      <=> r1_ordinal1(k6_classes1(A),B) ) ) ),
    file(classes1,t73_classes1),
    []).

fof(t74_classes1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,k4_classes1(B))
      <=> r2_hidden(k6_classes1(A),B) ) ) ),
    file(classes1,t74_classes1),
    []).

fof(t76_classes1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r2_hidden(k6_classes1(A),k6_classes1(B)) ) ),
    file(classes1,t76_classes1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_ordinal1,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).

fof(t9_ordinal2,axiom,(
    ! [A] : r1_tarski(k2_ordinal2(A),A) ),
    file(ordinal2,t9_ordinal2),
    []).