% Mizar problem: t35_zfrefle1,zfrefle1,1045,33 
fof(t35_zfrefle1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ ( r2_hidden(k5_ordinal2,A)
          & ! [B] : 
              ( m2_ordinal4(B,A)
             => ~ ( v2_ordinal2(B)
                  & v3_ordinal2(B)
                  & ! [C] : 
                      ( m1_ordinal4(C,A)
                     => ! [D] : 
                          ( ~ v1_xboole_0(D)
                         => ( ( k4_ordinal4(A,B,C) = C
                              & D = k4_classes1(C) )
                           => ( k1_xboole_0 = C
                              | r3_zfrefle1(D,A) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_classes2,cc1_ordinal1,cc1_ordinal2,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,connectedness_r1_ordinal1,d10_xboole_0,d3_tarski,d4_card_3,d4_ordinal2,d4_tarski,d5_funct_1,d5_zf_refle,d8_ordinal1,d9_relat_1,dt_k1_funct_1,dt_k1_ordinal1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ordinal1,dt_k2_ordinal2,dt_k2_ordinal4,dt_k2_relat_1,dt_k3_card_3,dt_k3_ordinal4,dt_k3_tarski,dt_k4_classes1,dt_k4_ordinal2,dt_k4_ordinal4,dt_k4_zf_refle,dt_k5_ordinal2,dt_k5_zf_refle,dt_k6_ordinal4,dt_k7_relat_1,dt_m1_ordinal1,dt_m1_ordinal4,dt_m1_subset_1,dt_m2_ordinal4,existence_m1_ordinal1,existence_m1_ordinal4,existence_m1_subset_1,existence_m2_ordinal4,fc1_ordinal1,fc1_ordinal2,fc2_classes2,fc2_ordinal1,fc2_ordinal2,fc3_ordinal1,fc3_ordinal2,fc4_ordinal1,fc5_ordinal1,fc7_classes2,rc1_classes2,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_classes2,rc2_ordinal1,rc2_ordinal2,rc3_ordinal1,rc4_ordinal1,redefinition_k2_ordinal1,redefinition_k4_ordinal4,redefinition_k4_zf_refle,redefinition_k5_zf_refle,redefinition_k6_ordinal4,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_tarski,reflexivity_r3_zfrefle1,s5_ordinal2__e2_39__zfrefle1,t10_ordinal1,t18_ordinal3,t19_ordinal1,t1_subset,t1_xboole_1,t23_ordinal1,t2_subset,t32_zfrefle1,t33_classes1,t33_ordinal1,t33_zfrefle1,t34_zfrefle1,t35_classes1,t35_ordinal4,t38_classes1,t39_classes1,t3_subset,t41_ordinal1,t42_classes1,t42_ordinal1,t43_classes1,t4_subset,t54_classes2,t55_classes2,t5_subset,t6_boole,t70_funct_1,t73_funct_1,t7_boole,t87_relat_1,t8_boole,t8_zf_refle,t92_zfmisc_1]),
    [file(zfrefle1,t35_zfrefle1)]).

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

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_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_ordinal1(B,A)
         => v1_ordinal2(B) ) ) ),
    file(ordinal2,cc1_ordinal2),
    []).

fof(cc2_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    []).

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

fof(cc3_classes2,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    []).

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

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(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_ordinal2,axiom,(
    k4_ordinal2 = k1_ordinal1(k1_xboole_0) ),
    file(ordinal2,d4_ordinal2),
    []).

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_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(d5_zf_refle,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal1(B,A)
         => ( v1_zf_refle(B,A)
          <=> k1_relat_1(B) = k2_ordinal2(A) ) ) ) ),
    file(zf_refle,d5_zf_refle),
    []).

fof(d8_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B) )
     => ( m1_ordinal1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(ordinal1,d8_ordinal1),
    []).

fof(d9_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_relat_1(A)
      <=> ~ r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(relat_1,d9_relat_1),
    []).

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

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_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v3_ordinal1(B) )
     => m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)) ) ),
    file(ordinal1,k2_ordinal1),
    []).

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

fof(dt_k2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m1_ordinal4(k2_ordinal4(A),A) ) ),
    file(ordinal4,k2_ordinal4),
    []).

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

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

fof(dt_k3_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( ~ v1_xboole_0(k3_ordinal4(A))
        & m1_ordinal4(k3_ordinal4(A),A) ) ) ),
    file(ordinal4,k3_ordinal4),
    []).

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

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

fof(dt_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    []).

fof(dt_k4_ordinal4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m2_ordinal4(B,A)
        & m1_ordinal4(C,A) )
     => m1_ordinal4(k4_ordinal4(A,B,C),A) ) ),
    file(ordinal4,k4_ordinal4),
    []).

fof(dt_k4_zf_refle,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & v2_relat_1(B)
        & v1_zf_refle(B,A)
        & m1_ordinal1(B,A) )
     => ( ~ v1_xboole_0(k4_zf_refle(A,B))
        & m1_subset_1(k4_zf_refle(A,B),k1_zfmisc_1(A)) ) ) ),
    file(zf_refle,k4_zf_refle),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_zf_refle,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & v2_relat_1(B)
        & v1_zf_refle(B,A)
        & m1_ordinal1(B,A)
        & m1_ordinal4(C,A) )
     => ( ~ v1_xboole_0(k5_zf_refle(A,B,C))
        & m1_subset_1(k5_zf_refle(A,B,C),A) ) ) ),
    file(zf_refle,k5_zf_refle),
    []).

fof(dt_k6_ordinal4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_ordinal4(B,A) )
     => ( ~ v1_xboole_0(k6_ordinal4(A,B))
        & m1_ordinal4(k6_ordinal4(A,B),A) ) ) ),
    file(ordinal4,k6_ordinal4),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_m1_ordinal1,axiom,(
    ! [A,B] : 
      ( m1_ordinal1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B) ) ) ),
    file(ordinal1,m1_ordinal1),
    []).

fof(dt_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
         => v3_ordinal1(B) ) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(dt_m2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m2_ordinal4(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) ) ) ) ),
    file(ordinal4,m2_ordinal4),
    []).

fof(existence_m1_ordinal1,axiom,(
    ! [A] : 
    ? [B] : m1_ordinal1(B,A) ),
    file(ordinal1,m1_ordinal1),
    []).

fof(existence_m1_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : m1_ordinal4(B,A) ) ),
    file(ordinal4,m1_ordinal4),
    []).

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

fof(existence_m2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : m2_ordinal4(B,A) ) ),
    file(ordinal4,m2_ordinal4),
    []).

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

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_ordinal1(k2_ordinal2(A))
        & v2_ordinal1(k2_ordinal2(A))
        & v3_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,fc2_classes2),
    []).

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_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v3_ordinal1(B) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_ordinal2(k7_relat_1(A,B)) ) ) ),
    file(ordinal2,fc2_ordinal2),
    []).

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(fc3_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k1_funct_1(A,B))
        & v2_ordinal1(k1_funct_1(A,B))
        & v3_ordinal1(k1_funct_1(A,B)) ) ) ),
    file(ordinal2,fc3_ordinal2),
    []).

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(fc5_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    []).

fof(fc7_classes2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v1_ordinal1(k4_classes1(A)) ) ),
    file(classes2,fc7_classes2),
    []).

fof(rc1_classes2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    []).

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

fof(rc1_ordinal2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    []).

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(rc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    []).

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_ordinal2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & v1_ordinal2(A) ) ),
    file(ordinal2,rc2_ordinal2),
    []).

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

fof(rc4_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    []).

fof(redefinition_k2_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v3_ordinal1(B) )
     => k2_ordinal1(A,B) = k7_relat_1(A,B) ) ),
    file(ordinal1,k2_ordinal1),
    []).

fof(redefinition_k4_ordinal4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m2_ordinal4(B,A)
        & m1_ordinal4(C,A) )
     => k4_ordinal4(A,B,C) = k1_funct_1(B,C) ) ),
    file(ordinal4,k4_ordinal4),
    []).

fof(redefinition_k4_zf_refle,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & v2_relat_1(B)
        & v1_zf_refle(B,A)
        & m1_ordinal1(B,A) )
     => k4_zf_refle(A,B) = k3_card_3(B) ) ),
    file(zf_refle,k4_zf_refle),
    []).

fof(redefinition_k5_zf_refle,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & v2_relat_1(B)
        & v1_zf_refle(B,A)
        & m1_ordinal1(B,A)
        & m1_ordinal4(C,A) )
     => k5_zf_refle(A,B,C) = k1_funct_1(B,C) ) ),
    file(zf_refle,k5_zf_refle),
    []).

fof(redefinition_k6_ordinal4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_ordinal4(B,A) )
     => k6_ordinal4(A,B) = k1_ordinal1(B) ) ),
    file(ordinal4,k6_ordinal4),
    []).

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(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_r3_zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => r3_zfrefle1(A,A) ) ),
    file(zfrefle1,r3_zfrefle1),
    []).

fof(s5_ordinal2__e2_39__zfrefle1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & v5_ordinal1(B)
          & k1_relat_1(B) = k2_ordinal2(A)
          & ( r2_hidden(k1_xboole_0,k2_ordinal2(A))
           => k1_funct_1(B,k1_xboole_0) = k4_classes1(k3_ordinal4(A)) )
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(k1_ordinal1(C),k2_ordinal2(A))
               => k1_funct_1(B,k1_ordinal1(C)) = k4_classes1(k1_ordinal1(C)) ) )
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r2_hidden(C,k2_ordinal2(A))
                  & v4_ordinal1(C) )
               => ( C = k1_xboole_0
                  | k1_funct_1(B,C) = k4_classes1(C) ) ) ) ) ) ),
    file(zfrefle1,s5_ordinal2__e2_39__zfrefle1),
    []).

fof(t10_ordinal1,axiom,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    []).

fof(t18_ordinal3,axiom,(
    k4_ordinal2 = k1_tarski(k1_xboole_0) ),
    file(ordinal3,t18_ordinal3),
    []).

fof(t19_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v1_ordinal1(C)
             => ( ( r2_hidden(C,A)
                  & r2_hidden(A,B) )
               => r2_hidden(C,B) ) ) ) ) ),
    file(ordinal1,t19_ordinal1),
    []).

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

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

fof(t32_zfrefle1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & v1_zf_refle(B,A)
            & m1_ordinal1(B,A) )
         => ~ ( r2_hidden(k5_ordinal2,A)
              & ! [C] : 
                  ( m1_ordinal4(C,A)
                 => ! [D] : 
                      ( m1_ordinal4(D,A)
                     => ( r2_hidden(C,D)
                       => r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D)) ) ) )
              & ! [C] : 
                  ( m1_ordinal4(C,A)
                 => ( v4_ordinal1(C)
                   => ( C = k1_xboole_0
                      | k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)) ) ) )
              & ! [C] : 
                  ( m2_ordinal4(C,A)
                 => ~ ( v2_ordinal2(C)
                      & v3_ordinal2(C)
                      & ! [D] : 
                          ( m1_ordinal4(D,A)
                         => ( k4_ordinal4(A,C,D) = D
                           => ( k1_xboole_0 = D
                              | r3_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) ) ) ) ) ) ) ) ) ),
    file(zfrefle1,t32_zfrefle1),
    []).

fof(t33_classes1,axiom,(
    k4_classes1(k1_xboole_0) = k1_xboole_0 ),
    file(classes1,t33_classes1),
    []).

fof(t33_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,B)
          <=> r1_ordinal1(k1_ordinal1(A),B) ) ) ) ),
    file(ordinal1,t33_ordinal1),
    []).

fof(t33_zfrefle1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
         => r2_hidden(k4_classes1(B),A) ) ) ),
    file(zfrefle1,t33_zfrefle1),
    []).

fof(t34_zfrefle1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
         => ( B != k1_xboole_0
           => ( ~ v1_xboole_0(k4_classes1(B))
              & m1_subset_1(k4_classes1(B),A) ) ) ) ) ),
    file(zfrefle1,t34_zfrefle1),
    []).

fof(t35_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
       => ( A = k1_xboole_0
          | ! [B] : 
              ( r2_hidden(B,k4_classes1(A))
            <=> ? [C] : 
                  ( v3_ordinal1(C)
                  & r2_hidden(C,A)
                  & r2_hidden(B,k4_classes1(C)) ) ) ) ) ) ),
    file(classes1,t35_classes1),
    []).

fof(t35_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( k2_ordinal4(A) = k1_xboole_0
        & k3_ordinal4(A) = k4_ordinal2 ) ) ),
    file(ordinal4,t35_ordinal4),
    []).

fof(t38_classes1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,k4_classes1(B))
       => r1_tarski(A,k4_classes1(B)) ) ) ),
    file(classes1,t38_classes1),
    []).

fof(t39_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))) ) ),
    file(classes1,t39_classes1),
    []).

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

fof(t41_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v4_ordinal1(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ( r2_hidden(B,A)
             => r2_hidden(k1_ordinal1(B),A) ) ) ) ) ),
    file(ordinal1,t41_ordinal1),
    []).

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(t42_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ ( ~ v4_ordinal1(A)
            & ! [B] : 
                ( v3_ordinal1(B)
               => A != k1_ordinal1(B) ) )
        & ~ ( ? [B] : 
                ( v3_ordinal1(B)
                & A = k1_ordinal1(B) )
            & v4_ordinal1(A) ) ) ) ),
    file(ordinal1,t42_ordinal1),
    []).

fof(t43_classes1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,B)
          <=> r1_tarski(k4_classes1(A),k4_classes1(B)) ) ) ) ),
    file(classes1,t43_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_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => A = k4_classes1(k2_ordinal2(A)) ) ),
    file(classes2,t54_classes2),
    []).

fof(t55_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( k2_ordinal2(A) != k1_xboole_0
        & v4_ordinal1(k2_ordinal2(A)) ) ) ),
    file(classes2,t55_classes2),
    []).

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(t70_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    []).

fof(t73_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(B,k1_relat_1(C))
          & r2_hidden(B,A) )
       => r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A))) ) ) ),
    file(funct_1,t73_funct_1),
    []).

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

fof(t87_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),A) ) ),
    file(relat_1,t87_relat_1),
    []).

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

fof(t8_zf_refle,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_ordinal4(B,A)
        <=> r2_hidden(B,k2_ordinal2(A)) ) ) ),
    file(zf_refle,t8_zf_refle),
    []).

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