% Mizar problem: t14_zfrefle1,zfrefle1,370,21 
fof(t14_zfrefle1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A)))
                & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) )
             => ~ ( r2_hidden(k1_card_1(B),k1_card_1(A))
                  & ! [D] : 
                      ( m2_ordinal4(D,A)
                     => ~ ( v2_ordinal2(D)
                          & v3_ordinal2(D)
                          & k4_ordinal4(A,D,k2_ordinal4(A)) = k2_ordinal4(A)
                          & ! [E] : 
                              ( m1_ordinal4(E,A)
                             => k4_ordinal4(A,D,k6_ordinal4(A,E)) = k7_ordinal2(k2_xboole_0(k1_tarski(k4_ordinal4(A,D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k6_ordinal4(A,E)))))) )
                          & ! [E] : 
                              ( m1_ordinal4(E,A)
                             => ( v4_ordinal1(E)
                               => ( E = k2_ordinal4(A)
                                  | k4_ordinal4(A,D,E) = k8_ordinal2(k2_ordinal1(D,E)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_classes2,cc1_funct_2,cc1_ordinal1,cc1_ordinal2,cc1_relset_1,cc2_classes2,cc2_ordinal1,cc3_classes2,cc3_ordinal1,cc5_funct_2,cc6_funct_2,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k5_xboole_0,d16_ordinal2,d17_ordinal2,d1_classes1,d1_tarski,d2_ordinal1,d2_ordinal2,d2_ordinal4,d2_xboole_0,d3_ordinal4,d3_tarski,d4_ordinal2,d5_funct_1,d6_xboole_0,d9_ordinal2,dt_k12_ordinal2,dt_k1_card_1,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_ordinal1,dt_k2_ordinal2,dt_k2_ordinal4,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ordinal4,dt_k3_xboole_0,dt_k4_funct_5,dt_k4_ordinal2,dt_k4_ordinal4,dt_k4_xboole_0,dt_k5_xboole_0,dt_k6_funct_5,dt_k6_ordinal4,dt_k7_ordinal2,dt_k7_relat_1,dt_k8_ordinal2,dt_k9_relat_1,dt_m1_ordinal1,dt_m1_ordinal4,dt_m1_relset_1,dt_m1_subset_1,dt_m2_ordinal4,dt_m2_relset_1,existence_m1_ordinal1,existence_m1_ordinal4,existence_m1_relset_1,existence_m1_subset_1,existence_m2_ordinal4,existence_m2_relset_1,fc1_funct_2,fc1_ordinal1,fc2_classes2,fc2_funct_2,fc2_ordinal1,fc2_ordinal2,fc3_ordinal1,fc3_ordinal2,fc5_ordinal1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_card_1,rc1_classes2,rc1_funct_2,rc1_ordinal1,rc1_ordinal2,rc1_partfun1,rc2_classes2,rc2_ordinal1,rc2_ordinal2,rc2_partfun1,rc3_ordinal1,rc4_ordinal1,redefinition_k2_ordinal1,redefinition_k4_ordinal4,redefinition_k6_ordinal4,redefinition_m2_relset_1,redefinition_r2_wellord2,reflexivity_r1_tarski,reflexivity_r2_wellord2,s11_ordinal2__e2_18__zfrefle1,s5_zf_refle__e5_18_3__zfrefle1,s5_zf_refle__e7_18_4__zfrefle1,symmetry_r2_wellord2,t12_relset_1,t12_zfrefle1,t13_card_2,t13_ordinal1,t144_relat_1,t15_ordinal4,t19_ordinal1,t1_boole,t1_subset,t1_xboole_1,t22_ordinal1,t23_ordinal1,t27_ordinal2,t28_zf_refle,t2_boole,t2_card_2,t2_classes1,t2_subset,t35_ordinal4,t3_boole,t3_subset,t48_funct_5,t4_boole,t4_subset,t5_boole,t5_subset,t62_classes2,t63_classes2,t66_classes2,t6_boole,t70_funct_1,t73_funct_1,t7_boole,t87_relat_1,t8_boole,t8_ordinal4,t8_zf_refle,t91_relat_1,t9_ordinal2]),
    [file(zfrefle1,t14_zfrefle1)]).

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_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

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(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k5_xboole_0(B,A) ),
    file(xboole_0,k5_xboole_0),
    []).

fof(d16_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ( v2_ordinal2(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ! [C] : 
                ( v3_ordinal1(C)
               => ( ( r2_hidden(B,C)
                    & r2_hidden(C,k1_relat_1(A)) )
                 => r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) ),
    file(ordinal2,d16_ordinal2),
    []).

fof(d17_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ( v3_ordinal2(A)
      <=> ! [B] : 
            ( v3_ordinal1(B)
           => ! [C] : 
                ( v3_ordinal1(C)
               => ( ( r2_hidden(B,k1_relat_1(A))
                    & v4_ordinal1(B)
                    & C = k1_funct_1(A,B) )
                 => ( B = k1_xboole_0
                    | r1_ordinal2(C,k2_ordinal1(A,B)) ) ) ) ) ) ) ),
    file(ordinal2,d17_ordinal2),
    []).

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_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

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(d2_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( m1_ordinal4(B,A)
          <=> r2_hidden(B,A) ) ) ) ),
    file(ordinal4,d2_ordinal4),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d3_ordinal4,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ( m2_ordinal4(B,A)
          <=> ( k1_relat_1(B) = k2_ordinal2(A)
              & r1_tarski(k2_relat_1(B),k2_ordinal2(A)) ) ) ) ) ),
    file(ordinal4,d3_ordinal4),
    []).

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

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(d6_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) ),
    file(xboole_0,d6_xboole_0),
    []).

fof(d9_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)) ) ),
    file(ordinal2,d9_ordinal2),
    []).

fof(dt_k12_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => v3_ordinal1(k12_ordinal2(A)) ) ),
    file(ordinal2,k12_ordinal2),
    []).

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

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_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_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_funct_5(A))
        & v1_funct_1(k4_funct_5(A)) ) ) ),
    file(funct_5,k4_funct_5),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_xboole_0,axiom,(
    $true ),
    file(xboole_0,k5_xboole_0),
    []).

fof(dt_k6_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k6_funct_5(A))
        & v1_funct_1(k6_funct_5(A)) ) ) ),
    file(funct_5,k6_funct_5),
    []).

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_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k7_ordinal2(A)) ),
    file(ordinal2,k7_ordinal2),
    []).

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_k8_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => v3_ordinal1(k8_ordinal2(A)) ) ),
    file(ordinal2,k8_ordinal2),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

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

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_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

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

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_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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_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_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

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(s11_ordinal2__e2_18__zfrefle1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A)))
        & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) )
     => ? [D] : 
          ( v1_relat_1(D)
          & v1_funct_1(D)
          & v5_ordinal1(D)
          & v1_ordinal2(D)
          & k1_relat_1(D) = k2_ordinal2(A)
          & ( r2_hidden(k1_xboole_0,k2_ordinal2(A))
           => k1_funct_1(D,k1_xboole_0) = k1_xboole_0 )
          & ! [E] : 
              ( v3_ordinal1(E)
             => ( r2_hidden(k1_ordinal1(E),k2_ordinal2(A))
               => k1_funct_1(D,k1_ordinal1(E)) = k7_ordinal2(k2_xboole_0(k1_tarski(k1_funct_1(D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k1_ordinal1(E)))))) ) )
          & ! [E] : 
              ( v3_ordinal1(E)
             => ( ( r2_hidden(E,k2_ordinal2(A))
                  & v4_ordinal1(E) )
               => ( E = k1_xboole_0
                  | k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) ) ) ) ) ) ),
    file(zfrefle1,s11_ordinal2__e2_18__zfrefle1),
    []).

fof(s5_zf_refle__e5_18_3__zfrefle1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B)
        & v1_ordinal2(B) )
     => ( ( r2_hidden(k1_funct_1(B,k2_ordinal4(A)),k2_ordinal2(A))
          & ! [C] : 
              ( m1_ordinal4(C,A)
             => ( r2_hidden(k1_funct_1(B,C),k2_ordinal2(A))
               => r2_hidden(k1_funct_1(B,k6_ordinal4(A,C)),k2_ordinal2(A)) ) )
          & ! [C] : 
              ( m1_ordinal4(C,A)
             => ( ( v4_ordinal1(C)
                  & ! [D] : 
                      ( m1_ordinal4(D,A)
                     => ( r2_hidden(D,C)
                       => r2_hidden(k1_funct_1(B,D),k2_ordinal2(A)) ) ) )
               => ( C = k2_ordinal4(A)
                  | r2_hidden(k1_funct_1(B,C),k2_ordinal2(A)) ) ) ) )
       => ! [C] : 
            ( m1_ordinal4(C,A)
           => r2_hidden(k1_funct_1(B,C),k2_ordinal2(A)) ) ) ) ),
    file(zfrefle1,s5_zf_refle__e5_18_3__zfrefle1),
    []).

fof(s5_zf_refle__e7_18_4__zfrefle1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m2_ordinal4(B,A)
        & m1_ordinal4(C,A) )
     => ( ( ( r2_hidden(C,k2_ordinal4(A))
           => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,k2_ordinal4(A))) )
          & ! [D] : 
              ( m1_ordinal4(D,A)
             => ( ( r2_hidden(C,D)
                 => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,D)) )
               => ( r2_hidden(C,k6_ordinal4(A,D))
                 => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,k6_ordinal4(A,D))) ) ) )
          & ! [D] : 
              ( m1_ordinal4(D,A)
             => ( ( v4_ordinal1(D)
                  & ! [E] : 
                      ( m1_ordinal4(E,A)
                     => ( r2_hidden(E,D)
                       => ( r2_hidden(C,E)
                         => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,E)) ) ) ) )
               => ( D = k2_ordinal4(A)
                  | ( r2_hidden(C,D)
                   => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,D)) ) ) ) ) )
       => ! [D] : 
            ( m1_ordinal4(D,A)
           => ( r2_hidden(C,D)
             => r2_hidden(k4_ordinal4(A,B,C),k1_funct_1(B,D)) ) ) ) ) ),
    file(zfrefle1,s5_zf_refle__e7_18_4__zfrefle1),
    []).

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

fof(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t12_zfrefle1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes2(B) )
         => ( ( r2_hidden(k1_relat_1(A),B)
              & r1_tarski(k2_relat_1(A),B) )
           => r2_hidden(k2_relat_1(A),B) ) ) ) ),
    file(zfrefle1,t12_zfrefle1),
    []).

fof(t13_card_2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B)))
      & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) ) ),
    file(card_2,t13_card_2),
    []).

fof(t13_ordinal1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,k1_ordinal1(B))
    <=> ( r2_hidden(A,B)
        | A = B ) ) ),
    file(ordinal1,t13_ordinal1),
    []).

fof(t144_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    []).

fof(t15_ordinal4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v2_ordinal2(A)
           => v2_ordinal2(k2_ordinal1(A,B)) ) ) ) ),
    file(ordinal4,t15_ordinal4),
    []).

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

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(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_ordinal1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    []).

fof(t27_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r2_hidden(A,B)
         => r2_hidden(A,k7_ordinal2(B)) ) ) ),
    file(ordinal2,t27_ordinal2),
    []).

fof(t28_zf_refle,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( r2_hidden(B,A)
         => r2_hidden(k7_ordinal2(B),A) ) ) ),
    file(zf_refle,t28_zf_refle),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

fof(t2_card_2,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_card_1(A),k1_card_1(B))
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & r1_tarski(A,k9_relat_1(C,B)) ) ) ),
    file(card_2,t2_card_2),
    []).

fof(t2_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_hidden(k1_card_1(B),k1_card_1(A)) )
           => r2_hidden(B,A) ) ) ) ),
    file(classes1,t2_classes1),
    []).

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

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(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t48_funct_5,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ( r1_tarski(k2_relat_1(k4_funct_5(C)),B)
          & r1_tarski(k2_relat_1(k6_funct_5(C)),B) ) ) ) ),
    file(funct_5,t48_funct_5),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t5_boole,axiom,(
    ! [A] : k5_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t5_boole),
    []).

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(t62_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k1_xboole_0,A) ) ),
    file(classes2,t62_classes2),
    []).

fof(t63_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,B)
       => r2_hidden(k1_tarski(A),B) ) ) ),
    file(classes2,t63_classes2),
    []).

fof(t66_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & v1_classes2(C) )
     => ( ( r2_hidden(A,C)
          & r2_hidden(B,C) )
       => ( r2_hidden(k2_xboole_0(A,B),C)
          & r2_hidden(k3_xboole_0(A,B),C)
          & r2_hidden(k4_xboole_0(A,B),C)
          & r2_hidden(k5_xboole_0(A,B),C) ) ) ) ),
    file(classes2,t66_classes2),
    []).

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_ordinal4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ( ( v4_ordinal1(k1_relat_1(A))
          & v2_ordinal2(A) )
       => ( k1_relat_1(A) = k1_xboole_0
          | ( r1_ordinal2(k8_ordinal2(A),A)
            & k12_ordinal2(A) = k8_ordinal2(A) ) ) ) ) ),
    file(ordinal4,t8_ordinal4),
    []).

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(t91_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    []).

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