% Mizar problem: t16_zf_fund1,zf_fund1,1178,29 
fof(t16_zf_fund1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(A)) )
                     => ! [F] : 
                          ( m1_subset_1(F,k5_ordinal2)
                         => ! [G] : 
                              ( ( v1_finset_1(G)
                                & m1_subset_1(G,k1_zfmisc_1(k5_ordinal2)) )
                             => ( ( v8_zf_fund1(E,A)
                                  & r2_hidden(B,E)
                                  & r1_tarski(B,E)
                                  & r2_hidden(C,k1_funct_2(G,B))
                                  & r1_tarski(D,k1_funct_2(k4_subset_1(k5_ordinal2,G,k7_zf_fund1(F)),B))
                                  & r2_hidden(D,E) )
                               => ( r2_hidden(F,G)
                                  | r2_hidden(a_5_1_zf_fund1(A,B,C,D,F),E) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_classes2,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc2_classes2,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_classes2,cc3_ordinal1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_subset_1,d10_xboole_0,d11_zf_fund1,d13_zf_fund1,d1_tarski,d2_funct_2,d2_tarski,d2_xboole_0,d3_tarski,d3_xboole_0,d4_tarski,d5_funct_1,d5_tarski,dt_k1_classes2,dt_k1_funct_1,dt_k1_funct_2,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zf_fund1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_tarski,dt_k3_xboole_0,dt_k4_subset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_ordinal2,dt_k6_subset_1,dt_k7_zf_fund1,dt_k9_classes2,dt_m1_subset_1,existence_m1_subset_1,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc1_finset_1,fc1_ordinal2,fc2_finset_1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,fraenkel_a_3_12_zf_fund1,fraenkel_a_3_2_zf_fund1,fraenkel_a_4_1_zf_fund1,fraenkel_a_4_3_zf_fund1,fraenkel_a_5_1_zf_fund1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,l36_zf_fund1,rc1_classes2,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc2_classes2,rc2_funct_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,redefinition_k1_classes2,redefinition_k4_subset_1,redefinition_k6_subset_1,redefinition_k7_zf_fund1,redefinition_k9_classes2,reflexivity_r1_tarski,symmetry_r1_xboole_0,t12_xboole_1,t14_zf_fund1,t15_zf_fund1,t1_boole,t1_subset,t1_zf_fund1,t2_boole,t2_subset,t2_tarski,t2_zf_fund1,t33_xboole_1,t37_xboole_1,t37_zfmisc_1,t3_boole,t3_subset,t3_xboole_0,t42_xboole_1,t4_boole,t4_subset,t4_zf_fund1,t56_zfmisc_1,t5_subset,t5_zf_fund1,t6_boole,t7_boole,t7_xboole_1,t83_xboole_1,t8_boole,t8_funct_1]),
    [file(zf_fund1,t16_zf_fund1)]).

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_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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

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

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(d11_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ( v6_zf_fund1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(a_3_2_zf_fund1(A,C,D),B) ) ) ) ) ) ) ),
    file(zf_fund1,d11_zf_fund1),
    []).

fof(d13_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ( v8_zf_fund1(B,A)
          <=> ( v1_zf_fund1(B,A)
              & v2_zf_fund1(B,A)
              & v3_zf_fund1(B,A)
              & v4_zf_fund1(B,A)
              & v5_zf_fund1(B,A)
              & v6_zf_fund1(B,A)
              & v7_zf_fund1(B,A) ) ) ) ) ),
    file(zf_fund1,d13_zf_fund1),
    []).

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

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_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

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

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

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_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k1_classes2(A,B),A) ) ),
    file(classes2,k1_classes2),
    []).

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_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_zf_fund1,axiom,(
    $true ),
    file(zf_fund1,k1_zf_fund1),
    []).

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

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

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

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k7_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_finset_1(k7_zf_fund1(A))
        & m1_subset_1(k7_zf_fund1(A),k1_zfmisc_1(k5_ordinal2)) ) ) ),
    file(zf_fund1,k7_zf_fund1),
    []).

fof(dt_k9_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k9_classes2(A,B,C),A) ) ),
    file(classes2,k9_classes2),
    []).

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(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

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_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_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(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(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fraenkel_a_3_12_zf_fund1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => ( r2_hidden(A,a_3_12_zf_fund1(B,C,D))
      <=> ? [E,F] : 
            ( m1_subset_1(E,B)
            & m1_subset_1(F,B)
            & A = k9_classes2(B,E,F)
            & r2_hidden(E,D)
            & r2_hidden(F,k1_classes2(B,C)) ) ) ) ),
    file(zf_fund1,a_3_12_zf_fund1),
    []).

fof(fraenkel_a_3_2_zf_fund1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => ( r2_hidden(A,a_3_2_zf_fund1(B,C,D))
      <=> ? [E,F] : 
            ( m1_subset_1(E,B)
            & m1_subset_1(F,B)
            & A = k9_classes2(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) ),
    file(zf_fund1,a_3_2_zf_fund1),
    []).

fof(fraenkel_a_4_1_zf_fund1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k5_ordinal2) )
     => ( r2_hidden(A,a_4_1_zf_fund1(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,B)
            & A = k2_xboole_0(k1_tarski(k4_tarski(E,F)),D)
            & r2_hidden(F,C) ) ) ) ),
    file(zf_fund1,a_4_1_zf_fund1),
    []).

fof(fraenkel_a_4_3_zf_fund1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k5_ordinal2) )
     => ( r2_hidden(A,a_4_3_zf_fund1(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,B)
            & A = k1_tarski(k4_tarski(E,F))
            & r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(E,F)),C),D) ) ) ) ),
    file(zf_fund1,a_4_3_zf_fund1),
    []).

fof(fraenkel_a_5_1_zf_fund1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,B)
        & m1_subset_1(F,k5_ordinal2) )
     => ( r2_hidden(A,a_5_1_zf_fund1(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,B)
            & A = G
            & r2_hidden(G,C)
            & r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(F,G)),D),E) ) ) ) ),
    file(zf_fund1,a_5_1_zf_fund1),
    []).

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(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(l36_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] : 
              ( m1_subset_1(C,k5_ordinal2)
             => ( v8_zf_fund1(B,A)
               => r2_hidden(C,B) ) ) ) ) ),
    file(zf_fund1,l36_zf_fund1),
    []).

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_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_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(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

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

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(redefinition_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => k1_classes2(A,B) = k1_tarski(B) ) ),
    file(classes2,k1_classes2),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(redefinition_k7_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => k7_zf_fund1(A) = k1_tarski(A) ) ),
    file(zf_fund1,k7_zf_fund1),
    []).

fof(redefinition_k9_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k9_classes2(A,B,C) = k4_xboole_0(B,C) ) ),
    file(classes2,k9_classes2),
    []).

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

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t12_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    []).

fof(t14_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(A)) )
             => ! [D,E] : 
                  ( ( v1_finset_1(E)
                    & m1_subset_1(E,k1_zfmisc_1(k5_ordinal2)) )
                 => ( ( v8_zf_fund1(C,A)
                      & r1_tarski(D,C)
                      & r2_hidden(B,k1_funct_2(E,D)) )
                   => r2_hidden(B,C) ) ) ) ) ) ),
    file(zf_fund1,t14_zf_fund1),
    []).

fof(t15_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(A)) )
                 => ! [E] : 
                      ( m1_subset_1(E,k5_ordinal2)
                     => ! [F] : 
                          ( ( v1_finset_1(F)
                            & m1_subset_1(F,k1_zfmisc_1(k5_ordinal2)) )
                         => ( ( v8_zf_fund1(D,A)
                              & r2_hidden(B,D)
                              & r1_tarski(B,D)
                              & r2_hidden(C,k1_funct_2(F,B)) )
                           => ( r2_hidden(E,F)
                              | r2_hidden(a_4_1_zf_fund1(A,B,C,E),D) ) ) ) ) ) ) ) ) ),
    file(zf_fund1,t15_zf_fund1),
    []).

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_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( r1_tarski(B,A)
              & ( r2_hidden(C,B)
               => m1_subset_1(C,A) )
              & ( ( r2_hidden(C,D)
                  & r2_hidden(D,B) )
               => m1_subset_1(C,A) ) ) ) ) ),
    file(zf_fund1,t1_zf_fund1),
    []).

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

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t2_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( v8_zf_fund1(B,A)
             => ( ( r2_hidden(C,B)
                 => r2_hidden(k1_tarski(C),B) )
                & ( r2_hidden(k1_tarski(C),B)
                 => r2_hidden(C,B) )
                & ( r2_hidden(D,B)
                 => r2_hidden(k3_tarski(D),B) ) ) ) ) ) ),
    file(zf_fund1,t2_zf_fund1),
    []).

fof(t33_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    []).

fof(t37_xboole_1,axiom,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

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(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t42_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C)) ),
    file(xboole_1,t42_xboole_1),
    []).

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(t4_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( ( v8_zf_fund1(B,A)
                & r2_hidden(C,B)
                & r2_hidden(D,B) )
             => ( r2_hidden(k2_xboole_0(C,D),B)
                & r2_hidden(k4_xboole_0(C,D),B)
                & r2_hidden(k1_zf_fund1(C,D),B) ) ) ) ) ),
    file(zf_fund1,t4_zf_fund1),
    []).

fof(t56_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    file(zfmisc_1,t56_zfmisc_1),
    []).

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(t5_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( ( v8_zf_fund1(B,A)
                & r2_hidden(C,B)
                & r2_hidden(D,B) )
             => r2_hidden(k3_xboole_0(C,D),B) ) ) ) ),
    file(zf_fund1,t5_zf_fund1),
    []).

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

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

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).

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

fof(t8_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    []).