% Mizar problem: t10_zfmodel1,zfmodel1,797,52 
fof(t10_zfmodel1,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => ( r1_zf_model(C,D,B)
                   => ( r2_hidden(A,k2_zf_model(B))
                      | r1_zf_model(C,D,k8_zf_lang(A,B)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,connectedness_r1_xreal_0,d1_zf_lang,d7_zf_lang,dt_k12_finseq_1,dt_k1_card_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zf_lang,dt_k1_zf_model,dt_k1_zfmisc_1,dt_k2_zf_model,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_zf_lang,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k7_finseq_1,dt_k8_finseq_1,dt_k8_zf_lang,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc1_subset_1,fc1_zf_lang,fc2_membered,fc4_subset_1,fc5_membered,fc6_membered,fc6_zf_lang,fraenkel_a_0_0_zf_lang,l10_zfmodel1,rc1_membered,rc1_subset_1,rc1_zf_lang,rc2_subset_1,redefinition_k12_finseq_1,redefinition_k2_zf_model,redefinition_k3_finseq_1,redefinition_k3_zf_lang,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s4_nat_1__e1_11__zfmodel1,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(zfmodel1,t10_zfmodel1)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d1_zf_lang,axiom,(
    k1_zf_lang = a_0_0_zf_lang ),
    file(zf_lang,d1_zf_lang),
    []).

fof(d7_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => k8_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,4),k3_zf_lang(A)),B) ) ) ),
    file(zf_lang,d7_zf_lang),
    []).

fof(dt_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_1(k12_finseq_1(A,B),A) ) ),
    file(finseq_1,k12_finseq_1),
    []).

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

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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

fof(dt_k1_zf_lang,axiom,(
    m1_subset_1(k1_zf_lang,k1_zfmisc_1(k5_numbers)) ),
    file(zf_lang,k1_zf_lang),
    []).

fof(dt_k1_zf_model,axiom,(
    $true ),
    file(zf_model,k1_zf_model),
    []).

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

fof(dt_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)) ) ),
    file(zf_model,k2_zf_model),
    []).

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    []).

fof(dt_k3_zf_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zf_lang)
     => m2_finseq_1(k3_zf_lang(A),k5_numbers) ) ),
    file(zf_lang,k3_zf_lang),
    []).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

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

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

fof(dt_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(dt_k8_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k8_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k8_zf_lang),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

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(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(fc1_zf_lang,axiom,(
    ~ v1_xboole_0(k1_zf_lang) ),
    file(zf_lang,fc1_zf_lang),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc6_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k8_zf_lang(A,B))
        & v1_funct_1(k8_zf_lang(A,B))
        & v1_finset_1(k8_zf_lang(A,B))
        & v1_finseq_1(k8_zf_lang(A,B))
        & v1_zf_lang(k8_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc6_zf_lang),
    []).

fof(fraenkel_a_0_0_zf_lang,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_zf_lang)
    <=> ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = B
          & r1_xreal_0(5,B) ) ) ),
    file(zf_lang,a_0_0_zf_lang),
    []).

fof(l10_zfmodel1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( ~ r1_xreal_0(A,B)
             => ! [C] : 
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                 => ! [D] : 
                      ( ~ v1_xboole_0(D)
                     => ! [E] : 
                          ( ( v1_zf_lang(E)
                            & m2_finseq_1(E,k5_numbers) )
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,k1_zf_lang,D)
                                & m2_relset_1(F,k1_zf_lang,D) )
                             => ( ( k3_finseq_1(E) = B
                                  & r1_zf_model(D,F,E) )
                               => ( r2_hidden(C,k2_zf_model(E))
                                  | r1_zf_model(D,F,k8_zf_lang(C,E)) ) ) ) ) ) ) ) )
       => ! [B] : 
            ( m2_subset_1(B,k5_numbers,k1_zf_lang)
           => ! [C] : 
                ( ~ v1_xboole_0(C)
               => ! [D] : 
                    ( ( v1_zf_lang(D)
                      & m2_finseq_1(D,k5_numbers) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k1_zf_lang,C)
                          & m2_relset_1(E,k1_zf_lang,C) )
                       => ( ( k3_finseq_1(D) = A
                            & r1_zf_model(C,E,D) )
                         => ( r2_hidden(B,k2_zf_model(D))
                            | r1_zf_model(C,E,k8_zf_lang(B,D)) ) ) ) ) ) ) ) ) ),
    file(zfmodel1,l10_zfmodel1),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

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(rc1_zf_lang,axiom,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_zf_lang(A) ) ),
    file(zf_lang,rc1_zf_lang),
    []).

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(redefinition_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k12_finseq_1(A,B) = k5_finseq_1(B) ) ),
    file(finseq_1,k12_finseq_1),
    []).

fof(redefinition_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k2_zf_model(A) = k1_zf_model(A) ) ),
    file(zf_model,k2_zf_model),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

fof(redefinition_k3_zf_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zf_lang)
     => k3_zf_lang(A) = k5_finseq_1(A) ) ),
    file(zf_lang,k3_zf_lang),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(s4_nat_1__e1_11__zfmodel1,axiom,
    ( ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(A,B)
               => ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => ! [D] : 
                        ( ~ v1_xboole_0(D)
                       => ! [E] : 
                            ( ( v1_zf_lang(E)
                              & m2_finseq_1(E,k5_numbers) )
                           => ! [F] : 
                                ( ( v1_funct_1(F)
                                  & v1_funct_2(F,k1_zf_lang,D)
                                  & m2_relset_1(F,k1_zf_lang,D) )
                               => ( ( k3_finseq_1(E) = B
                                    & r1_zf_model(D,F,E) )
                                 => ( r2_hidden(C,k2_zf_model(E))
                                    | r1_zf_model(D,F,k8_zf_lang(C,E)) ) ) ) ) ) ) ) )
         => ! [G] : 
              ( m2_subset_1(G,k5_numbers,k1_zf_lang)
             => ! [H] : 
                  ( ~ v1_xboole_0(H)
                 => ! [I] : 
                      ( ( v1_zf_lang(I)
                        & m2_finseq_1(I,k5_numbers) )
                     => ! [J] : 
                          ( ( v1_funct_1(J)
                            & v1_funct_2(J,k1_zf_lang,H)
                            & m2_relset_1(J,k1_zf_lang,H) )
                         => ( ( k3_finseq_1(I) = A
                              & r1_zf_model(H,J,I) )
                           => ( r2_hidden(G,k2_zf_model(I))
                              | r1_zf_model(H,J,k8_zf_lang(G,I)) ) ) ) ) ) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ! [K] : 
            ( m2_subset_1(K,k5_numbers,k1_zf_lang)
           => ! [L] : 
                ( ~ v1_xboole_0(L)
               => ! [M] : 
                    ( ( v1_zf_lang(M)
                      & m2_finseq_1(M,k5_numbers) )
                   => ! [N] : 
                        ( ( v1_funct_1(N)
                          & v1_funct_2(N,k1_zf_lang,L)
                          & m2_relset_1(N,k1_zf_lang,L) )
                       => ( ( k3_finseq_1(M) = A
                            & r1_zf_model(L,N,M) )
                         => ( r2_hidden(K,k2_zf_model(M))
                            | r1_zf_model(L,N,k8_zf_lang(K,M)) ) ) ) ) ) ) ) ),
    file(zfmodel1,s4_nat_1__e1_11__zfmodel1),
    []).

fof(spc4_boole,axiom,(
    ~ v1_xboole_0(4) ),
    file(boole,spc4_boole),
    []).

fof(spc4_numerals,axiom,
    ( v2_xreal_0(4)
    & m1_subset_1(4,k5_numbers) ),
    file(numerals,spc4_numerals),
    []).

fof(spc5_boole,axiom,(
    ~ v1_xboole_0(5) ),
    file(boole,spc5_boole),
    []).

fof(spc5_numerals,axiom,
    ( v2_xreal_0(5)
    & m1_subset_1(5,k5_numbers) ),
    file(numerals,spc5_numerals),
    []).

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

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

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

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