% Mizar problem: t8_zfmodel1,zfmodel1,521,58 
fof(t8_zfmodel1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_ordinal1(A)
       => ( r2_zf_model(A,k10_zf_model)
        <=> ! [B] : 
              ( m1_subset_1(B,A)
             => r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A) ) ) ) ) ),
    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,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,connectedness_r1_xreal_0,d10_xboole_0,d10_zf_model,d17_zf_lang,d18_zf_lang,d19_zf_lang,d1_zf_lang,d2_ordinal1,d2_zf_lang,d3_tarski,d3_xboole_0,d4_zf_lang,d5_zf_lang,d5_zf_model,d6_zf_lang,d7_zf_lang,dt_k10_zf_model,dt_k11_zf_lang,dt_k12_finseq_1,dt_k12_zf_lang,dt_k13_zf_lang,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zf_lang,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zf_lang,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_k3_zf_lang,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_zf_lang,dt_k6_zf_lang,dt_k7_finseq_1,dt_k7_zf_lang,dt_k8_finseq_1,dt_k8_funct_2,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,fc27_membered,fc28_membered,fc29_membered,fc2_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_zf_lang,fc4_subset_1,fc4_zf_lang,fc5_membered,fc5_zf_lang,fc6_membered,fc6_zf_lang,fraenkel_a_0_0_zf_lang,idempotence_k3_xboole_0,rc1_membered,rc1_subset_1,rc1_zf_lang,rc2_subset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k3_zf_lang,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_k8_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,t13_zf_model,t16_zf_model,t18_zf_model,t19_zf_model,t1_arithm,t1_numerals,t1_subset,t20_zf_model,t21_zf_model,t25_zf_model,t2_boole,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(zfmodel1,t8_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(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_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(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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d10_zf_model,axiom,(
    k10_zf_model = k8_zf_lang(k2_zf_lang(0),k13_zf_lang(k2_zf_lang(1),k8_zf_lang(k2_zf_lang(2),k12_zf_lang(k5_zf_lang(k2_zf_lang(2),k2_zf_lang(1)),k8_zf_lang(k2_zf_lang(3),k11_zf_lang(k5_zf_lang(k2_zf_lang(3),k2_zf_lang(2)),k5_zf_lang(k2_zf_lang(3),k2_zf_lang(0)))))))) ),
    file(zf_model,d10_zf_model),
    []).

fof(d17_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k11_zf_lang(A,B) = k6_zf_lang(k7_zf_lang(A,k6_zf_lang(B))) ) ) ),
    file(zf_lang,d17_zf_lang),
    []).

fof(d18_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k12_zf_lang(A,B) = k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)) ) ) ),
    file(zf_lang,d18_zf_lang),
    []).

fof(d19_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k13_zf_lang(A,B) = k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))) ) ) ),
    file(zf_lang,d19_zf_lang),
    []).

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

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

fof(d2_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_zf_lang(A) = k1_nat_1(5,A) ) ),
    file(zf_lang,d2_zf_lang),
    []).

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_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k5_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,1),k3_zf_lang(A)),k3_zf_lang(B)) ) ) ),
    file(zf_lang,d4_zf_lang),
    []).

fof(d5_zf_lang,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => k6_zf_lang(A) = k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,2),A) ) ),
    file(zf_lang,d5_zf_lang),
    []).

fof(d5_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ( r2_zf_model(A,B)
          <=> ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_zf_lang,A)
                  & m2_relset_1(C,k1_zf_lang,A) )
               => r1_zf_model(A,C,B) ) ) ) ) ),
    file(zf_model,d5_zf_model),
    []).

fof(d6_zf_lang,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => k7_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,3),A),B) ) ) ),
    file(zf_lang,d6_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_k10_zf_model,axiom,
    ( v1_zf_lang(k10_zf_model)
    & m2_finseq_1(k10_zf_model,k5_numbers) ),
    file(zf_model,k10_zf_model),
    []).

fof(dt_k11_zf_lang,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k11_zf_lang(A,B))
        & m2_finseq_1(k11_zf_lang(A,B),k5_numbers) ) ) ),
    file(zf_lang,k11_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_k12_zf_lang,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k12_zf_lang(A,B))
        & m2_finseq_1(k12_zf_lang(A,B),k5_numbers) ) ) ),
    file(zf_lang,k12_zf_lang),
    []).

fof(dt_k13_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_zf_lang(k13_zf_lang(A,B))
        & m2_finseq_1(k13_zf_lang(A,B),k5_numbers) ) ) ),
    file(zf_lang,k13_zf_lang),
    []).

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k2_zf_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k2_zf_lang),
    []).

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

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

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_k5_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => m2_finseq_1(k5_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k5_zf_lang),
    []).

fof(dt_k6_zf_lang,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k5_numbers)
     => m2_finseq_1(k6_zf_lang(A),k5_numbers) ) ),
    file(zf_lang,k6_zf_lang),
    []).

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_k7_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k5_numbers)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k7_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k7_zf_lang),
    []).

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_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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(fc27_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(A,B)) ) ),
    file(membered,fc27_membered),
    []).

fof(fc28_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(B,A)) ) ),
    file(membered,fc28_membered),
    []).

fof(fc29_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc29_membered),
    []).

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

fof(fc30_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc30_membered),
    []).

fof(fc31_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc31_membered),
    []).

fof(fc32_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc32_membered),
    []).

fof(fc33_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc33_membered),
    []).

fof(fc34_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc34_membered),
    []).

fof(fc35_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B))
        & v5_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc35_membered),
    []).

fof(fc36_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A))
        & v5_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc36_membered),
    []).

fof(fc3_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => ( v1_relat_1(k5_zf_lang(A,B))
        & v1_funct_1(k5_zf_lang(A,B))
        & v1_finset_1(k5_zf_lang(A,B))
        & v1_finseq_1(k5_zf_lang(A,B))
        & v1_zf_lang(k5_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc3_zf_lang),
    []).

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(fc4_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_relat_1(k6_zf_lang(A))
        & v1_funct_1(k6_zf_lang(A))
        & v1_finset_1(k6_zf_lang(A))
        & v1_finseq_1(k6_zf_lang(A))
        & v1_zf_lang(k6_zf_lang(A)) ) ) ),
    file(zf_lang,fc4_zf_lang),
    []).

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(fc5_zf_lang,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k7_zf_lang(A,B))
        & v1_funct_1(k7_zf_lang(A,B))
        & v1_finset_1(k7_zf_lang(A,B))
        & v1_finseq_1(k7_zf_lang(A,B))
        & v1_zf_lang(k7_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc5_zf_lang),
    []).

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

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_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(spc3_boole,axiom,(
    ~ v1_xboole_0(3) ),
    file(boole,spc3_boole),
    []).

fof(spc3_numerals,axiom,
    ( v2_xreal_0(3)
    & m1_subset_1(3,k5_numbers) ),
    file(numerals,spc3_numerals),
    []).

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(t13_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k5_zf_lang(C,D))
                  <=> r2_hidden(k8_funct_2(k1_zf_lang,A,B,C),k8_funct_2(k1_zf_lang,A,B,D)) ) ) ) ) ) ),
    file(zf_model,t13_zf_model),
    []).

fof(t16_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k8_zf_lang(D,C))
                  <=> ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k1_zf_lang,A)
                          & m2_relset_1(E,k1_zf_lang,A) )
                       => ( ! [F] : 
                              ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
                               => D = F ) )
                         => r1_zf_model(A,E,C) ) ) ) ) ) ) ) ),
    file(zf_model,t16_zf_model),
    []).

fof(t18_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k11_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                     => r1_zf_model(A,B,D) ) ) ) ) ) ) ),
    file(zf_model,t18_zf_model),
    []).

fof(t19_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( r1_zf_model(A,B,k12_zf_lang(C,D))
                  <=> ( r1_zf_model(A,B,C)
                    <=> r1_zf_model(A,B,D) ) ) ) ) ) ) ),
    file(zf_model,t19_zf_model),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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

fof(t20_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_zf_model(A,B,k13_zf_lang(D,C))
                  <=> ? [E] : 
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k1_zf_lang,A)
                        & m2_relset_1(E,k1_zf_lang,A)
                        & ! [F] : 
                            ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                           => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
                             => D = F ) )
                        & r1_zf_model(A,E,C) ) ) ) ) ) ) ),
    file(zf_model,t20_zf_model),
    []).

fof(t21_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ? [E] : 
                      ( v1_funct_1(E)
                      & v1_funct_2(E,k1_zf_lang,A)
                      & m2_relset_1(E,k1_zf_lang,A)
                      & k8_funct_2(k1_zf_lang,A,E,C) = D
                      & ! [F] : 
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( F != C
                           => k8_funct_2(k1_zf_lang,A,E,F) = k8_funct_2(k1_zf_lang,A,B,F) ) ) ) ) ) ) ) ),
    file(zf_model,t21_zf_model),
    []).

fof(t25_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( r2_zf_model(C,k8_zf_lang(B,A))
              <=> r2_zf_model(C,A) ) ) ) ) ),
    file(zf_model,t25_zf_model),
    []).

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(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),
    []).