% Mizar problem: t2_zf_model,zf_model,1061,49 
fof(t2_zf_model,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( k8_funct_2(k1_zf_lang,A,D,B) = k8_funct_2(k1_zf_lang,A,D,C)
                  <=> r2_hidden(D,k5_zf_model(k4_zf_lang(B,C),A)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,commutativity_k3_xboole_0,connectedness_r1_xreal_0,d1_zf_lang,d2_zf_model,d3_zf_lang,d4_zf_lang,d5_zf_lang,d6_zf_lang,d7_zf_lang,dt_k12_finseq_1,dt_k18_zf_lang,dt_k19_zf_lang,dt_k1_funct_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zf_lang,dt_k1_zfmisc_1,dt_k20_zf_lang,dt_k21_zf_lang,dt_k22_zf_lang,dt_k23_zf_lang,dt_k24_zf_lang,dt_k2_zfmisc_1,dt_k3_tarski,dt_k3_xboole_0,dt_k3_zf_lang,dt_k3_zf_model,dt_k4_xboole_0,dt_k4_zf_lang,dt_k4_zf_model,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_zf_lang,dt_k5_zf_model,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_xboole_0,fc1_zf_lang,fc1_zf_model,fc2_subset_1,fc2_zf_lang,fc3_zf_lang,fc4_subset_1,fc4_zf_lang,fc5_zf_lang,fc6_zf_lang,fraenkel_a_0_0_zf_lang,fraenkel_a_2_2_zf_model,fraenkel_a_2_3_zf_model,fraenkel_a_2_4_zf_model,fraenkel_a_3_4_zf_model,idempotence_k3_xboole_0,l7_zf_model,rc1_subset_1,rc1_xboole_0,rc1_zf_lang,rc2_subset_1,rc2_xboole_0,redefinition_k12_finseq_1,redefinition_k3_zf_lang,redefinition_k5_numbers,redefinition_k5_zf_model,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,t16_zf_lang,t1_numerals,t1_subset,t2_boole,t2_subset,t2_tarski,t3_boole,t3_subset,t4_boole,t4_subset,t53_zf_lang,t5_subset,t6_boole,t6_zf_lang,t7_boole,t8_boole]),
    [file(zf_model,t2_zf_model)]).

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

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

fof(d2_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( B = k3_zf_model(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,A)
                & m2_relset_1(C,k1_zf_lang,A) ) ) ) ) ),
    file(zf_model,d2_zf_model),
    []).

fof(d3_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k4_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,0),k3_zf_lang(A)),k3_zf_lang(B)) ) ) ),
    file(zf_lang,d3_zf_lang),
    []).

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(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_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_k18_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k18_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k18_zf_lang),
    []).

fof(dt_k19_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k19_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k19_zf_lang),
    []).

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

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

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_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_k20_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k20_zf_lang(A))
        & m2_finseq_1(k20_zf_lang(A),k5_numbers) ) ) ),
    file(zf_lang,k20_zf_lang),
    []).

fof(dt_k21_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k21_zf_lang(A))
        & m2_finseq_1(k21_zf_lang(A),k5_numbers) ) ) ),
    file(zf_lang,k21_zf_lang),
    []).

fof(dt_k22_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k22_zf_lang(A))
        & m2_finseq_1(k22_zf_lang(A),k5_numbers) ) ) ),
    file(zf_lang,k22_zf_lang),
    []).

fof(dt_k23_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m2_subset_1(k23_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k23_zf_lang),
    []).

fof(dt_k24_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_zf_lang(k24_zf_lang(A))
        & m2_finseq_1(k24_zf_lang(A),k5_numbers) ) ) ),
    file(zf_lang,k24_zf_lang),
    []).

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

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_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_k3_zf_model,axiom,(
    $true ),
    file(zf_model,k3_zf_model),
    []).

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

fof(dt_k4_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => m2_finseq_1(k4_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k4_zf_lang),
    []).

fof(dt_k4_zf_model,axiom,(
    $true ),
    file(zf_model,k4_zf_model),
    []).

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_k5_zf_model,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => m1_subset_1(k5_zf_model(A,B),k1_zfmisc_1(k3_zf_model(B))) ) ),
    file(zf_model,k5_zf_model),
    []).

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_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

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

fof(fc1_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k3_zf_model(A)) ) ),
    file(zf_model,fc1_zf_model),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_subset_1(B,k1_zf_lang) )
     => ( v1_relat_1(k4_zf_lang(A,B))
        & v1_funct_1(k4_zf_lang(A,B))
        & v1_finset_1(k4_zf_lang(A,B))
        & v1_finseq_1(k4_zf_lang(A,B))
        & v1_zf_lang(k4_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc2_zf_lang),
    []).

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_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_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(fraenkel_a_2_2_zf_model,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(B)
        & m2_finseq_1(B,k5_numbers)
        & ~ v1_xboole_0(C) )
     => ( r2_hidden(A,a_2_2_zf_model(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k3_zf_model(C))
            & A = D
            & ! [E] : 
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,k1_zf_lang,C)
                  & m2_relset_1(E,k1_zf_lang,C) )
               => ( E = D
                 => k8_funct_2(k1_zf_lang,C,E,k18_zf_lang(B)) = k8_funct_2(k1_zf_lang,C,E,k19_zf_lang(B)) ) ) ) ) ) ),
    file(zf_model,a_2_2_zf_model),
    []).

fof(fraenkel_a_2_3_zf_model,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(B)
        & m2_finseq_1(B,k5_numbers)
        & ~ v1_xboole_0(C) )
     => ( r2_hidden(A,a_2_3_zf_model(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k3_zf_model(C))
            & A = D
            & ! [E] : 
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,k1_zf_lang,C)
                  & m2_relset_1(E,k1_zf_lang,C) )
               => ( E = D
                 => r2_hidden(k8_funct_2(k1_zf_lang,C,E,k18_zf_lang(B)),k8_funct_2(k1_zf_lang,C,E,k19_zf_lang(B))) ) ) ) ) ) ),
    file(zf_model,a_2_3_zf_model),
    []).

fof(fraenkel_a_2_4_zf_model,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(B)
        & m2_finseq_1(B,k5_numbers)
        & ~ v1_xboole_0(C) )
     => ( r2_hidden(A,a_2_4_zf_model(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k3_zf_model(C))
            & A = D
            & ! [E,F] : 
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,k1_zf_lang,C)
                  & m2_relset_1(F,k1_zf_lang,C) )
               => ( ( E = k4_zf_model(k24_zf_lang(B),C)
                    & F = D )
                 => ( r2_hidden(F,E)
                    & ! [G] : 
                        ( ( v1_funct_1(G)
                          & v1_funct_2(G,k1_zf_lang,C)
                          & m2_relset_1(G,k1_zf_lang,C) )
                       => ( ! [H] : 
                              ( m2_subset_1(H,k5_numbers,k1_zf_lang)
                             => ( k8_funct_2(k1_zf_lang,C,G,H) != k8_funct_2(k1_zf_lang,C,F,H)
                               => k23_zf_lang(B) = H ) )
                         => r2_hidden(G,E) ) ) ) ) ) ) ) ) ),
    file(zf_model,a_2_4_zf_model),
    []).

fof(fraenkel_a_3_4_zf_model,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & m2_subset_1(C,k5_numbers,k1_zf_lang)
        & m2_subset_1(D,k5_numbers,k1_zf_lang) )
     => ( r2_hidden(A,a_3_4_zf_model(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k3_zf_model(B))
            & A = E
            & ! [F] : 
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,k1_zf_lang,B)
                  & m2_relset_1(F,k1_zf_lang,B) )
               => ( F = E
                 => k8_funct_2(k1_zf_lang,B,F,k18_zf_lang(k4_zf_lang(C,D))) = k8_funct_2(k1_zf_lang,B,F,k19_zf_lang(k4_zf_lang(C,D))) ) ) ) ) ) ),
    file(zf_model,a_3_4_zf_model),
    []).

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

fof(l7_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( ( v2_zf_lang(A)
             => k4_zf_model(A,B) = a_2_2_zf_model(A,B) )
            & ( v3_zf_lang(A)
             => k4_zf_model(A,B) = a_2_3_zf_model(A,B) )
            & ( v4_zf_lang(A)
             => k4_zf_model(A,B) = k4_xboole_0(k3_zf_model(B),k3_tarski(k1_tarski(k4_zf_model(k20_zf_lang(A),B)))) )
            & ( v5_zf_lang(A)
             => ! [C,D] : 
                  ( ( C = k4_zf_model(k21_zf_lang(A),B)
                    & D = k4_zf_model(k22_zf_lang(A),B) )
                 => k4_zf_model(A,B) = k3_xboole_0(k3_tarski(k1_tarski(C)),k3_tarski(k1_tarski(D))) ) )
            & ( v6_zf_lang(A)
             => k4_zf_model(A,B) = a_2_4_zf_model(A,B) ) ) ) ) ),
    file(zf_model,l7_zf_model),
    []).

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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

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(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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_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_k5_zf_model,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => k5_zf_model(A,B) = k4_zf_model(A,B) ) ),
    file(zf_model,k5_zf_model),
    []).

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(t16_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( ~ ( v2_zf_lang(A)
            & ! [B] : 
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => A != k4_zf_lang(B,C) ) ) )
        & ( ? [B] : 
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                  & A = k4_zf_lang(B,C) ) )
         => v2_zf_lang(A) )
        & ~ ( v3_zf_lang(A)
            & ! [B] : 
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                   => A != k5_zf_lang(B,C) ) ) )
        & ( ? [B] : 
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k1_zf_lang)
                  & A = k5_zf_lang(B,C) ) )
         => v3_zf_lang(A) )
        & ~ ( v4_zf_lang(A)
            & ! [B] : 
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => A != k6_zf_lang(B) ) )
        & ( ? [B] : 
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & A = k6_zf_lang(B) )
         => v4_zf_lang(A) )
        & ~ ( v5_zf_lang(A)
            & ! [B] : 
                ( ( v1_zf_lang(B)
                  & m2_finseq_1(B,k5_numbers) )
               => ! [C] : 
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k7_zf_lang(B,C) ) ) )
        & ( ? [B] : 
              ( v1_zf_lang(B)
              & m2_finseq_1(B,k5_numbers)
              & ? [C] : 
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k7_zf_lang(B,C) ) )
         => v5_zf_lang(A) )
        & ~ ( v6_zf_lang(A)
            & ! [B] : 
                ( m2_subset_1(B,k5_numbers,k1_zf_lang)
               => ! [C] : 
                    ( ( v1_zf_lang(C)
                      & m2_finseq_1(C,k5_numbers) )
                   => A != k8_zf_lang(B,C) ) ) )
        & ( ? [B] : 
              ( m2_subset_1(B,k5_numbers,k1_zf_lang)
              & ? [C] : 
                  ( v1_zf_lang(C)
                  & m2_finseq_1(C,k5_numbers)
                  & A = k8_zf_lang(B,C) ) )
         => v6_zf_lang(A) ) ) ) ),
    file(zf_lang,t16_zf_lang),
    []).

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(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_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(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(t53_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ( v2_zf_lang(A)
       => A = k4_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) ) ) ),
    file(zf_lang,t53_zf_lang),
    []).

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(t6_zf_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k4_zf_lang(A,B) = k4_zf_lang(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) ),
    file(zf_lang,t6_zf_lang),
    []).

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),
    []).