% Mizar problem: t1_zfmodel2,zfmodel2,33,45 
fof(t1_zfmodel2,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B))) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc1_xreal_0,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_xreal_0,cc3_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,d1_tarski,d2_tarski,d2_xboole_0,d3_tarski,d4_xboole_0,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zf_lang,dt_k1_zf_model,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zf_model,dt_k2_zfmisc_1,dt_k4_subset_1,dt_k4_xboole_0,dt_k4_zf_lang,dt_k5_numbers,dt_k5_ordinal2,dt_k5_zf_lang,dt_k5_zf_lang1,dt_k6_zf_lang,dt_k6_zf_lang1,dt_k7_zf_lang,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,fc12_finset_1,fc14_finset_1,fc1_finset_1,fc1_zf_lang,fc2_finseq_1,fc2_finset_1,fc2_zf_lang,fc3_zf_lang,fc4_zf_lang,fc5_zf_lang,fc6_zf_lang,fc9_finset_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_arytm_3,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_xreal_0,rc1_zf_lang,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k2_zf_model,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k6_zf_lang1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_zf_lang1__e5_1__zfmodel2,t13_xboole_1,t166_zf_lang1,t168_zf_lang1,t170_zf_lang1,t172_zf_lang1,t173_zf_lang1,t174_zf_lang1,t1_boole,t1_subset,t1_xboole_1,t2_subset,t33_xboole_1,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t63_zf_lang1,t64_zf_lang1,t65_zf_lang1,t66_zf_lang1,t67_zf_lang1,t6_boole,t7_boole,t8_boole]),
    [file(zfmodel2,t1_zfmodel2)]).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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_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(cc1_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

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

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(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

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_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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

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_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_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_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_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_relat_1(k5_zf_lang1(A,B,C))
        & v1_funct_1(k5_zf_lang1(A,B,C)) ) ) ),
    file(zf_lang1,k5_zf_lang1),
    []).

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_k6_zf_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => ( v1_zf_lang(k6_zf_lang1(A,B,C))
        & m2_finseq_1(k6_zf_lang1(A,B,C),k5_numbers) ) ) ),
    file(zf_lang1,k6_zf_lang1),
    []).

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_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(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(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_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_zf_lang,axiom,(
    ~ v1_xboole_0(k1_zf_lang) ),
    file(zf_lang,fc1_zf_lang),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

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_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_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(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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_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(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    []).

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

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_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

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_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    []).

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(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_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_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_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k6_zf_lang1,axiom,(
    ! [A,B,C] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k1_zf_lang)
        & m1_subset_1(C,k1_zf_lang) )
     => k6_zf_lang1(A,B,C) = k5_zf_lang1(A,B,C) ) ),
    file(zf_lang1,k6_zf_lang1),
    []).

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(s1_zf_lang1__e5_1__zfmodel2,axiom,(
    ! [A,B] : 
      ( ( m2_subset_1(A,k5_numbers,k1_zf_lang)
        & 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)
                 => ( r1_tarski(k2_zf_model(k6_zf_lang1(k4_zf_lang(C,D),A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(k4_zf_lang(C,D)),k1_tarski(A)),k1_tarski(B)))
                    & r1_tarski(k2_zf_model(k6_zf_lang1(k5_zf_lang(C,D),A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(k5_zf_lang(C,D)),k1_tarski(A)),k1_tarski(B))) ) ) )
          & ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B)))
               => r1_tarski(k2_zf_model(k6_zf_lang1(k6_zf_lang(C),A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(k6_zf_lang(C)),k1_tarski(A)),k1_tarski(B))) ) )
          & ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ( ( r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B)))
                      & r1_tarski(k2_zf_model(k6_zf_lang1(D,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(D),k1_tarski(A)),k1_tarski(B))) )
                   => r1_tarski(k2_zf_model(k6_zf_lang1(k7_zf_lang(C,D),A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(k7_zf_lang(C,D)),k1_tarski(A)),k1_tarski(B))) ) ) )
          & ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B)))
                   => r1_tarski(k2_zf_model(k6_zf_lang1(k8_zf_lang(D,C),A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(k8_zf_lang(D,C)),k1_tarski(A)),k1_tarski(B))) ) ) ) )
       => ! [C] : 
            ( ( v1_zf_lang(C)
              & m2_finseq_1(C,k5_numbers) )
           => r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B))) ) ) ) ),
    file(zfmodel2,s1_zf_lang1__e5_1__zfmodel2),
    []).

fof(t13_xboole_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    []).

fof(t166_zf_lang1,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)
                 => ! [E] : 
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] : 
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F)
                          <=> ~ ( ~ ( A != C
                                    & B != C
                                    & E = A
                                    & F = B )
                                & ~ ( A = C
                                    & B != C
                                    & E = D
                                    & F = B )
                                & ~ ( A != C
                                    & B = C
                                    & E = A
                                    & F = D )
                                & ~ ( A = C
                                    & B = C
                                    & E = D
                                    & F = D ) ) ) ) ) ) ) ) ) ),
    file(zf_lang1,t166_zf_lang1),
    []).

fof(t168_zf_lang1,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)
                 => ! [E] : 
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] : 
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F)
                          <=> ~ ( ~ ( A != C
                                    & B != C
                                    & E = A
                                    & F = B )
                                & ~ ( A = C
                                    & B != C
                                    & E = D
                                    & F = B )
                                & ~ ( A != C
                                    & B = C
                                    & E = A
                                    & F = D )
                                & ~ ( A = C
                                    & B = C
                                    & E = D
                                    & F = D ) ) ) ) ) ) ) ) ) ),
    file(zf_lang1,t168_zf_lang1),
    []).

fof(t170_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k6_zf_lang(A) = k5_zf_lang1(k6_zf_lang(B),C,D)
                  <=> A = k5_zf_lang1(B,C,D) ) ) ) ) ) ),
    file(zf_lang1,t170_zf_lang1),
    []).

fof(t172_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_zf_lang(D)
                    & m2_finseq_1(D,k5_numbers) )
                 => ! [E] : 
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ! [F] : 
                          ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                         => ( k7_zf_lang(A,B) = k6_zf_lang1(k7_zf_lang(C,D),E,F)
                          <=> ( A = k6_zf_lang1(C,E,F)
                              & B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) ),
    file(zf_lang1,t172_zf_lang1),
    []).

fof(t173_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ! [E] : 
                      ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                     => ( C != D
                       => ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(C,B),D,E)
                        <=> A = k6_zf_lang1(B,D,E) ) ) ) ) ) ) ) ),
    file(zf_lang1,t173_zf_lang1),
    []).

fof(t174_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_zf_lang)
                 => ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(D,B),D,C)
                  <=> A = k6_zf_lang1(B,D,C) ) ) ) ) ) ),
    file(zf_lang1,t174_zf_lang1),
    []).

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

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

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

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(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(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(t63_zf_lang1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) ),
    file(zf_lang1,t63_zf_lang1),
    []).

fof(t64_zf_lang1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) ),
    file(zf_lang1,t64_zf_lang1),
    []).

fof(t65_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A) ) ),
    file(zf_lang1,t65_zf_lang1),
    []).

fof(t66_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => k2_zf_model(k7_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ),
    file(zf_lang1,t66_zf_lang1),
    []).

fof(t67_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k8_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) ),
    file(zf_lang1,t67_zf_lang1),
    []).

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),
    []).