% Mizar problem: t17_henmodel,henmodel,1565,30 
fof(t17_henmodel,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] : 
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] : 
                  ( ( v1_henmodel(D)
                    & m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang)) )
                 => ! [E] : 
                      ( m1_henmodel(E,D)
                     => ( r1_valuat_1(k2_henmodel,k8_cqc_lang(A,B,C),E,k4_henmodel)
                      <=> r1_henmodel(D,k8_cqc_lang(A,B,C)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relset_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_ordinal1,cc2_xreal_0,cc3_int_1,cc3_ordinal1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,d12_valuat_1,d5_henmodel,d6_henmodel,d7_henmodel,dt_k11_valuat_1,dt_k12_valuat_1,dt_k13_cqc_sim1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_valuat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_henmodel,dt_k2_qc_lang1,dt_k2_valuat_1,dt_k2_zfmisc_1,dt_k3_henmodel,dt_k3_margrel1,dt_k4_henmodel,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k5_relat_1,dt_k6_margrel1,dt_k6_qc_lang1,dt_k6_relat_1,dt_k7_cqc_lang,dt_k7_qc_lang1,dt_k8_cqc_lang,dt_k8_funct_2,dt_k8_margrel1,dt_k8_qc_lang1,dt_k8_valuat_1,dt_k9_qc_lang1,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_henmodel,dt_m1_qc_lang1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_valuat_1,dt_m2_finseq_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_fraenkel,existence_m1_henmodel,existence_m1_qc_lang1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_valuat_1,existence_m2_finseq_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc14_finset_1,fc1_funct_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc2_cqc_lang,fc2_finseq_1,fc2_funct_1,fc2_ordinal1,fc2_qc_lang1,fc4_subset_1,fc5_qc_lang1,fc6_qc_lang1,rc1_cqc_lang,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_henmodel,rc1_int_1,rc1_ordinal1,rc1_subset_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_ordinal1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,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_k11_valuat_1,redefinition_k13_cqc_sim1,redefinition_k1_fraenkel,redefinition_k2_valuat_1,redefinition_k3_henmodel,redefinition_k5_numbers,redefinition_k8_cqc_lang,redefinition_k8_funct_2,redefinition_k8_valuat_1,redefinition_m2_finseq_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_margrel1,reflexivity_r1_margrel1,reflexivity_r1_tarski,symmetry_r1_margrel1,t14_henmodel,t16_valuat_1,t1_subset,t2_subset,t3_qc_lang3,t3_subset,t3_substut2,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(henmodel,t17_henmodel)]).

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

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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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_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_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

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

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

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(d12_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => ! [D] : 
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ( r1_valuat_1(A,B,C,D)
                  <=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,B),D) = k8_margrel1 ) ) ) ) ) ),
    file(valuat_1,d12_valuat_1),
    []).

fof(d5_henmodel,axiom,(
    k2_henmodel = k2_qc_lang1 ),
    file(henmodel,d5_henmodel),
    []).

fof(d6_henmodel,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] : 
          ( m1_valuat_1(B,k2_henmodel)
         => ( m1_henmodel(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k5_qc_lang1)
               => ! [D] : 
                    ( m1_subset_1(D,k3_margrel1(k2_henmodel))
                   => ( r1_margrel1(k2_henmodel,k8_funct_2(k5_qc_lang1,k3_margrel1(k2_henmodel),B,C),D)
                     => ! [E] : 
                          ( r2_hidden(E,D)
                        <=> ? [F] : 
                              ( v1_cqc_lang(F,k6_qc_lang1(C))
                              & m1_qc_lang1(F,k6_qc_lang1(C))
                              & E = F
                              & r1_henmodel(A,k3_henmodel(C,F)) ) ) ) ) ) ) ) ) ),
    file(henmodel,d6_henmodel),
    []).

fof(d7_henmodel,axiom,(
    k4_henmodel = k13_cqc_sim1(k2_qc_lang1) ),
    file(henmodel,d7_henmodel),
    []).

fof(dt_k11_valuat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_valuat_1(C,A)
        & m1_subset_1(D,k7_qc_lang1(B)) )
     => m1_subset_1(k11_valuat_1(A,B,C,D),k3_margrel1(A)) ) ),
    file(valuat_1,k11_valuat_1),
    []).

fof(dt_k12_valuat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_valuat_1(B,A)
        & m1_subset_1(C,k7_cqc_lang) )
     => m2_fraenkel(k12_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ),
    file(valuat_1,k12_valuat_1),
    []).

fof(dt_k13_cqc_sim1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k13_cqc_sim1(A),A,A,k1_fraenkel(A,A)) ) ),
    file(cqc_sim1,k13_cqc_sim1),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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

fof(dt_k1_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k1_qc_lang1),
    []).

fof(dt_k1_valuat_1,axiom,(
    $true ),
    file(valuat_1,k1_valuat_1),
    []).

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

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

fof(dt_k2_henmodel,axiom,(
    ~ v1_xboole_0(k2_henmodel) ),
    file(henmodel,k2_henmodel),
    []).

fof(dt_k2_qc_lang1,axiom,(
    m1_subset_1(k2_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ),
    file(qc_lang1,k2_qc_lang1),
    []).

fof(dt_k2_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_fraenkel(k2_valuat_1(A),k2_qc_lang1,A) ) ),
    file(valuat_1,k2_valuat_1),
    []).

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

fof(dt_k3_henmodel,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_qc_lang1)
        & v1_cqc_lang(B,k6_qc_lang1(A))
        & m1_qc_lang1(B,k6_qc_lang1(A)) )
     => m2_subset_1(k3_henmodel(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(henmodel,k3_henmodel),
    []).

fof(dt_k3_margrel1,axiom,(
    $true ),
    file(margrel1,k3_margrel1),
    []).

fof(dt_k4_henmodel,axiom,(
    m2_fraenkel(k4_henmodel,k2_qc_lang1,k2_henmodel,k2_valuat_1(k2_henmodel)) ),
    file(henmodel,k4_henmodel),
    []).

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_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k5_qc_lang1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

fof(dt_k6_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_qc_lang1)
     => m2_subset_1(k6_qc_lang1(A),k1_numbers,k5_numbers) ) ),
    file(qc_lang1,k6_qc_lang1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_cqc_lang,axiom,(
    m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ),
    file(cqc_lang,k7_cqc_lang),
    []).

fof(dt_k7_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)) ) ),
    file(qc_lang1,k7_qc_lang1),
    []).

fof(dt_k8_cqc_lang,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A) )
     => m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k8_cqc_lang),
    []).

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_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    []).

fof(dt_k8_qc_lang1,axiom,(
    ~ v1_xboole_0(k8_qc_lang1) ),
    file(qc_lang1,k8_qc_lang1),
    []).

fof(dt_k8_valuat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_cqc_lang(C,B)
        & m1_qc_lang1(C,B)
        & m1_subset_1(D,k2_valuat_1(A)) )
     => m2_finseq_1(k8_valuat_1(A,B,C,D),A) ) ),
    file(valuat_1,k8_valuat_1),
    []).

fof(dt_k9_qc_lang1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_qc_lang1)
        & m1_finseq_1(B,k1_qc_lang1) )
     => m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1) ) ),
    file(qc_lang1,k9_qc_lang1),
    []).

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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_henmodel,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ! [B] : 
          ( m1_henmodel(B,A)
         => m1_valuat_1(B,k2_henmodel) ) ) ),
    file(henmodel,m1_henmodel),
    []).

fof(dt_m1_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ! [B] : 
          ( m1_qc_lang1(B,A)
         => m2_finseq_1(B,k1_qc_lang1) ) ) ),
    file(qc_lang1,m1_qc_lang1),
    []).

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_m1_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k5_qc_lang1,k3_margrel1(A))
            & m2_relset_1(B,k5_qc_lang1,k3_margrel1(A)) ) ) ) ),
    file(valuat_1,m1_valuat_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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(existence_m1_henmodel,axiom,(
    ! [A] : 
      ( ( v1_henmodel(A)
        & m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
     => ? [B] : m1_henmodel(B,A) ) ),
    file(henmodel,m1_henmodel),
    []).

fof(existence_m1_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m1_qc_lang1(B,A) ) ),
    file(qc_lang1,m1_qc_lang1),
    []).

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_m1_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_valuat_1(B,A) ) ),
    file(valuat_1,m1_valuat_1),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_qc_lang1,axiom,(
    ~ v1_xboole_0(k1_qc_lang1) ),
    file(qc_lang1,fc1_qc_lang1),
    []).

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

fof(fc2_cqc_lang,axiom,(
    ~ v1_xboole_0(k7_cqc_lang) ),
    file(cqc_lang,fc2_cqc_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_funct_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_qc_lang1,axiom,(
    ~ v1_xboole_0(k2_qc_lang1) ),
    file(qc_lang1,fc2_qc_lang1),
    []).

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

fof(fc5_qc_lang1,axiom,(
    ~ v1_xboole_0(k5_qc_lang1) ),
    file(qc_lang1,fc5_qc_lang1),
    []).

fof(fc6_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ~ v1_xboole_0(k7_qc_lang1(A)) ) ),
    file(qc_lang1,fc6_qc_lang1),
    []).

fof(rc1_cqc_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( m1_qc_lang1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v1_cqc_lang(B,A) ) ) ),
    file(cqc_lang,rc1_cqc_lang),
    []).

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_henmodel,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
      & v1_henmodel(A) ) ),
    file(henmodel,rc1_henmodel),
    []).

fof(rc1_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    []).

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

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_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

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_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(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_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_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

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_k11_valuat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_valuat_1(C,A)
        & m1_subset_1(D,k7_qc_lang1(B)) )
     => k11_valuat_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(valuat_1,k11_valuat_1),
    []).

fof(redefinition_k13_cqc_sim1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k13_cqc_sim1(A) = k6_relat_1(A) ) ),
    file(cqc_sim1,k13_cqc_sim1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k2_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k2_valuat_1(A) = k1_valuat_1(A) ) ),
    file(valuat_1,k2_valuat_1),
    []).

fof(redefinition_k3_henmodel,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_qc_lang1)
        & v1_cqc_lang(B,k6_qc_lang1(A))
        & m1_qc_lang1(B,k6_qc_lang1(A)) )
     => k3_henmodel(A,B) = k9_qc_lang1(A,B) ) ),
    file(henmodel,k3_henmodel),
    []).

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

fof(redefinition_k8_cqc_lang,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A) )
     => k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C) ) ),
    file(cqc_lang,k8_cqc_lang),
    []).

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_k8_valuat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_cqc_lang(C,B)
        & m1_qc_lang1(C,B)
        & m1_subset_1(D,k2_valuat_1(A)) )
     => k8_valuat_1(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(valuat_1,k8_valuat_1),
    []).

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

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(redefinition_r1_margrel1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_margrel1(A))
        & m1_subset_1(C,k3_margrel1(A)) )
     => ( r1_margrel1(A,B,C)
      <=> B = C ) ) ),
    file(margrel1,r1_margrel1),
    []).

fof(reflexivity_r1_margrel1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_margrel1(A))
        & m1_subset_1(C,k3_margrel1(A)) )
     => r1_margrel1(A,B,B) ) ),
    file(margrel1,r1_margrel1),
    []).

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

fof(symmetry_r1_margrel1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k3_margrel1(A))
        & m1_subset_1(C,k3_margrel1(A)) )
     => ( r1_margrel1(A,B,C)
       => r1_margrel1(A,C,B) ) ) ),
    file(margrel1,r1_margrel1),
    []).

fof(t14_henmodel,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_cqc_lang(B,A)
            & m1_qc_lang1(B,A) )
         => k8_valuat_1(k2_henmodel,A,B,k4_henmodel) = B ) ) ),
    file(henmodel,t14_henmodel),
    []).

fof(t16_valuat_1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] : 
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,B)
                         => ! [G] : 
                              ( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,k3_margrel1(B))
                                 => ( ( E = k8_cqc_lang(A,G,D)
                                      & r1_margrel1(B,H,k11_valuat_1(B,A,F,G)) )
                                   => ( r2_hidden(k8_valuat_1(B,A,D,C),H)
                                    <=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k12_valuat_1(B,F,E),C) = k8_margrel1 ) ) ) ) ) ) ) ) ) ) ),
    file(valuat_1,t16_valuat_1),
    []).

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

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

fof(t3_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_qc_lang1)
     => m2_subset_1(A,k5_qc_lang1,k7_qc_lang1(k6_qc_lang1(A))) ) ),
    file(qc_lang3,t3_qc_lang3),
    []).

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

fof(t3_substut2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(C))
                      & m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(D)) )
                   => C = D ) ) ) ) ) ),
    file(substut2,t3_substut2),
    []).

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),
    []).