% Mizar problem: t70_sublemma,sublemma,1599,27 
fof(t70_sublemma,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ! [E] : 
                      ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                     => ( k8_relset_1(k2_qc_lang1,A,D,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,E,k24_qc_lang1(C))
                       => ( r1_valuat_1(A,C,B,D)
                        <=> r1_valuat_1(A,C,B,E) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_nat_1,cc3_nat_1,d4_cqc_lang,dt_k10_cqc_lang,dt_k11_cqc_lang,dt_k11_qc_lang1,dt_k12_qc_lang1,dt_k13_qc_lang1,dt_k14_qc_lang1,dt_k15_cqc_lang,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_valuat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k24_qc_lang1,dt_k2_qc_lang1,dt_k2_valuat_1,dt_k2_zfmisc_1,dt_k3_margrel1,dt_k3_qc_lang1,dt_k4_qc_lang1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k5_qc_lang3,dt_k6_qc_lang3,dt_k7_cqc_lang,dt_k7_qc_lang1,dt_k7_relat_1,dt_k8_cqc_lang,dt_k8_qc_lang1,dt_k8_relset_1,dt_k9_cqc_lang,dt_k9_qc_lang1,dt_m1_finseq_1,dt_m1_fraenkel,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_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,fc12_relat_1,fc13_relat_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc2_cqc_lang,fc2_qc_lang1,fc3_qc_lang1,fc4_funct_1,fc4_qc_lang1,fc4_relat_1,fc4_subset_1,fc5_qc_lang1,fc6_qc_lang1,fraenkel_a_0_0_cqc_lang,rc1_cqc_lang,rc1_fraenkel,rc1_funct_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc4_funct_1,redefinition_k10_cqc_lang,redefinition_k11_cqc_lang,redefinition_k15_cqc_lang,redefinition_k2_valuat_1,redefinition_k5_numbers,redefinition_k8_cqc_lang,redefinition_k8_relset_1,redefinition_k9_cqc_lang,redefinition_m2_finseq_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_cqc_lang__e2_85__sublemma,t1_subset,t2_subset,t2_tarski,t3_subset,t44_valuat_1,t4_subset,t5_subset,t61_sublemma,t62_sublemma,t63_sublemma,t68_sublemma,t6_boole,t7_boole,t8_boole]),
    [file(sublemma,t70_sublemma)]).

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

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_nat_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) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_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(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_nat_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) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(d4_cqc_lang,axiom,(
    k7_cqc_lang = a_0_0_cqc_lang ),
    file(cqc_lang,d4_cqc_lang),
    []).

fof(dt_k10_cqc_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k10_cqc_lang),
    []).

fof(dt_k11_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k11_cqc_lang),
    []).

fof(dt_k11_qc_lang1,axiom,(
    m1_subset_1(k11_qc_lang1,k8_qc_lang1) ),
    file(qc_lang1,k11_qc_lang1),
    []).

fof(dt_k12_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k12_qc_lang1(A),k8_qc_lang1) ) ),
    file(qc_lang1,k12_qc_lang1),
    []).

fof(dt_k13_qc_lang1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1) ) ),
    file(qc_lang1,k13_qc_lang1),
    []).

fof(dt_k14_qc_lang1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1) ) ),
    file(qc_lang1,k14_qc_lang1),
    []).

fof(dt_k15_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(cqc_lang,k15_cqc_lang),
    []).

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_k24_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(qc_lang1,k24_qc_lang1),
    []).

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_margrel1,axiom,(
    $true ),
    file(margrel1,k3_margrel1),
    []).

fof(dt_k3_qc_lang1,axiom,(
    m1_subset_1(k3_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ),
    file(qc_lang1,k3_qc_lang1),
    []).

fof(dt_k4_qc_lang1,axiom,(
    m1_subset_1(k4_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ),
    file(qc_lang1,k4_qc_lang1),
    []).

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_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k5_qc_lang3(A),k1_zfmisc_1(k4_qc_lang1)) ) ),
    file(qc_lang3,k5_qc_lang3),
    []).

fof(dt_k6_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k6_qc_lang3(A),k1_zfmisc_1(k3_qc_lang1)) ) ),
    file(qc_lang3,k6_qc_lang3),
    []).

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_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

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_qc_lang1,axiom,(
    ~ v1_xboole_0(k8_qc_lang1) ),
    file(qc_lang1,k8_qc_lang1),
    []).

fof(dt_k8_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ),
    file(relset_1,k8_relset_1),
    []).

fof(dt_k9_cqc_lang,axiom,(
    m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) ),
    file(cqc_lang,k9_cqc_lang),
    []).

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_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_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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_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_qc_lang1,axiom,(
    ~ v1_xboole_0(k2_qc_lang1) ),
    file(qc_lang1,fc2_qc_lang1),
    []).

fof(fc3_qc_lang1,axiom,(
    ~ v1_xboole_0(k3_qc_lang1) ),
    file(qc_lang1,fc3_qc_lang1),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_qc_lang1,axiom,(
    ~ v1_xboole_0(k4_qc_lang1) ),
    file(qc_lang1,fc4_qc_lang1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

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(fraenkel_a_0_0_cqc_lang,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_cqc_lang)
    <=> ? [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
          & A = B
          & k6_qc_lang3(B) = k1_xboole_0
          & k5_qc_lang3(B) = k1_xboole_0 ) ) ),
    file(cqc_lang,a_0_0_cqc_lang),
    []).

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_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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(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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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(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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_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(redefinition_k10_cqc_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => k10_cqc_lang(A) = k12_qc_lang1(A) ) ),
    file(cqc_lang,k10_cqc_lang),
    []).

fof(redefinition_k11_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k11_cqc_lang(A,B) = k13_qc_lang1(A,B) ) ),
    file(cqc_lang,k11_cqc_lang),
    []).

fof(redefinition_k15_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => k15_cqc_lang(A,B) = k14_qc_lang1(A,B) ) ),
    file(cqc_lang,k15_cqc_lang),
    []).

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_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_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(relset_1,k8_relset_1),
    []).

fof(redefinition_k9_cqc_lang,axiom,(
    k9_cqc_lang = k11_qc_lang1 ),
    file(cqc_lang,k9_cqc_lang),
    []).

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

fof(s1_cqc_lang__e2_85__sublemma,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_valuat_1(B,A) )
     => ( ! [C] : 
            ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
           => ! [D] : 
                ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
               => ! [E] : 
                    ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                   => ! [F] : 
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ! [G] : 
                            ( ( v1_cqc_lang(G,F)
                              & m1_qc_lang1(G,F) )
                           => ! [H] : 
                                ( m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F))
                               => ( ! [I] : 
                                      ( m2_fraenkel(I,k2_qc_lang1,A,k2_valuat_1(A))
                                     => ! [J] : 
                                          ( m2_fraenkel(J,k2_qc_lang1,A,k2_valuat_1(A))
                                         => ( k8_relset_1(k2_qc_lang1,A,I,k24_qc_lang1(k9_cqc_lang)) = k8_relset_1(k2_qc_lang1,A,J,k24_qc_lang1(k9_cqc_lang))
                                           => ( r1_valuat_1(A,k9_cqc_lang,B,I)
                                            <=> r1_valuat_1(A,k9_cqc_lang,B,J) ) ) ) )
                                  & ! [K] : 
                                      ( m2_fraenkel(K,k2_qc_lang1,A,k2_valuat_1(A))
                                     => ! [L] : 
                                          ( m2_fraenkel(L,k2_qc_lang1,A,k2_valuat_1(A))
                                         => ( k8_relset_1(k2_qc_lang1,A,K,k24_qc_lang1(k8_cqc_lang(F,H,G))) = k8_relset_1(k2_qc_lang1,A,L,k24_qc_lang1(k8_cqc_lang(F,H,G)))
                                           => ( r1_valuat_1(A,k8_cqc_lang(F,H,G),B,K)
                                            <=> r1_valuat_1(A,k8_cqc_lang(F,H,G),B,L) ) ) ) )
                                  & ( ! [M] : 
                                        ( m2_fraenkel(M,k2_qc_lang1,A,k2_valuat_1(A))
                                       => ! [N] : 
                                            ( m2_fraenkel(N,k2_qc_lang1,A,k2_valuat_1(A))
                                           => ( k8_relset_1(k2_qc_lang1,A,M,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,N,k24_qc_lang1(C))
                                             => ( r1_valuat_1(A,C,B,M)
                                              <=> r1_valuat_1(A,C,B,N) ) ) ) )
                                   => ! [O] : 
                                        ( m2_fraenkel(O,k2_qc_lang1,A,k2_valuat_1(A))
                                       => ! [P] : 
                                            ( m2_fraenkel(P,k2_qc_lang1,A,k2_valuat_1(A))
                                           => ( k8_relset_1(k2_qc_lang1,A,O,k24_qc_lang1(k10_cqc_lang(C))) = k8_relset_1(k2_qc_lang1,A,P,k24_qc_lang1(k10_cqc_lang(C)))
                                             => ( r1_valuat_1(A,k10_cqc_lang(C),B,O)
                                              <=> r1_valuat_1(A,k10_cqc_lang(C),B,P) ) ) ) ) )
                                  & ( ( ! [Q] : 
                                          ( m2_fraenkel(Q,k2_qc_lang1,A,k2_valuat_1(A))
                                         => ! [R] : 
                                              ( m2_fraenkel(R,k2_qc_lang1,A,k2_valuat_1(A))
                                             => ( k8_relset_1(k2_qc_lang1,A,Q,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,R,k24_qc_lang1(C))
                                               => ( r1_valuat_1(A,C,B,Q)
                                                <=> r1_valuat_1(A,C,B,R) ) ) ) )
                                      & ! [S] : 
                                          ( m2_fraenkel(S,k2_qc_lang1,A,k2_valuat_1(A))
                                         => ! [T] : 
                                              ( m2_fraenkel(T,k2_qc_lang1,A,k2_valuat_1(A))
                                             => ( k8_relset_1(k2_qc_lang1,A,S,k24_qc_lang1(D)) = k8_relset_1(k2_qc_lang1,A,T,k24_qc_lang1(D))
                                               => ( r1_valuat_1(A,D,B,S)
                                                <=> r1_valuat_1(A,D,B,T) ) ) ) ) )
                                   => ! [U] : 
                                        ( m2_fraenkel(U,k2_qc_lang1,A,k2_valuat_1(A))
                                       => ! [V] : 
                                            ( m2_fraenkel(V,k2_qc_lang1,A,k2_valuat_1(A))
                                           => ( k8_relset_1(k2_qc_lang1,A,U,k24_qc_lang1(k11_cqc_lang(C,D))) = k8_relset_1(k2_qc_lang1,A,V,k24_qc_lang1(k11_cqc_lang(C,D)))
                                             => ( r1_valuat_1(A,k11_cqc_lang(C,D),B,U)
                                              <=> r1_valuat_1(A,k11_cqc_lang(C,D),B,V) ) ) ) ) )
                                  & ( ! [W] : 
                                        ( m2_fraenkel(W,k2_qc_lang1,A,k2_valuat_1(A))
                                       => ! [X] : 
                                            ( m2_fraenkel(X,k2_qc_lang1,A,k2_valuat_1(A))
                                           => ( k8_relset_1(k2_qc_lang1,A,W,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,X,k24_qc_lang1(C))
                                             => ( r1_valuat_1(A,C,B,W)
                                              <=> r1_valuat_1(A,C,B,X) ) ) ) )
                                   => ! [Y] : 
                                        ( m2_fraenkel(Y,k2_qc_lang1,A,k2_valuat_1(A))
                                       => ! [Z] : 
                                            ( m2_fraenkel(Z,k2_qc_lang1,A,k2_valuat_1(A))
                                           => ( k8_relset_1(k2_qc_lang1,A,Y,k24_qc_lang1(k15_cqc_lang(E,C))) = k8_relset_1(k2_qc_lang1,A,Z,k24_qc_lang1(k15_cqc_lang(E,C)))
                                             => ( r1_valuat_1(A,k15_cqc_lang(E,C),B,Y)
                                              <=> r1_valuat_1(A,k15_cqc_lang(E,C),B,Z) ) ) ) ) ) ) ) ) ) ) ) )
       => ! [C] : 
            ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
           => ! [A1] : 
                ( m2_fraenkel(A1,k2_qc_lang1,A,k2_valuat_1(A))
               => ! [B1] : 
                    ( m2_fraenkel(B1,k2_qc_lang1,A,k2_valuat_1(A))
                   => ( k8_relset_1(k2_qc_lang1,A,A1,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,B1,k24_qc_lang1(C))
                     => ( r1_valuat_1(A,C,B,A1)
                      <=> r1_valuat_1(A,C,B,B1) ) ) ) ) ) ) ) ),
    file(sublemma,s1_cqc_lang__e2_85__sublemma),
    []).

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

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

fof(t44_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => r1_valuat_1(A,k9_cqc_lang,C,B) ) ) ) ),
    file(valuat_1,t44_valuat_1),
    []).

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(t61_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_valuat_1(C,B)
             => ! [D] : 
                  ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(A))
                 => ! [E] : 
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] : 
                          ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                         => ! [G] : 
                              ( m2_fraenkel(G,k2_qc_lang1,B,k2_valuat_1(B))
                             => ( k8_relset_1(k2_qc_lang1,B,F,k24_qc_lang1(k8_cqc_lang(A,D,E))) = k8_relset_1(k2_qc_lang1,B,G,k24_qc_lang1(k8_cqc_lang(A,D,E)))
                               => ( r1_valuat_1(B,k8_cqc_lang(A,D,E),C,F)
                                <=> r1_valuat_1(B,k8_cqc_lang(A,D,E),C,G) ) ) ) ) ) ) ) ) ) ),
    file(sublemma,t61_sublemma),
    []).

fof(t62_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_valuat_1(C,B)
             => ( ! [D] : 
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,B,k2_valuat_1(B))
                       => ( k8_relset_1(k2_qc_lang1,B,D,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,B,E,k24_qc_lang1(A))
                         => ( r1_valuat_1(B,A,C,D)
                          <=> r1_valuat_1(B,A,C,E) ) ) ) )
               => ! [D] : 
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,B,k2_valuat_1(B))
                       => ( k8_relset_1(k2_qc_lang1,B,D,k24_qc_lang1(k10_cqc_lang(A))) = k8_relset_1(k2_qc_lang1,B,E,k24_qc_lang1(k10_cqc_lang(A)))
                         => ( r1_valuat_1(B,k10_cqc_lang(A),C,D)
                          <=> r1_valuat_1(B,k10_cqc_lang(A),C,E) ) ) ) ) ) ) ) ) ),
    file(sublemma,t62_sublemma),
    []).

fof(t63_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_valuat_1(D,C)
                 => ( ( ! [E] : 
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] : 
                              ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                             => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(A))
                               => ( r1_valuat_1(C,A,D,E)
                                <=> r1_valuat_1(C,A,D,F) ) ) ) )
                      & ! [E] : 
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] : 
                              ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                             => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(B)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(B))
                               => ( r1_valuat_1(C,B,D,E)
                                <=> r1_valuat_1(C,B,D,F) ) ) ) ) )
                   => ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(k11_cqc_lang(A,B))) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(k11_cqc_lang(A,B)))
                             => ( r1_valuat_1(C,k11_cqc_lang(A,B),D,E)
                              <=> r1_valuat_1(C,k11_cqc_lang(A,B),D,F) ) ) ) ) ) ) ) ) ) ),
    file(sublemma,t63_sublemma),
    []).

fof(t68_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_valuat_1(D,C)
                 => ( ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(A))
                             => ( r1_valuat_1(C,A,D,E)
                              <=> r1_valuat_1(C,A,D,F) ) ) ) )
                   => ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(k15_cqc_lang(B,A))) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(k15_cqc_lang(B,A)))
                             => ( r1_valuat_1(C,k15_cqc_lang(B,A),D,E)
                              <=> r1_valuat_1(C,k15_cqc_lang(B,A),D,F) ) ) ) ) ) ) ) ) ) ),
    file(sublemma,t68_sublemma),
    []).

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),
    []).