% Mizar problem: t12_substut2,substut2,279,40 
fof(t12_substut2,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m1_subset_1(B,k1_substut1)
         => ? [C] : 
              ( m2_subset_1(C,k16_substut1,k38_substut1)
              & k2_sublemma(C) = A
              & k19_substut1(C) = B ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_int_1,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,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_k16_substut1,dt_k19_substut1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_substut1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_sublemma,dt_k2_zfmisc_1,dt_k38_substut1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k7_cqc_lang,dt_k7_qc_lang1,dt_k8_cqc_lang,dt_k8_qc_lang1,dt_k9_cqc_lang,dt_k9_qc_lang1,dt_m1_finseq_1,dt_m1_qc_lang1,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_qc_lang1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc12_relat_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc1_substut1,fc2_cqc_lang,fc2_qc_lang1,fc2_substut1,fc4_relat_1,fc4_subset_1,fc4_substut1,fc5_qc_lang1,fc6_qc_lang1,fc7_substut1,rc1_cqc_lang,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_subset_1,rc2_substut1,rc2_xreal_0,rc3_funct_1,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,redefinition_k10_cqc_lang,redefinition_k11_cqc_lang,redefinition_k15_cqc_lang,redefinition_k19_substut1,redefinition_k2_sublemma,redefinition_k5_numbers,redefinition_k8_cqc_lang,redefinition_k9_cqc_lang,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_cqc_lang__e2_13__substut2,t11_substut2,t1_subset,t1_substut2,t2_subset,t2_substut2,t3_subset,t4_subset,t4_substut2,t5_subset,t5_substut2,t6_boole,t7_boole,t8_boole]),
    [file(substut2,t12_substut2)]).

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

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_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_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(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_k16_substut1,axiom,(
    ~ v1_xboole_0(k16_substut1) ),
    file(substut1,k16_substut1),
    []).

fof(dt_k19_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k16_substut1)
     => m1_subset_1(k19_substut1(A),k1_substut1) ) ),
    file(substut1,k19_substut1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

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_substut1,axiom,(
    $true ),
    file(substut1,k1_substut1),
    []).

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_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

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_sublemma,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k2_sublemma(A),k8_qc_lang1,k7_cqc_lang) ) ),
    file(sublemma,k2_sublemma),
    []).

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

fof(dt_k38_substut1,axiom,(
    m1_subset_1(k38_substut1,k1_zfmisc_1(k16_substut1)) ),
    file(substut1,k38_substut1),
    []).

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

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_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_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_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_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_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(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(fc1_substut1,axiom,(
    ~ v1_xboole_0(k1_substut1) ),
    file(substut1,fc1_substut1),
    []).

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(fc2_substut1,axiom,
    ( ~ v1_xboole_0(k1_substut1)
    & v1_fraenkel(k1_substut1) ),
    file(substut1,fc2_substut1),
    []).

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(fc4_substut1,axiom,
    ( ~ v1_xboole_0(k16_substut1)
    & v1_substut1(k16_substut1) ),
    file(substut1,fc4_substut1),
    []).

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(fc7_substut1,axiom,(
    ~ v1_xboole_0(k38_substut1) ),
    file(substut1,fc7_substut1),
    []).

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

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_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(rc2_substut1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_substut1(A) ) ),
    file(substut1,rc2_substut1),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_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_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(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_k19_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k16_substut1)
     => k19_substut1(A) = k2_mcart_1(A) ) ),
    file(substut1,k19_substut1),
    []).

fof(redefinition_k2_sublemma,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k38_substut1)
     => k2_sublemma(A) = k1_mcart_1(A) ) ),
    file(sublemma,k2_sublemma),
    []).

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_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_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_13__substut2,axiom,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ! [C] : 
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( ( v1_cqc_lang(E,D)
                          & m1_qc_lang1(E,D) )
                       => ! [F] : 
                            ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                           => ( ! [G] : 
                                  ( m1_subset_1(G,k1_substut1)
                                 => ? [H] : 
                                      ( m2_subset_1(H,k16_substut1,k38_substut1)
                                      & k2_sublemma(H) = k9_cqc_lang
                                      & k19_substut1(H) = G ) )
                              & ! [I] : 
                                  ( m1_subset_1(I,k1_substut1)
                                 => ? [J] : 
                                      ( m2_subset_1(J,k16_substut1,k38_substut1)
                                      & k2_sublemma(J) = k8_cqc_lang(D,F,E)
                                      & k19_substut1(J) = I ) )
                              & ( ! [K] : 
                                    ( m1_subset_1(K,k1_substut1)
                                   => ? [L] : 
                                        ( m2_subset_1(L,k16_substut1,k38_substut1)
                                        & k2_sublemma(L) = A
                                        & k19_substut1(L) = K ) )
                               => ! [M] : 
                                    ( m1_subset_1(M,k1_substut1)
                                   => ? [N] : 
                                        ( m2_subset_1(N,k16_substut1,k38_substut1)
                                        & k2_sublemma(N) = k10_cqc_lang(A)
                                        & k19_substut1(N) = M ) ) )
                              & ( ( ! [O] : 
                                      ( m1_subset_1(O,k1_substut1)
                                     => ? [P] : 
                                          ( m2_subset_1(P,k16_substut1,k38_substut1)
                                          & k2_sublemma(P) = A
                                          & k19_substut1(P) = O ) )
                                  & ! [Q] : 
                                      ( m1_subset_1(Q,k1_substut1)
                                     => ? [R] : 
                                          ( m2_subset_1(R,k16_substut1,k38_substut1)
                                          & k2_sublemma(R) = B
                                          & k19_substut1(R) = Q ) ) )
                               => ! [S] : 
                                    ( m1_subset_1(S,k1_substut1)
                                   => ? [T] : 
                                        ( m2_subset_1(T,k16_substut1,k38_substut1)
                                        & k2_sublemma(T) = k11_cqc_lang(A,B)
                                        & k19_substut1(T) = S ) ) )
                              & ( ! [U] : 
                                    ( m1_subset_1(U,k1_substut1)
                                   => ? [V] : 
                                        ( m2_subset_1(V,k16_substut1,k38_substut1)
                                        & k2_sublemma(V) = A
                                        & k19_substut1(V) = U ) )
                               => ! [W] : 
                                    ( m1_subset_1(W,k1_substut1)
                                   => ? [X] : 
                                        ( m2_subset_1(X,k16_substut1,k38_substut1)
                                        & k2_sublemma(X) = k15_cqc_lang(C,A)
                                        & k19_substut1(X) = W ) ) ) ) ) ) ) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [Y] : 
            ( m1_subset_1(Y,k1_substut1)
           => ? [Z] : 
                ( m2_subset_1(Z,k16_substut1,k38_substut1)
                & k2_sublemma(Z) = A
                & k19_substut1(Z) = Y ) ) ) ),
    file(substut2,s1_cqc_lang__e2_13__substut2),
    []).

fof(t11_substut2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( ! [C] : 
                ( m1_subset_1(C,k1_substut1)
               => ? [D] : 
                    ( m2_subset_1(D,k16_substut1,k38_substut1)
                    & k2_sublemma(D) = A
                    & k19_substut1(D) = C ) )
           => ! [C] : 
                ( m1_subset_1(C,k1_substut1)
               => ? [D] : 
                    ( m2_subset_1(D,k16_substut1,k38_substut1)
                    & k2_sublemma(D) = k15_cqc_lang(B,A)
                    & k19_substut1(D) = C ) ) ) ) ) ),
    file(substut2,t11_substut2),
    []).

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

fof(t1_substut2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_substut1)
     => ? [B] : 
          ( m2_subset_1(B,k16_substut1,k38_substut1)
          & k2_sublemma(B) = k9_cqc_lang
          & k19_substut1(B) = A ) ) ),
    file(substut2,t1_substut2),
    []).

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_substut2,axiom,(
    ! [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] : 
                  ( m1_subset_1(D,k1_substut1)
                 => ? [E] : 
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                      & k2_sublemma(E) = k8_cqc_lang(A,B,C)
                      & k19_substut1(E) = D ) ) ) ) ) ),
    file(substut2,t2_substut2),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t4_substut2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( ! [B] : 
            ( m1_subset_1(B,k1_substut1)
           => ? [C] : 
                ( m2_subset_1(C,k16_substut1,k38_substut1)
                & k2_sublemma(C) = A
                & k19_substut1(C) = B ) )
       => ! [B] : 
            ( m1_subset_1(B,k1_substut1)
           => ? [C] : 
                ( m2_subset_1(C,k16_substut1,k38_substut1)
                & k2_sublemma(C) = k10_cqc_lang(A)
                & k19_substut1(C) = B ) ) ) ) ),
    file(substut2,t4_substut2),
    []).

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(t5_substut2,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( ! [C] : 
                  ( m1_subset_1(C,k1_substut1)
                 => ? [D] : 
                      ( m2_subset_1(D,k16_substut1,k38_substut1)
                      & k2_sublemma(D) = A
                      & k19_substut1(D) = C ) )
              & ! [C] : 
                  ( m1_subset_1(C,k1_substut1)
                 => ? [D] : 
                      ( m2_subset_1(D,k16_substut1,k38_substut1)
                      & k2_sublemma(D) = B
                      & k19_substut1(D) = C ) ) )
           => ! [C] : 
                ( m1_subset_1(C,k1_substut1)
               => ? [D] : 
                    ( m2_subset_1(D,k16_substut1,k38_substut1)
                    & k2_sublemma(D) = k11_cqc_lang(A,B)
                    & k19_substut1(D) = C ) ) ) ) ) ),
    file(substut2,t5_substut2),
    []).

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),
    []).