% Mizar problem: t23_substut2,substut2,600,59 
fof(t23_substut2,conjecture,(
    ! [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)
               => k6_cqc_sim1(A) = k6_cqc_sim1(k39_substut1(k2_substut2(A,C))) )
           => ! [C] : 
                ( m1_subset_1(C,k1_substut1)
               => k6_cqc_sim1(k15_cqc_lang(B,A)) = k6_cqc_sim1(k39_substut1(k2_substut2(k15_cqc_lang(B,A),C))) ) ) ) ) ),
    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,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,d28_substut1,d3_substut2,d4_substut2,d5_substut2,d5_tarski,d6_sublemma,d7_sublemma,dt_k10_sublemma,dt_k11_sublemma,dt_k12_sublemma,dt_k14_qc_lang1,dt_k15_cqc_lang,dt_k15_substut1,dt_k16_substut1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_substut1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_substut1,dt_k24_substut1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_substut2,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k31_substut1,dt_k32_substut1,dt_k35_substut1,dt_k37_substut1,dt_k38_substut1,dt_k39_substut1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k6_cqc_sim1,dt_k6_substut2,dt_k7_cqc_lang,dt_k7_relat_1,dt_k7_substut2,dt_k8_funct_2,dt_k8_qc_lang1,dt_k8_sublemma,dt_k8_substut2,dt_k9_sublemma,dt_m1_relset_1,dt_m1_subset_1,dt_m1_substut1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_substut1,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_xreal_0,fc12_relat_1,fc12_xreal_0,fc13_relat_1,fc1_int_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc1_substut1,fc2_cqc_lang,fc2_qc_lang1,fc2_subset_1,fc2_substut1,fc3_subset_1,fc3_xreal_0,fc4_funct_1,fc4_relat_1,fc4_subset_1,fc4_substut1,fc6_int_1,fc7_substut1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_relat_1,rc1_sublemma,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_k15_cqc_lang,redefinition_k1_nat_1,redefinition_k22_substut1,redefinition_k2_substut2,redefinition_k39_substut1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_k8_sublemma,redefinition_k9_sublemma,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,t18_cqc_sim1,t1_subset,t21_substut1,t22_substut2,t29_sublemma,t2_subset,t32_sublemma,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole]),
    [file(substut2,t23_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(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(d28_substut1,axiom,(
    ! [A] : 
      ( v7_substut1(A)
    <=> ? [B] : 
          ( m1_subset_1(B,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
          & ? [C] : 
              ( m1_substut1(C,B)
              & A = k24_substut1(B,C)
              & v3_substut1(B) ) ) ) ),
    file(substut1,d28_substut1),
    []).

fof(d3_substut2,axiom,(
    k6_substut2 = k7_relat_1(k15_substut1,k38_substut1) ),
    file(substut2,d3_substut2),
    []).

fof(d4_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)
             => k7_substut2(A,B,C) = k8_sublemma(k2_substut2(A,k8_funct_2(k38_substut1,k1_substut1,k6_substut2,k2_substut2(k15_cqc_lang(B,A),C))),B) ) ) ) ),
    file(substut2,d4_substut2),
    []).

fof(d5_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)
             => k8_substut2(A,B,C) = C ) ) ) ),
    file(substut2,d5_substut2),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_sublemma,axiom,(
    ! [A] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] : 
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => k10_sublemma(A,B) = k24_substut1(A,B) ) ) ) ),
    file(sublemma,d6_sublemma),
    []).

fof(d7_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v7_substut1(A)
       => k11_sublemma(A) = k31_substut1(A) ) ) ),
    file(sublemma,d7_sublemma),
    []).

fof(dt_k10_sublemma,axiom,(
    ! [A,B] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
        & m1_substut1(B,A) )
     => m2_subset_1(k10_sublemma(A,B),k16_substut1,k38_substut1) ) ),
    file(sublemma,k10_sublemma),
    []).

fof(dt_k11_sublemma,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k11_sublemma(A),k16_substut1,k38_substut1) ) ),
    file(sublemma,k11_sublemma),
    []).

fof(dt_k12_sublemma,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k12_sublemma(A,B),k8_qc_lang1,k7_cqc_lang) ) ),
    file(sublemma,k12_sublemma),
    []).

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_k15_substut1,axiom,
    ( v1_relat_1(k15_substut1)
    & v1_funct_1(k15_substut1) ),
    file(substut1,k15_substut1),
    []).

fof(dt_k16_substut1,axiom,(
    ~ v1_xboole_0(k16_substut1) ),
    file(substut1,k16_substut1),
    []).

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

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k22_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => m1_subset_1(k22_substut1(A),k16_substut1) ) ),
    file(substut1,k22_substut1),
    []).

fof(dt_k24_substut1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
        & m1_substut1(B,A) )
     => m1_subset_1(k24_substut1(A,B),k16_substut1) ) ),
    file(substut1,k24_substut1),
    []).

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_substut2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k1_substut1) )
     => m2_subset_1(k2_substut2(A,B),k16_substut1,k38_substut1) ) ),
    file(substut2,k2_substut2),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k31_substut1,axiom,(
    ! [A] : m1_subset_1(k31_substut1(A),k16_substut1) ),
    file(substut1,k31_substut1),
    []).

fof(dt_k32_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k16_substut1)
     => m1_subset_1(k32_substut1(A),k2_zfmisc_1(k8_qc_lang1,k1_substut1)) ) ),
    file(substut1,k32_substut1),
    []).

fof(dt_k35_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k8_qc_lang1,k1_substut1))
     => m2_subset_1(k35_substut1(A),k1_qc_lang1,k2_qc_lang1) ) ),
    file(substut1,k35_substut1),
    []).

fof(dt_k37_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k16_substut1)
     => m1_subset_1(k37_substut1(A),k8_qc_lang1) ) ),
    file(substut1,k37_substut1),
    []).

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

fof(dt_k39_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k39_substut1(A),k8_qc_lang1,k7_cqc_lang) ) ),
    file(substut1,k39_substut1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_k6_cqc_sim1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k6_cqc_sim1(A),k1_numbers,k5_numbers) ) ),
    file(cqc_sim1,k6_cqc_sim1),
    []).

fof(dt_k6_substut2,axiom,
    ( v1_funct_1(k6_substut2)
    & v1_funct_2(k6_substut2,k38_substut1,k1_substut1)
    & m2_relset_1(k6_substut2,k38_substut1,k1_substut1) ),
    file(substut2,k6_substut2),
    []).

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_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_k7_substut2,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k1_substut1) )
     => ( v1_sublemma(k7_substut2(A,B,C))
        & m1_subset_1(k7_substut2(A,B,C),k2_zfmisc_1(k16_substut1,k2_qc_lang1)) ) ) ),
    file(substut2,k7_substut2),
    []).

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

fof(dt_k8_sublemma,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k2_qc_lang1) )
     => ( v1_sublemma(k8_sublemma(A,B))
        & m1_subset_1(k8_sublemma(A,B),k2_zfmisc_1(k16_substut1,k2_qc_lang1)) ) ) ),
    file(sublemma,k8_sublemma),
    []).

fof(dt_k8_substut2,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k1_substut1) )
     => m1_substut1(k8_substut2(A,B,C),k7_substut2(A,B,C)) ) ),
    file(substut2,k8_substut2),
    []).

fof(dt_k9_sublemma,axiom,(
    ! [A] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => m2_subset_1(k9_sublemma(A),k16_substut1,k38_substut1) ) ),
    file(sublemma,k9_sublemma),
    []).

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_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => ! [B] : 
          ( m1_substut1(B,A)
         => m1_subset_1(B,k1_substut1) ) ) ),
    file(substut1,m1_substut1),
    []).

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_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_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => ? [B] : m1_substut1(B,A) ) ),
    file(substut1,m1_substut1),
    []).

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(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

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(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

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_int_1,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

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

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

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_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(fc6_int_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    []).

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

fof(fc7_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

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_sublemma,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
      & v1_sublemma(A) ) ),
    file(sublemma,rc1_sublemma),
    []).

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_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_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k22_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => k22_substut1(A) = k1_mcart_1(A) ) ),
    file(substut1,k22_substut1),
    []).

fof(redefinition_k2_substut2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k1_substut1) )
     => k2_substut2(A,B) = k4_tarski(A,B) ) ),
    file(substut2,k2_substut2),
    []).

fof(redefinition_k39_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k38_substut1)
     => k39_substut1(A) = k37_substut1(A) ) ),
    file(substut1,k39_substut1),
    []).

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

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_sublemma,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k2_qc_lang1) )
     => k8_sublemma(A,B) = k4_tarski(A,B) ) ),
    file(sublemma,k8_sublemma),
    []).

fof(redefinition_k9_sublemma,axiom,(
    ! [A] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => k9_sublemma(A) = k1_mcart_1(A) ) ),
    file(sublemma,k9_sublemma),
    []).

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(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(t18_cqc_sim1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => k6_cqc_sim1(k15_cqc_lang(B,A)) = k1_nat_1(k6_cqc_sim1(A),1) ) ) ),
    file(cqc_sim1,t18_cqc_sim1),
    []).

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

fof(t21_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => ! [B] : 
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => k31_substut1(k24_substut1(A,B)) = k22_substut1(A) ) ) ) ),
    file(substut1,t21_substut1),
    []).

fof(t22_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)
             => ( k2_substut2(k15_cqc_lang(B,A),C) = k10_sublemma(k7_substut2(A,B,C),k8_substut2(A,B,C))
                & v3_substut1(k7_substut2(A,B,C)) ) ) ) ) ),
    file(substut2,t22_substut2),
    []).

fof(t29_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v7_substut1(A)
       => k39_substut1(A) = k12_sublemma(A,k39_substut1(k11_sublemma(A))) ) ) ),
    file(sublemma,t29_sublemma),
    []).

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

fof(t32_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] : 
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => k12_sublemma(k10_sublemma(k8_sublemma(B,A),C),k39_substut1(B)) = k15_cqc_lang(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k39_substut1(B)) ) ) ) ) ),
    file(sublemma,t32_sublemma),
    []).

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(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(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).