% Mizar problem: t63_cqc_the3,cqc_the3,992,60 
fof(t63_cqc_the3,conjecture,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => r1_tarski(k24_qc_lang1(B),k24_qc_lang1(k17_cqc_lang(B,A))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,commutativity_k2_xboole_0,commutativity_k4_subset_1,dt_k11_qc_lang1,dt_k12_qc_lang1,dt_k13_qc_lang1,dt_k14_qc_lang1,dt_k17_cqc_lang,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_qc_lang1,dt_k23_qc_lang1,dt_k24_qc_lang1,dt_k2_qc_lang1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k3_qc_lang3,dt_k4_cqc_lang,dt_k4_qc_lang1,dt_k4_subset_1,dt_k4_xboole_0,dt_k5_cqc_lang,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k6_cqc_lang,dt_k6_subset_1,dt_k7_cqc_lang,dt_k7_qc_lang1,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,fc10_membered,fc11_membered,fc1_cqc_lang,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_cqc_lang,fc2_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,fc5_membered,fc6_membered,fc7_membered,fc8_membered,fc9_membered,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_arytm_3,rc1_membered,redefinition_k23_qc_lang1,redefinition_k4_subset_1,redefinition_k5_cqc_lang,redefinition_k5_numbers,redefinition_k6_cqc_lang,redefinition_k6_subset_1,redefinition_k9_cqc_lang,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_qc_lang1__e6_70__cqc_the3,spc0_boole,t11_qc_lang3,t13_xboole_1,t14_qc_lang3,t16_qc_lang3,t1_boole,t1_numerals,t1_subset,t28_cqc_lang,t2_subset,t30_cqc_lang,t32_cqc_lang,t33_xboole_1,t34_cqc_lang,t37_cqc_lang,t38_cqc_lang,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t61_cqc_the3,t6_boole,t7_boole,t8_boole,t9_qc_lang3]),
    [file(cqc_the3,t63_cqc_the3)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

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

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

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

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

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

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(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_k17_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1) ) ),
    file(cqc_lang,k17_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_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_qc_lang1,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k1_qc_lang1)
     => m1_subset_1(k22_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(qc_lang1,k22_qc_lang1),
    []).

fof(dt_k23_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_qc_lang1)
     => m1_subset_1(k23_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)) ) ),
    file(qc_lang1,k23_qc_lang1),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    []).

fof(dt_k3_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k3_qc_lang3(A),k1_qc_lang1,k4_qc_lang1) ) ),
    file(qc_lang3,k3_qc_lang3),
    []).

fof(dt_k4_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k1_qc_lang1)
        & v1_funct_1(B)
        & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
     => m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1) ) ),
    file(cqc_lang,k4_cqc_lang),
    []).

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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_cqc_lang,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_qc_lang1(B,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
     => m1_qc_lang1(k5_cqc_lang(A,B,C),A) ) ),
    file(cqc_lang,k5_cqc_lang),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_qc_lang1,axiom,(
    $true ),
    file(qc_lang1,k5_qc_lang1),
    []).

fof(dt_k6_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k4_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => ( v1_funct_1(k6_cqc_lang(A,B))
        & m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) ) ) ),
    file(cqc_lang,k6_cqc_lang),
    []).

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_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_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(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc1_cqc_lang,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    []).

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

fof(fc2_cqc_lang,axiom,(
    ~ v1_xboole_0(k7_cqc_lang) ),
    file(cqc_lang,fc2_cqc_lang),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc37_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    []).

fof(fc38_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    []).

fof(fc39_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc39_membered),
    []).

fof(fc40_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc40_membered),
    []).

fof(fc41_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B))
        & v5_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc41_membered),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(redefinition_k23_qc_lang1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_qc_lang1)
     => k23_qc_lang1(A) = k1_tarski(A) ) ),
    file(qc_lang1,k23_qc_lang1),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k5_cqc_lang,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_qc_lang1(B,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
     => k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C) ) ),
    file(cqc_lang,k5_cqc_lang),
    []).

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

fof(redefinition_k6_cqc_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k4_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => k6_cqc_lang(A,B) = k3_cqc_lang(A,B) ) ),
    file(cqc_lang,k6_cqc_lang),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_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_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_qc_lang1__e6_70__cqc_the3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ( ( ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ! [C] : 
                  ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
                 => ! [D] : 
                      ( m1_qc_lang1(D,B)
                     => r1_tarski(k24_qc_lang1(k9_qc_lang1(C,D)),k24_qc_lang1(k17_cqc_lang(k9_qc_lang1(C,D),A))) ) ) )
          & r1_tarski(k24_qc_lang1(k11_qc_lang1),k24_qc_lang1(k17_cqc_lang(k11_qc_lang1,A)))
          & ! [B] : 
              ( m1_subset_1(B,k8_qc_lang1)
             => ( r1_tarski(k24_qc_lang1(B),k24_qc_lang1(k17_cqc_lang(B,A)))
               => r1_tarski(k24_qc_lang1(k12_qc_lang1(B)),k24_qc_lang1(k17_cqc_lang(k12_qc_lang1(B),A))) ) )
          & ! [B] : 
              ( m1_subset_1(B,k8_qc_lang1)
             => ! [C] : 
                  ( m1_subset_1(C,k8_qc_lang1)
                 => ( ( r1_tarski(k24_qc_lang1(B),k24_qc_lang1(k17_cqc_lang(B,A)))
                      & r1_tarski(k24_qc_lang1(C),k24_qc_lang1(k17_cqc_lang(C,A))) )
                   => r1_tarski(k24_qc_lang1(k13_qc_lang1(B,C)),k24_qc_lang1(k17_cqc_lang(k13_qc_lang1(B,C),A))) ) ) )
          & ! [B] : 
              ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
             => ! [C] : 
                  ( m1_subset_1(C,k8_qc_lang1)
                 => ( r1_tarski(k24_qc_lang1(C),k24_qc_lang1(k17_cqc_lang(C,A)))
                   => r1_tarski(k24_qc_lang1(k14_qc_lang1(B,C)),k24_qc_lang1(k17_cqc_lang(k14_qc_lang1(B,C),A))) ) ) ) )
       => ! [B] : 
            ( m1_subset_1(B,k8_qc_lang1)
           => r1_tarski(k24_qc_lang1(B),k24_qc_lang1(k17_cqc_lang(B,A))) ) ) ) ),
    file(cqc_the3,s1_qc_lang1__e6_70__cqc_the3),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(t11_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => k24_qc_lang1(k12_qc_lang1(A)) = k24_qc_lang1(A) ) ),
    file(qc_lang3,t11_qc_lang3),
    []).

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

fof(t14_qc_lang3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k13_qc_lang1(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) ),
    file(qc_lang3,t14_qc_lang3),
    []).

fof(t16_qc_lang3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k14_qc_lang1(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)) ) ) ),
    file(qc_lang3,t16_qc_lang3),
    []).

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

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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

fof(t28_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang ) ),
    file(cqc_lang,t28_cqc_lang),
    []).

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

fof(t30_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
             => ! [D] : 
                  ( m1_qc_lang1(D,A)
                 => k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(0),B))) ) ) ) ) ),
    file(cqc_lang,t30_cqc_lang),
    []).

fof(t32_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_cqc_lang(k12_qc_lang1(B),A) = k12_qc_lang1(k17_cqc_lang(B,A)) ) ) ),
    file(cqc_lang,t32_cqc_lang),
    []).

fof(t33_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    []).

fof(t34_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] : 
              ( m1_subset_1(C,k8_qc_lang1)
             => k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) ) ) ) ),
    file(cqc_lang,t34_cqc_lang),
    []).

fof(t37_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_cqc_lang(k14_qc_lang1(A,B),A) = k14_qc_lang1(A,B) ) ) ),
    file(cqc_lang,t37_cqc_lang),
    []).

fof(t38_cqc_lang,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m1_subset_1(C,k8_qc_lang1)
             => ( A != B
               => k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B)) ) ) ) ) ),
    file(cqc_lang,t38_cqc_lang),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t61_cqc_the3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_qc_lang1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
             => ! [D] : 
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => r1_tarski(k22_qc_lang1(B),k22_qc_lang1(k5_cqc_lang(A,B,k6_cqc_lang(C,D)))) ) ) ) ) ),
    file(cqc_the3,t61_cqc_the3),
    []).

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),
    []).

fof(t9_qc_lang3,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] : 
              ( m1_qc_lang1(C,A)
             => k24_qc_lang1(k9_qc_lang1(B,C)) = k22_qc_lang1(C) ) ) ) ),
    file(qc_lang3,t9_qc_lang3),
    []).