% Mizar problem: t25_sublemma,sublemma,500,47 
fof(t25_sublemma,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] : 
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ( k19_substut1(D) = k19_substut1(E)
                       => ( ( r1_sublemma(D,A,k1_sublemma(A,C,k3_sublemma(D,A,C)),B)
                            & r1_sublemma(E,A,k1_sublemma(A,C,k3_sublemma(E,A,C)),B) )
                        <=> r1_sublemma(k7_sublemma(D,E),A,k1_sublemma(A,C,k3_sublemma(k7_sublemma(D,E),A,C)),B) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,d1_sublemma,d2_sublemma,d3_sublemma,d4_cqc_lang,dt_k11_cqc_lang,dt_k13_qc_lang1,dt_k16_substut1,dt_k19_substut1,dt_k1_funct_4,dt_k1_mcart_1,dt_k1_qc_lang1,dt_k1_sublemma,dt_k1_substut1,dt_k1_valuat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_sublemma,dt_k2_substut1,dt_k2_valuat_1,dt_k2_zfmisc_1,dt_k38_substut1,dt_k3_margrel1,dt_k3_qc_lang1,dt_k3_sublemma,dt_k4_qc_lang1,dt_k5_qc_lang1,dt_k5_qc_lang3,dt_k5_relat_1,dt_k6_qc_lang3,dt_k7_cqc_lang,dt_k7_relset_1,dt_k7_sublemma,dt_k8_qc_lang1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_valuat_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_valuat_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc10_relat_1,fc12_relat_1,fc1_funct_1,fc1_qc_lang1,fc1_subset_1,fc1_substut1,fc2_cqc_lang,fc2_qc_lang1,fc2_substut1,fc3_qc_lang1,fc4_qc_lang1,fc4_relat_1,fc4_subset_1,fc4_substut1,fc5_qc_lang1,fc7_substut1,fc9_relat_1,fraenkel_a_0_0_cqc_lang,idempotence_k1_funct_4,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_substut1,rc3_funct_1,rc3_relat_1,rc4_funct_1,redefinition_k11_cqc_lang,redefinition_k19_substut1,redefinition_k2_sublemma,redefinition_k2_valuat_1,redefinition_k7_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t1_subset,t21_sublemma,t23_sublemma,t29_valuat_1,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(sublemma,t25_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_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(d1_sublemma,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_qc_lang1,A) )
             => k1_sublemma(A,B,C) = k1_funct_4(B,C) ) ) ) ),
    file(sublemma,d1_sublemma),
    []).

fof(d2_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => k3_sublemma(A,B,C) = k7_relset_1(k2_qc_lang1,k2_qc_lang1,k2_qc_lang1,B,k2_substut1(k19_substut1(A)),C) ) ) ) ),
    file(sublemma,d2_sublemma),
    []).

fof(d3_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] : 
                  ( m1_valuat_1(D,B)
                 => ( r1_sublemma(A,B,C,D)
                  <=> r1_valuat_1(B,k2_sublemma(A),D,C) ) ) ) ) ) ),
    file(sublemma,d3_sublemma),
    []).

fof(d4_cqc_lang,axiom,(
    k7_cqc_lang = a_0_0_cqc_lang ),
    file(cqc_lang,d4_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_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_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_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

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

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

fof(dt_k1_sublemma,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_valuat_1(A))
        & v1_funct_1(C)
        & m1_relset_1(C,k2_qc_lang1,A) )
     => m2_fraenkel(k1_sublemma(A,B,C),k2_qc_lang1,A,k2_valuat_1(A)) ) ),
    file(sublemma,k1_sublemma),
    []).

fof(dt_k1_substut1,axiom,(
    $true ),
    file(substut1,k1_substut1),
    []).

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

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

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

fof(dt_k2_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_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_substut1)
     => ( v1_funct_1(k2_substut1(A))
        & m2_relset_1(k2_substut1(A),k2_qc_lang1,k2_qc_lang1) ) ) ),
    file(substut1,k2_substut1),
    []).

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_k38_substut1,axiom,(
    m1_subset_1(k38_substut1,k1_zfmisc_1(k16_substut1)) ),
    file(substut1,k38_substut1),
    []).

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_k3_sublemma,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k38_substut1)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_valuat_1(B)) )
     => ( v1_funct_1(k3_sublemma(A,B,C))
        & m2_relset_1(k3_sublemma(A,B,C),k2_qc_lang1,B) ) ) ),
    file(sublemma,k3_sublemma),
    []).

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_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_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k6_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_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ),
    file(relset_1,k7_relset_1),
    []).

fof(dt_k7_sublemma,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k38_substut1) )
     => m2_subset_1(k7_sublemma(A,B),k16_substut1,k38_substut1) ) ),
    file(sublemma,k7_sublemma),
    []).

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

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

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_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(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_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(fc3_qc_lang1,axiom,(
    ~ v1_xboole_0(k3_qc_lang1) ),
    file(qc_lang1,fc3_qc_lang1),
    []).

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

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

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(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

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_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_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(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(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_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_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_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_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(relset_1,k7_relset_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(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t21_sublemma,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] : 
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( k19_substut1(A) = k19_substut1(B)
           => ( k2_sublemma(k7_sublemma(A,B)) = k11_cqc_lang(k2_sublemma(A),k2_sublemma(B))
              & k19_substut1(k7_sublemma(A,B)) = k19_substut1(A) ) ) ) ) ),
    file(sublemma,t21_sublemma),
    []).

fof(t23_sublemma,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ! [D] : 
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( k19_substut1(C) = k19_substut1(D)
                   => ( k3_sublemma(C,A,B) = k3_sublemma(k7_sublemma(C,D),A,B)
                      & k3_sublemma(D,A,B) = k3_sublemma(k7_sublemma(C,D),A,B) ) ) ) ) ) ) ),
    file(sublemma,t23_sublemma),
    []).

fof(t29_valuat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k11_cqc_lang(C,D),E,B)
                      <=> ( r1_valuat_1(A,C,E,B)
                          & r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ) ),
    file(valuat_1,t29_valuat_1),
    []).

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

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

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

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