% Mizar problem: t37_sublemma,sublemma,753,64 
fof(t37_sublemma,conjecture,(
    ! [A] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] : 
          ( m1_substut1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
             => ! [D] : 
                  ( m1_substut1(D,C)
                 => ( ( v3_substut1(A)
                      & v3_substut1(C)
                      & k10_sublemma(A,B) = k24_substut1(C,D) )
                   => ( k23_substut1(A) = k23_substut1(C)
                      & B = D ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,d6_sublemma,dt_k10_sublemma,dt_k16_substut1,dt_k1_qc_lang1,dt_k1_substut1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k23_substut1,dt_k24_substut1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_zfmisc_1,dt_k38_substut1,dt_m1_subset_1,dt_m1_substut1,dt_m2_subset_1,existence_m1_subset_1,existence_m1_substut1,existence_m2_subset_1,fc12_relat_1,fc1_qc_lang1,fc1_subset_1,fc1_substut1,fc2_qc_lang1,fc2_substut1,fc4_relat_1,fc4_subset_1,fc4_substut1,fc7_substut1,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc1_sublemma,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_substut1,rc3_funct_1,rc3_relat_1,rc4_funct_1,redefinition_k23_substut1,redefinition_m2_subset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t36_sublemma,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(sublemma,t37_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(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(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_k16_substut1,axiom,(
    ~ v1_xboole_0(k16_substut1) ),
    file(substut1,k16_substut1),
    []).

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_k23_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => m2_subset_1(k23_substut1(A),k1_qc_lang1,k2_qc_lang1) ) ),
    file(substut1,k23_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_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_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_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_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_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_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_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(fc7_substut1,axiom,(
    ~ v1_xboole_0(k38_substut1) ),
    file(substut1,fc7_substut1),
    []).

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_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(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_k23_substut1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => k23_substut1(A) = k2_mcart_1(A) ) ),
    file(substut1,k23_substut1),
    []).

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

fof(t36_sublemma,axiom,(
    ! [A] : 
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] : 
          ( m1_substut1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
             => ! [D] : 
                  ( m1_substut1(D,C)
                 => ( ( v3_substut1(A)
                      & v3_substut1(C)
                      & k24_substut1(A,B) = k24_substut1(C,D) )
                   => ( k23_substut1(A) = k23_substut1(C)
                      & B = D ) ) ) ) ) ) ),
    file(sublemma,t36_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(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).