% Mizar problem: t13_hilbert1,hilbert1,424,40 
fof(t13_hilbert1,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ( v6_hilbert1(A)
       => r1_tarski(k6_hilbert1,A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_fraenkel,cc1_hilbert1,cc3_hilbert1,d12_hilbert1,dt_k1_hilbert1,dt_k1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_hilbert1,dt_k6_hilbert1,dt_m1_subset_1,existence_m1_subset_1,fc1_hilbert1,fc2_finseq_1,fc2_hilbert1,fc3_hilbert1,rc1_finseq_1,rc1_fraenkel,rc1_hilbert1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,t10_hilbert1,t12_hilbert1,t1_subset,t2_subset,t2_xboole_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(hilbert1,t13_hilbert1)]).

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

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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_hilbert1,axiom,(
    ! [A] : 
      ( v5_hilbert1(A)
     => ( ~ v1_xboole_0(A)
        & v1_hilbert1(A)
        & v2_hilbert1(A)
        & v3_hilbert1(A)
        & v4_hilbert1(A) ) ) ),
    file(hilbert1,cc1_hilbert1),
    []).

fof(cc3_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_hilbert1)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A) ) ) ),
    file(hilbert1,cc3_hilbert1),
    []).

fof(d12_hilbert1,axiom,(
    k6_hilbert1 = k5_hilbert1(k1_subset_1(k1_hilbert1)) ),
    file(hilbert1,d12_hilbert1),
    []).

fof(dt_k1_hilbert1,axiom,(
    $true ),
    file(hilbert1,k1_hilbert1),
    []).

fof(dt_k1_subset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k1_subset_1(A))
      & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) ) ),
    file(subset_1,k1_subset_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_k5_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => m1_subset_1(k5_hilbert1(A),k1_zfmisc_1(k1_hilbert1)) ) ),
    file(hilbert1,k5_hilbert1),
    []).

fof(dt_k6_hilbert1,axiom,(
    m1_subset_1(k6_hilbert1,k1_zfmisc_1(k1_hilbert1)) ),
    file(hilbert1,k6_hilbert1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc1_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) ),
    file(hilbert1,fc1_hilbert1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_fraenkel(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) ),
    file(hilbert1,fc2_hilbert1),
    []).

fof(fc3_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => v6_hilbert1(k5_hilbert1(A)) ) ),
    file(hilbert1,fc3_hilbert1),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_hilbert1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_hilbert1(A)
      & v2_hilbert1(A)
      & v3_hilbert1(A)
      & v4_hilbert1(A)
      & v5_hilbert1(A) ) ),
    file(hilbert1,rc1_hilbert1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t10_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1))
         => ( r1_tarski(A,B)
           => r1_tarski(k5_hilbert1(A),k5_hilbert1(B)) ) ) ) ),
    file(hilbert1,t10_hilbert1),
    []).

fof(t12_hilbert1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ( v6_hilbert1(A)
      <=> k5_hilbert1(A) = A ) ) ),
    file(hilbert1,t12_hilbert1),
    []).

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(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).

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),
    []).