% Mizar ND problem: t3_partit1,partit1,51,29 
fof(dh_c1_3__partit1,definition,
    ( k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) = k3_tarski(c1_3__partit1)
   => ! [A] : k3_tarski(k4_xboole_0(A,k1_tarski(k1_xboole_0))) = k3_tarski(A) ),
    introduced(definition,[new_symbol(c1_3__partit1),file(partit1,c1_3__partit1)]),
    [interesting(0.8),axiom,file(partit1,c1_3__partit1)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(fc10_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc37_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    [interesting(0.9),axiom,file(membered,fc37_membered)]).

fof(fc38_membered,theorem,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    [interesting(0.9),axiom,file(membered,fc38_membered)]).

fof(fc39_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,fc39_membered)]).

fof(fc40_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,fc40_membered)]).

fof(fc41_membered,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(membered,fc41_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(dt_c1_3__partit1,assumption,(
    $true ),
    introduced(assumption,[file(partit1,c1_3__partit1)]),
    [interesting(0.8),axiom,file(partit1,c1_3__partit1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc6_membered,theorem,
    ( 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),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(dt_c1_3_2__partit1,assumption,(
    $true ),
    introduced(assumption,[file(partit1,c1_3_2__partit1)]),
    [interesting(0.65),axiom,file(partit1,c1_3_2__partit1)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_3_2__partit1,definition,
    ( ~ ( r2_hidden(c1_3_2__partit1,k3_tarski(c1_3__partit1))
        & ~ r2_hidden(c1_3_2__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k3_tarski(c1_3__partit1))
          & ~ r2_hidden(A,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ) ),
    introduced(definition,[new_symbol(c1_3_2__partit1),file(partit1,c1_3_2__partit1)]),
    [interesting(0.65),axiom,file(partit1,c1_3_2__partit1)]).

fof(e1_3_2__partit1,assumption,(
    r2_hidden(c1_3_2__partit1,k3_tarski(c1_3__partit1)) ),
    introduced(assumption,[file(partit1,e1_3_2__partit1)]),
    [interesting(0.65),axiom,file(partit1,e1_3_2__partit1)]).

fof(dh_c2_3_2__partit1,definition,
    ( ? [A] : 
        ( r2_hidden(c1_3_2__partit1,A)
        & r2_hidden(A,c1_3__partit1) )
   => ( r2_hidden(c1_3_2__partit1,c2_3_2__partit1)
      & r2_hidden(c2_3_2__partit1,c1_3__partit1) ) ),
    introduced(definition,[new_symbol(c2_3_2__partit1),file(partit1,c2_3_2__partit1)]),
    [interesting(0.65),axiom,file(partit1,c2_3_2__partit1)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e2_3_2__partit1,plain,(
    ? [A] : 
      ( r2_hidden(c1_3_2__partit1,A)
      & r2_hidden(A,c1_3__partit1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_c1_3__partit1,dt_c1_3_2__partit1,t1_subset,t7_boole,e1_3_2__partit1,d4_tarski]),
    [interesting(0.65),file(partit1,e2_3_2__partit1),[file(partit1,e2_3_2__partit1)]]).

fof(dt_c2_3_2__partit1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[dh_c2_3_2__partit1,e2_3_2__partit1]),
    [interesting(0.65),file(partit1,c2_3_2__partit1),[file(partit1,c2_3_2__partit1)]]).

fof(e3_3_2__partit1,plain,
    ( r2_hidden(c1_3_2__partit1,c2_3_2__partit1)
    & r2_hidden(c2_3_2__partit1,c1_3__partit1) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[dh_c2_3_2__partit1,e2_3_2__partit1]),
    [interesting(0.65),file(partit1,e3_3_2__partit1),[file(partit1,e3_3_2__partit1)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e4_3_2__partit1,plain,(
    ~ r2_hidden(c2_3_2__partit1,k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3__partit1,dt_c1_3_2__partit1,dt_c2_3_2__partit1,fc2_subset_1,fc6_membered,t1_subset,t6_boole,t7_boole,e3_3_2__partit1,d1_tarski]),
    [interesting(0.65),file(partit1,e4_3_2__partit1),[file(partit1,e4_3_2__partit1)]]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]).

fof(e5_3_2__partit1,plain,(
    r2_hidden(c2_3_2__partit1,k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k4_xboole_0,dt_c1_3__partit1,dt_c1_3_2__partit1,dt_c2_3_2__partit1,fc2_subset_1,fc6_membered,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e4_3_2__partit1,e3_3_2__partit1,d4_xboole_0]),
    [interesting(0.65),file(partit1,e5_3_2__partit1),[file(partit1,e5_3_2__partit1)]]).

fof(e6_3_2__partit1,plain,(
    r2_hidden(c1_3_2__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,dt_c1_3_2__partit1,dt_c2_3_2__partit1,fc2_subset_1,fc6_membered,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e5_3_2__partit1,e3_3_2__partit1,d4_tarski]),
    [interesting(0.65),file(partit1,e6_3_2__partit1),[file(partit1,e6_3_2__partit1)]]).

fof(i3_3_2__partit1,theorem,(
    $true ),
    introduced(tautology,[file(partit1,i3_3_2__partit1)]),
    [interesting(0.65),trivial,file(partit1,i3_3_2__partit1)]).

fof(i2_3_2__partit1,plain,(
    r2_hidden(c1_3_2__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1,e1_3_2__partit1])],[e6_3_2__partit1,i3_3_2__partit1]),
    [interesting(0.65),file(partit1,i2_3_2__partit1),[file(partit1,i2_3_2__partit1)]]).

fof(i1_3_2__partit1,plain,(
    ~ ( r2_hidden(c1_3_2__partit1,k3_tarski(c1_3__partit1))
      & ~ r2_hidden(c1_3_2__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_2__partit1]),discharge_asm(discharge,[e1_3_2__partit1])],[e1_3_2__partit1,i2_3_2__partit1]),
    [interesting(0.65),file(partit1,i1_3_2__partit1),[file(partit1,i1_3_2__partit1)]]).

fof(i1_3_2_tmp__partit1,plain,(
    ~ ( r2_hidden(c1_3_2__partit1,k3_tarski(c1_3__partit1))
      & ~ r2_hidden(c1_3_2__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__partit1]),discharge_asm(discharge,[dt_c1_3_2__partit1])],[dt_c1_3_2__partit1,i1_3_2__partit1]),
    [interesting(0.8),e2_3__partit1]).

fof(e2_3__partit1,plain,(
    r1_tarski(k3_tarski(c1_3__partit1),k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ),
    inference(let,[status(thm),assumptions([dt_c1_3__partit1])],[i1_3_2_tmp__partit1,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,fc2_subset_1,fc6_membered,d3_tarski,dh_c1_3_2__partit1]),
    [interesting(0.8),file(partit1,e2_3__partit1),[file(partit1,e2_3__partit1)]]).

fof(dt_c1_3_1__partit1,assumption,(
    $true ),
    introduced(assumption,[file(partit1,c1_3_1__partit1)]),
    [interesting(0.65),axiom,file(partit1,c1_3_1__partit1)]).

fof(dh_c1_3_1__partit1,definition,
    ( ~ ( r2_hidden(c1_3_1__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))))
        & ~ r2_hidden(c1_3_1__partit1,k3_tarski(c1_3__partit1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))))
          & ~ r2_hidden(A,k3_tarski(c1_3__partit1)) ) ),
    introduced(definition,[new_symbol(c1_3_1__partit1),file(partit1,c1_3_1__partit1)]),
    [interesting(0.65),axiom,file(partit1,c1_3_1__partit1)]).

fof(e1_3_1__partit1,assumption,(
    r2_hidden(c1_3_1__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0)))) ),
    introduced(assumption,[file(partit1,e1_3_1__partit1)]),
    [interesting(0.65),axiom,file(partit1,e1_3_1__partit1)]).

fof(dh_c2_3_1__partit1,definition,
    ( ? [A] : 
        ( r2_hidden(c1_3_1__partit1,A)
        & r2_hidden(A,k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) )
   => ( r2_hidden(c1_3_1__partit1,c2_3_1__partit1)
      & r2_hidden(c2_3_1__partit1,k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) ) ),
    introduced(definition,[new_symbol(c2_3_1__partit1),file(partit1,c2_3_1__partit1)]),
    [interesting(0.65),axiom,file(partit1,c2_3_1__partit1)]).

fof(e2_3_1__partit1,plain,(
    ? [A] : 
      ( r2_hidden(c1_3_1__partit1,A)
      & r2_hidden(A,k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,dt_c1_3_1__partit1,fc2_subset_1,fc6_membered,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e1_3_1__partit1,d4_tarski]),
    [interesting(0.65),file(partit1,e2_3_1__partit1),[file(partit1,e2_3_1__partit1)]]).

fof(dt_c2_3_1__partit1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[dh_c2_3_1__partit1,e2_3_1__partit1]),
    [interesting(0.65),file(partit1,c2_3_1__partit1),[file(partit1,c2_3_1__partit1)]]).

fof(e3_3_1__partit1,plain,
    ( r2_hidden(c1_3_1__partit1,c2_3_1__partit1)
    & r2_hidden(c2_3_1__partit1,k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[dh_c2_3_1__partit1,e2_3_1__partit1]),
    [interesting(0.65),file(partit1,e3_3_1__partit1),[file(partit1,e3_3_1__partit1)]]).

fof(e4_3_1__partit1,plain,
    ( r2_hidden(c2_3_1__partit1,c1_3__partit1)
    & ~ r2_hidden(c2_3_1__partit1,k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k4_xboole_0,dt_c1_3__partit1,dt_c1_3_1__partit1,dt_c2_3_1__partit1,fc2_subset_1,fc6_membered,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e3_3_1__partit1,d4_xboole_0]),
    [interesting(0.65),file(partit1,e4_3_1__partit1),[file(partit1,e4_3_1__partit1)]]).

fof(e5_3_1__partit1,plain,(
    r2_hidden(c1_3_1__partit1,k3_tarski(c1_3__partit1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,dt_c1_3_1__partit1,dt_c2_3_1__partit1,fc2_subset_1,fc6_membered,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e4_3_1__partit1,e3_3_1__partit1,d4_tarski]),
    [interesting(0.65),file(partit1,e5_3_1__partit1),[file(partit1,e5_3_1__partit1)]]).

fof(i3_3_1__partit1,theorem,(
    $true ),
    introduced(tautology,[file(partit1,i3_3_1__partit1)]),
    [interesting(0.65),trivial,file(partit1,i3_3_1__partit1)]).

fof(i2_3_1__partit1,plain,(
    r2_hidden(c1_3_1__partit1,k3_tarski(c1_3__partit1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1,e1_3_1__partit1])],[e5_3_1__partit1,i3_3_1__partit1]),
    [interesting(0.65),file(partit1,i2_3_1__partit1),[file(partit1,i2_3_1__partit1)]]).

fof(i1_3_1__partit1,plain,(
    ~ ( r2_hidden(c1_3_1__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))))
      & ~ r2_hidden(c1_3_1__partit1,k3_tarski(c1_3__partit1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__partit1,dt_c1_3_1__partit1]),discharge_asm(discharge,[e1_3_1__partit1])],[e1_3_1__partit1,i2_3_1__partit1]),
    [interesting(0.65),file(partit1,i1_3_1__partit1),[file(partit1,i1_3_1__partit1)]]).

fof(i1_3_1_tmp__partit1,plain,(
    ~ ( r2_hidden(c1_3_1__partit1,k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))))
      & ~ r2_hidden(c1_3_1__partit1,k3_tarski(c1_3__partit1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__partit1]),discharge_asm(discharge,[dt_c1_3_1__partit1])],[dt_c1_3_1__partit1,i1_3_1__partit1]),
    [interesting(0.8),e1_3__partit1]).

fof(e1_3__partit1,plain,(
    r1_tarski(k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))),k3_tarski(c1_3__partit1)) ),
    inference(let,[status(thm),assumptions([dt_c1_3__partit1])],[i1_3_1_tmp__partit1,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,fc2_subset_1,fc6_membered,d3_tarski,dh_c1_3_1__partit1]),
    [interesting(0.8),file(partit1,e1_3__partit1),[file(partit1,e1_3__partit1)]]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(e3_3__partit1,plain,(
    k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) = k3_tarski(c1_3__partit1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__partit1])],[antisymmetry_r2_hidden,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc37_membered,fc38_membered,fc39_membered,fc40_membered,fc41_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_xboole_0,dt_c1_3__partit1,fc2_subset_1,fc6_membered,t3_boole,t3_subset,t4_boole,t6_boole,e2_3__partit1,e1_3__partit1,d10_xboole_0]),
    [interesting(0.8),file(partit1,e3_3__partit1),[file(partit1,e3_3__partit1)]]).

fof(i2_3__partit1,theorem,(
    $true ),
    introduced(tautology,[file(partit1,i2_3__partit1)]),
    [interesting(0.8),trivial,file(partit1,i2_3__partit1)]).

fof(i1_3__partit1,plain,(
    k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) = k3_tarski(c1_3__partit1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__partit1])],[e3_3__partit1,i2_3__partit1]),
    [interesting(0.8),file(partit1,i1_3__partit1),[file(partit1,i1_3__partit1)]]).

fof(i1_3_tmp__partit1,plain,(
    k3_tarski(k4_xboole_0(c1_3__partit1,k1_tarski(k1_xboole_0))) = k3_tarski(c1_3__partit1) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__partit1])],[dt_c1_3__partit1,i1_3__partit1]),
    [interesting(1),t3_partit1]).

fof(t3_partit1,theorem,(
    ! [A] : k3_tarski(k4_xboole_0(A,k1_tarski(k1_xboole_0))) = k3_tarski(A) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__partit1,dh_c1_3__partit1]),
    [interesting(1),file(partit1,t3_partit1),[file(partit1,t3_partit1)]]).