% Mizar ND problem: t2_borsuk_4,borsuk_4,84,54 
fof(dh_c1_4__borsuk_4,definition,
    ( ( ~ v1_xboole_0(c1_4__borsuk_4)
     => ! [A] : 
          ( ( ~ v1_xboole_0(A)
            & m1_subset_1(A,k1_zfmisc_1(c1_4__borsuk_4)) )
         => ( v1_realset1(A)
          <=> ? [B] : 
                ( m1_subset_1(B,c1_4__borsuk_4)
                & A = k1_tarski(B) ) ) ) )
   => ! [C] : 
        ( ~ v1_xboole_0(C)
       => ! [D] : 
            ( ( ~ v1_xboole_0(D)
              & m1_subset_1(D,k1_zfmisc_1(C)) )
           => ( v1_realset1(D)
            <=> ? [E] : 
                  ( m1_subset_1(E,C)
                  & D = k1_tarski(E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__borsuk_4),file(borsuk_4,c1_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,c1_4__borsuk_4)]).

fof(dh_c2_4__borsuk_4,definition,
    ( ( ( ~ v1_xboole_0(c2_4__borsuk_4)
        & m1_subset_1(c2_4__borsuk_4,k1_zfmisc_1(c1_4__borsuk_4)) )
     => ( v1_realset1(c2_4__borsuk_4)
      <=> ? [A] : 
            ( m1_subset_1(A,c1_4__borsuk_4)
            & c2_4__borsuk_4 = k1_tarski(A) ) ) )
   => ! [B] : 
        ( ( ~ v1_xboole_0(B)
          & m1_subset_1(B,k1_zfmisc_1(c1_4__borsuk_4)) )
       => ( v1_realset1(B)
        <=> ? [C] : 
              ( m1_subset_1(C,c1_4__borsuk_4)
              & B = k1_tarski(C) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__borsuk_4),file(borsuk_4,c2_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,c2_4__borsuk_4)]).

fof(e1_4_1__borsuk_4,assumption,(
    v1_realset1(c2_4__borsuk_4) ),
    introduced(assumption,[file(borsuk_4,e1_4_1__borsuk_4)]),
    [interesting(0.65),axiom,file(borsuk_4,e1_4_1__borsuk_4)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

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(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

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

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

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(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(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

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(cc3_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]).

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

fof(cc5_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]).

fof(cc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc7_tex_2)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(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(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

fof(rc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]).

fof(rc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc7_tex_2)]).

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_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),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_m2_subset_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(subset_1,m2_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_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),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

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(cc1_realset1,theorem,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    [interesting(0.9),axiom,file(realset1,cc1_realset1)]).

fof(cc1_yellow13,theorem,(
    ! [A] : 
      ( v1_realset1(A)
     => v1_finset_1(A) ) ),
    file(yellow13,cc1_yellow13),
    [interesting(0.9),axiom,file(yellow13,cc1_yellow13)]).

fof(cc2_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

fof(cc4_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc4_tex_2)]).

fof(cc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc6_tex_2)]).

fof(rc1_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    [interesting(0.9),axiom,file(realset1,rc1_realset1)]).

fof(rc1_tex_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc1_tex_2)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    [interesting(0.9),axiom,file(realset1,rc2_realset1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc5_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]).

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

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

fof(dt_c1_4__borsuk_4,assumption,(
    ~ v1_xboole_0(c1_4__borsuk_4) ),
    introduced(assumption,[file(borsuk_4,c1_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,c1_4__borsuk_4)]).

fof(dh_c1_4_1__borsuk_4,definition,
    ( ? [A] : 
        ( m2_subset_1(A,c1_4__borsuk_4,c2_4__borsuk_4)
        & c2_4__borsuk_4 = k1_tarski(A) )
   => ( m2_subset_1(c1_4_1__borsuk_4,c1_4__borsuk_4,c2_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(c1_4_1__borsuk_4) ) ),
    introduced(definition,[new_symbol(c1_4_1__borsuk_4),file(borsuk_4,c1_4_1__borsuk_4)]),
    [interesting(0.65),axiom,file(borsuk_4,c1_4_1__borsuk_4)]).

fof(redefinition_k6_domain_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

fof(dt_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

fof(dt_c2_4__borsuk_4,assumption,
    ( ~ v1_xboole_0(c2_4__borsuk_4)
    & m1_subset_1(c2_4__borsuk_4,k1_zfmisc_1(c1_4__borsuk_4)) ),
    introduced(assumption,[file(borsuk_4,c2_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,c2_4__borsuk_4)]).

fof(fc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(tex_2,fc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,fc1_tex_2)]).

fof(fc3_realset1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    [interesting(0.9),axiom,file(realset1,fc3_realset1)]).

fof(d1_tex_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_realset1(A)
      <=> ? [B] : 
            ( m1_subset_1(B,A)
            & A = k6_domain_1(A,B) ) ) ) ),
    file(tex_2,d1_tex_2),
    [interesting(0.9),axiom,file(tex_2,d1_tex_2)]).

fof(e2_4_1__borsuk_4,plain,(
    ? [A] : 
      ( m2_subset_1(A,c1_4__borsuk_4,c2_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e1_4_1__borsuk_4])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_tex_2,cc1_xreal_0,cc2_xreal_0,cc3_tex_2,cc5_tex_2,cc7_tex_2,cc7_xreal_0,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,fc1_xboole_0,fc6_membered,rc1_membered,rc5_tex_2,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k6_domain_1,redefinition_m2_subset_1,dt_k1_tarski,dt_k6_domain_1,dt_m1_subset_1,dt_m2_subset_1,dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,cc15_membered,cc1_realset1,cc1_yellow13,fc1_tex_2,fc3_realset1,rc1_realset1,rc1_tex_2,rc1_xboole_0,rc2_realset1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,e1_4_1__borsuk_4,d1_tex_2]),
    [interesting(0.65),file(borsuk_4,e2_4_1__borsuk_4),[file(borsuk_4,e2_4_1__borsuk_4)]]).

fof(dt_c1_4_1__borsuk_4,plain,(
    m2_subset_1(c1_4_1__borsuk_4,c1_4__borsuk_4,c2_4__borsuk_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e1_4_1__borsuk_4])],[dh_c1_4_1__borsuk_4,e2_4_1__borsuk_4]),
    [interesting(0.65),file(borsuk_4,c1_4_1__borsuk_4),[file(borsuk_4,c1_4_1__borsuk_4)]]).

fof(e3_4_1__borsuk_4,plain,(
    c2_4__borsuk_4 = k1_tarski(c1_4_1__borsuk_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e1_4_1__borsuk_4])],[dh_c1_4_1__borsuk_4,e2_4_1__borsuk_4]),
    [interesting(0.65),file(borsuk_4,e3_4_1__borsuk_4),[file(borsuk_4,e3_4_1__borsuk_4)]]).

fof(e4_4_1__borsuk_4,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e1_4_1__borsuk_4])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc3_tex_2,cc4_membered,cc5_tex_2,cc7_tex_2,fc1_xboole_0,fc6_membered,rc1_membered,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,t1_subset,t4_subset,t5_subset,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_m2_subset_1,cc15_membered,cc1_realset1,cc1_yellow13,cc2_tex_2,cc4_tex_2,cc6_tex_2,rc1_realset1,rc1_tex_2,rc1_xboole_0,rc2_realset1,rc2_xboole_0,rc5_tex_2,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_tarski,dt_m1_subset_1,dt_c1_4__borsuk_4,dt_c1_4_1__borsuk_4,dt_c2_4__borsuk_4,fc1_tex_2,fc3_realset1,e3_4_1__borsuk_4]),
    [interesting(0.65),file(borsuk_4,e4_4_1__borsuk_4),[file(borsuk_4,e4_4_1__borsuk_4)]]).

fof(i2_4_1__borsuk_4,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_4,i2_4_1__borsuk_4)]),
    [interesting(0.65),trivial,file(borsuk_4,i2_4_1__borsuk_4)]).

fof(i1_4_1__borsuk_4,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(A) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e1_4_1__borsuk_4])],[e4_4_1__borsuk_4,i2_4_1__borsuk_4]),
    [interesting(0.65),file(borsuk_4,i1_4_1__borsuk_4),[file(borsuk_4,i1_4_1__borsuk_4)]]).

fof(e1_4__borsuk_4,plain,(
    ~ ( v1_realset1(c2_4__borsuk_4)
      & ! [A] : 
          ( m1_subset_1(A,c1_4__borsuk_4)
         => c2_4__borsuk_4 != k1_tarski(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4]),discharge_asm(discharge,[e1_4_1__borsuk_4])],[e1_4_1__borsuk_4,i1_4_1__borsuk_4]),
    [interesting(0.8),file(borsuk_4,e1_4__borsuk_4),[file(borsuk_4,e1_4__borsuk_4)]]).

fof(e2_4__borsuk_4,assumption,(
    ? [A] : 
      ( m1_subset_1(A,c1_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(A) ) ),
    introduced(assumption,[file(borsuk_4,e2_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,e2_4__borsuk_4)]).

fof(dh_c3_4__borsuk_4,definition,
    ( ? [A] : 
        ( m1_subset_1(A,c1_4__borsuk_4)
        & c2_4__borsuk_4 = k1_tarski(A) )
   => ( m1_subset_1(c3_4__borsuk_4,c1_4__borsuk_4)
      & c2_4__borsuk_4 = k1_tarski(c3_4__borsuk_4) ) ),
    introduced(definition,[new_symbol(c3_4__borsuk_4),file(borsuk_4,c3_4__borsuk_4)]),
    [interesting(0.8),axiom,file(borsuk_4,c3_4__borsuk_4)]).

fof(dt_c3_4__borsuk_4,plain,(
    m1_subset_1(c3_4__borsuk_4,c1_4__borsuk_4) ),
    inference(consider,[status(thm),assumptions([e2_4__borsuk_4])],[dh_c3_4__borsuk_4,e2_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,c3_4__borsuk_4),[file(borsuk_4,c3_4__borsuk_4)]]).

fof(e3_4__borsuk_4,plain,(
    c2_4__borsuk_4 = k1_tarski(c3_4__borsuk_4) ),
    inference(consider,[status(thm),assumptions([e2_4__borsuk_4])],[dh_c3_4__borsuk_4,e2_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,e3_4__borsuk_4),[file(borsuk_4,e3_4__borsuk_4)]]).

fof(e4_4__borsuk_4,plain,(
    v1_realset1(c2_4__borsuk_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e2_4__borsuk_4])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_membered,cc3_membered,cc3_tex_2,cc4_membered,cc5_tex_2,cc7_tex_2,fc1_xboole_0,fc6_membered,rc1_membered,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_4__borsuk_4,cc15_membered,cc2_tex_2,cc4_tex_2,cc6_tex_2,rc1_realset1,rc1_tex_2,rc1_xboole_0,rc2_realset1,rc2_xboole_0,rc5_tex_2,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,dt_k1_tarski,dt_c2_4__borsuk_4,dt_c3_4__borsuk_4,cc1_realset1,cc1_yellow13,fc1_tex_2,fc3_realset1,e3_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,e4_4__borsuk_4),[file(borsuk_4,e4_4__borsuk_4)]]).

fof(i5_4__borsuk_4,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_4,i5_4__borsuk_4)]),
    [interesting(0.8),trivial,file(borsuk_4,i5_4__borsuk_4)]).

fof(i4_4__borsuk_4,plain,(
    v1_realset1(c2_4__borsuk_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4,e2_4__borsuk_4])],[e4_4__borsuk_4,i5_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,i4_4__borsuk_4),[file(borsuk_4,i4_4__borsuk_4)]]).

fof(i3_4__borsuk_4,plain,
    ( ? [A] : 
        ( m1_subset_1(A,c1_4__borsuk_4)
        & c2_4__borsuk_4 = k1_tarski(A) )
   => v1_realset1(c2_4__borsuk_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4]),discharge_asm(discharge,[e2_4__borsuk_4])],[e2_4__borsuk_4,i4_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,i3_4__borsuk_4),[file(borsuk_4,i3_4__borsuk_4)]]).

fof(i2_4__borsuk_4,plain,
    ( v1_realset1(c2_4__borsuk_4)
  <=> ? [A] : 
        ( m1_subset_1(A,c1_4__borsuk_4)
        & c2_4__borsuk_4 = k1_tarski(A) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__borsuk_4,dt_c2_4__borsuk_4])],[e1_4__borsuk_4,i3_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,i2_4__borsuk_4),[file(borsuk_4,i2_4__borsuk_4)]]).

fof(i2_4_tmp__borsuk_4,plain,
    ( ( ~ v1_xboole_0(c2_4__borsuk_4)
      & m1_subset_1(c2_4__borsuk_4,k1_zfmisc_1(c1_4__borsuk_4)) )
   => ( v1_realset1(c2_4__borsuk_4)
    <=> ? [A] : 
          ( m1_subset_1(A,c1_4__borsuk_4)
          & c2_4__borsuk_4 = k1_tarski(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_4]),discharge_asm(discharge,[dt_c2_4__borsuk_4])],[dt_c2_4__borsuk_4,i2_4__borsuk_4]),
    [interesting(0.8),i1_4__borsuk_4]).

fof(i1_4__borsuk_4,plain,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(c1_4__borsuk_4)) )
     => ( v1_realset1(A)
      <=> ? [B] : 
            ( m1_subset_1(B,c1_4__borsuk_4)
            & A = k1_tarski(B) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__borsuk_4])],[i2_4_tmp__borsuk_4,dh_c2_4__borsuk_4]),
    [interesting(0.8),file(borsuk_4,i1_4__borsuk_4),[file(borsuk_4,i1_4__borsuk_4)]]).

fof(i1_4_tmp__borsuk_4,plain,
    ( ~ v1_xboole_0(c1_4__borsuk_4)
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(c1_4__borsuk_4)) )
       => ( v1_realset1(A)
        <=> ? [B] : 
              ( m1_subset_1(B,c1_4__borsuk_4)
              & A = k1_tarski(B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__borsuk_4])],[dt_c1_4__borsuk_4,i1_4__borsuk_4]),
    [interesting(1),t2_borsuk_4]).

fof(t2_borsuk_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ( v1_realset1(B)
          <=> ? [C] : 
                ( m1_subset_1(C,A)
                & B = k1_tarski(C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__borsuk_4,dh_c1_4__borsuk_4]),
    [interesting(1),file(borsuk_4,t2_borsuk_4),[file(borsuk_4,t2_borsuk_4)]]).