fof(t12_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_urysohn1(k4_t_1topsp(A)) ) ),
    inference(mizar_proof,[status(thm)],[d10_borsuk_1,t10_t_1topsp,d4_t_1topsp,d1_xboole_0,d3_t_1topsp,d3_tarski,d1_t_1topsp,d2_tops_2,t44_pre_topc,d6_pre_topc,d5_pre_topc,t4_t_1topsp,t36_xboole_1,d10_borsuk_1,d10_borsuk_1,d10_borsuk_1,d5_pre_topc,d6_pre_topc,t27_urysohn1]),
    [file(t_1topsp,t12_t_1topsp),interesting(1.00)]).

fof(t10_t_1topsp,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_eqrel_1(C,B)
         => ~ ( r2_hidden(A,C)
              & ! [D] : 
                  ( m1_subset_1(D,B)
                 => A != k1_t_1topsp(B,D,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d1_xboole_0,d1_t_1topsp]),
    [file(t_1topsp,t10_t_1topsp),interesting(0.91)]).

fof(t7_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m1_eqrel_1(k1_tarski(A),A) ) ),
    inference(mizar_proof,[status(thm)],[t80_zfmisc_1,t31_zfmisc_1,d1_tarski,d1_tarski,d1_tarski,d6_eqrel_1]),
    [file(t_1topsp,t7_t_1topsp),interesting(0.87)]).

fof(t4_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_hidden(B,C)
               => k3_tarski(k4_xboole_0(C,k1_tarski(B))) = k4_xboole_0(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_tarski,t3_t_1topsp,d6_eqrel_1,t31_zfmisc_1]),
    [file(t_1topsp,t4_t_1topsp),interesting(0.82)]).

fof(t3_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => k4_xboole_0(k5_setfam_1(A,B),k3_tarski(C)) = k3_tarski(k4_xboole_0(B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_xboole_0,d4_tarski,d4_tarski,d4_xboole_0,d4_tarski,d10_xboole_0,d3_tarski,d4_tarski,d4_xboole_0,d4_tarski,d6_eqrel_1,t3_xboole_0,d4_tarski,d4_xboole_0]),
    [file(t_1topsp,t3_t_1topsp),interesting(0.77)]).

fof(l10_t_1topsp,theorem,(
    ! [A] : m1_t_1topsp(k1_xboole_0,A) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d2_t_1topsp]),
    [file(t_1topsp,l10_t_1topsp),interesting(0.70)]).

fof(t6_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( ! [D] : 
                    ( m1_subset_1(D,A)
                   => k1_t_1topsp(A,D,B) = k1_t_1topsp(A,D,C) )
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d1_t_1topsp,d1_t_1topsp,d6_eqrel_1,d1_t_1topsp,d1_t_1topsp,t44_setfam_1]),
    [file(t_1topsp,t6_t_1topsp),interesting(0.69)]).

fof(t9_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( ~ r1_xboole_0(k1_t_1topsp(A,C,B),k1_t_1topsp(A,D,B))
                   => k1_t_1topsp(A,C,B) = k1_t_1topsp(A,D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_eqrel_1,t28_eqrel_1,d5_eqrel_1,d1_t_1topsp,t28_eqrel_1,d5_eqrel_1,d1_t_1topsp,t32_eqrel_1]),
    [file(t_1topsp,t9_t_1topsp),interesting(0.68)]).

fof(t8_t_1topsp,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ( v1_t_1topsp(k1_tarski(B),A)
        & m1_t_1topsp(k1_tarski(B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_tarski,d1_tarski,d2_t_1topsp,d3_t_1topsp]),
    [file(t_1topsp,t8_t_1topsp),interesting(0.59)]).

fof(t5_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k16_borsuk_1(A,B))))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k3_tarski(C)
                   => ( v4_pre_topc(C,k16_borsuk_1(A,B))
                    <=> v4_pre_topc(D,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_borsuk_1,d6_eqrel_1,t3_t_1topsp,d10_borsuk_1,d6_pre_topc,d10_borsuk_1,d5_pre_topc,t69_borsuk_1,d5_pre_topc,d6_pre_topc,d6_pre_topc,d5_pre_topc,d10_borsuk_1,t69_borsuk_1,d5_pre_topc,d6_pre_topc]),
    [file(t_1topsp,t5_t_1topsp),interesting(0.44)]).

fof(t11_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_t_1topsp(a_1_0_t_1topsp(A),u1_struct_0(A))
        & m1_t_1topsp(a_1_0_t_1topsp(A),u1_struct_0(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_t_1topsp,d3_t_1topsp]),
    [file(t_1topsp,t11_t_1topsp),interesting(0.42)]).

fof(t16_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ~ ( v1_urysohn1(B)
                  & ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k4_t_1topsp(A)),u1_struct_0(B))
                        & v5_pre_topc(D,k4_t_1topsp(A),B)
                        & m2_relset_1(D,u1_struct_0(k4_t_1topsp(A)),u1_struct_0(B)) )
                     => C != k4_borsuk_1(A,k4_t_1topsp(A),B,k5_t_1topsp(A),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_t_1topsp,d1_funct_2,t12_relset_1,d1_funct_2,t12_relset_1,d10_borsuk_1,t10_t_1topsp,t14_t_1topsp,d5_funct_1,d10_borsuk_1,t10_t_1topsp,d5_funct_1,d6_eqrel_1,t14_t_1topsp,d1_t_1topsp,d1_xboole_0,t3_xboole_0,s2_funct_1,d5_funct_1,d1_tarski,d13_funct_1,d13_funct_1,d1_tarski,s2_funct_1,t44_relat_1,d10_xboole_0,d3_tarski,t15_t_1topsp,t21_funct_1,d3_tarski,t25_funct_1,d3_tarski,d5_funct_1,t1_xboole_1,t44_relat_1,d10_xboole_0,d3_tarski,d5_funct_1,t21_funct_1,d5_funct_1,d10_borsuk_1,t10_t_1topsp,d1_funct_2,d11_borsuk_1,d1_borsuk_1,d1_t_1topsp,t3_xboole_0,t9_t_1topsp,t14_t_1topsp,d5_funct_1,t22_funct_1,t23_funct_1,t9_funct_1,d1_funct_2,t11_relset_1,d12_pre_topc,d3_tarski,d4_tarski,d10_borsuk_1,d12_pre_topc,t181_relat_1,t2_t_1topsp,t5_t_1topsp]),
    [file(t_1topsp,t16_t_1topsp),interesting(0.41)]).

fof(t2_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k16_borsuk_1(A,B))))
             => k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),C) = k3_tarski(C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_borsuk_1,d11_borsuk_1,t31_borsuk_1]),
    [file(t_1topsp,t2_t_1topsp),interesting(0.31)]).

fof(t15_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_urysohn1(B)
               => ! [D] : ~ ( r2_hidden(D,u1_struct_0(k4_t_1topsp(A)))
                    & ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ~ ( r2_hidden(E,k2_relat_1(C))
                            & r1_tarski(D,k5_pre_topc(A,B,C,k1_struct_0(B,E))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_borsuk_1,t10_t_1topsp,d1_funct_2,t12_relset_1,t14_t_1topsp,d5_funct_1]),
    [file(t_1topsp,t15_t_1topsp),interesting(0.21)]).

fof(t13_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_urysohn1(B)
               => ( m1_eqrel_1(a_3_1_t_1topsp(A,B,C),u1_struct_0(A))
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ( r2_hidden(D,a_3_1_t_1topsp(A,B,C))
                       => v4_pre_topc(D,A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,d3_tarski,d10_xboole_0,d3_tarski,d5_funct_1,d1_tarski,d13_funct_1,d4_tarski,d5_funct_1,d1_tarski,d13_funct_1,t3_xboole_0,d13_funct_1,d1_tarski,d6_eqrel_1,t27_urysohn1,d12_pre_topc]),
    [file(t_1topsp,t13_t_1topsp),interesting(0.18)]).

fof(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

fof(d2_t_1topsp,definition,(
    ! [A,B] : 
      ( m1_t_1topsp(B,A)
    <=> r1_tarski(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(t_1topsp,d2_t_1topsp),
    [interesting(0.00)]).

fof(l14_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( v1_t_1topsp(C,A)
                & m1_t_1topsp(C,A) )
             => ! [D] : ~ ( r2_hidden(D,a_3_2_t_1topsp(A,B,C))
                  & ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ~ ( r2_hidden(E,C)
                          & D = k1_t_1topsp(A,B,E) ) ) ) ) ) ) ),
    file(t_1topsp,l14_t_1topsp),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d3_t_1topsp,definition,(
    ! [A,B] : 
      ( m1_t_1topsp(B,A)
     => ( v1_t_1topsp(B,A)
      <=> ! [C] : 
            ( r2_hidden(C,B)
           => m1_eqrel_1(C,A) ) ) ) ),
    file(t_1topsp,d3_t_1topsp),
    [interesting(0.00)]).

fof(d10_borsuk_1,definition,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_eqrel_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_pre_topc(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ( C = k16_borsuk_1(A,B)
              <=> ( u1_struct_0(C) = B
                  & u1_pre_topc(C) = a_2_2_borsuk_1(A,B) ) ) ) ) ) ),
    file(borsuk_1,d10_borsuk_1),
    [interesting(0.00)]).

fof(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(d1_t_1topsp,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k1_t_1topsp(A,B,C)
                  <=> ( r2_hidden(B,D)
                      & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(t_1topsp,d1_t_1topsp),
    [interesting(0.00)]).

fof(d4_t_1topsp,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_t_1topsp(B,A)
            & m1_t_1topsp(B,A) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,A) )
             => ( C = k2_t_1topsp(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k1_t_1topsp(A,D,C) = k1_setfam_1(a_3_0_t_1topsp(A,B,D)) ) ) ) ) ) ),
    file(t_1topsp,d4_t_1topsp),
    [interesting(0.00)]).

fof(d2_tops_2,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tops_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v4_pre_topc(C,A) ) ) ) ) ) ),
    file(tops_2,d2_tops_2),
    [interesting(0.00)]).

fof(t44_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v4_pre_topc(C,A) ) )
           => v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A) ) ) ) ),
    file(pre_topc,t44_pre_topc),
    [interesting(0.00)]).

fof(d6_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A) ) ) ) ),
    file(pre_topc,d6_pre_topc),
    [interesting(0.00)]).

fof(d5_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ),
    file(pre_topc,d5_pre_topc),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.00)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t27_urysohn1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_urysohn1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => v4_pre_topc(k1_struct_0(A,B),A) ) ) ) ),
    file(urysohn1,t27_urysohn1),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.00)]).

fof(d12_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( v4_pre_topc(D,B)
                     => v4_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ),
    file(pre_topc,d12_pre_topc),
    [interesting(0.00)]).

fof(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.00)]).

fof(t14_t_1topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_urysohn1(B)
               => ! [D,E] : 
                    ( m1_subset_1(E,u1_struct_0(A))
                   => ( D = k1_t_1topsp(u1_struct_0(A),E,k2_t_1topsp(u1_struct_0(A),k3_t_1topsp(A)))
                     => r1_tarski(D,k5_pre_topc(A,B,C,k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,d3_tarski,t13_t_1topsp,t13_t_1topsp,d2_tops_2,d1_tarski,d13_funct_1,d5_funct_1,d1_t_1topsp,d4_t_1topsp,d1_setfam_1]),
    [file(t_1topsp,t14_t_1topsp),interesting(0.00)]).

fof(s2_funct_1,theorem,
    ( ( ! [A,B,C] : 
          ( ( r2_hidden(A,f1_s2_funct_1)
            & p1_s2_funct_1(A,B)
            & p1_s2_funct_1(A,C) )
         => B = C )
      & ! [A] : ~ ( r2_hidden(A,f1_s2_funct_1)
          & ! [B] : ~ p1_s2_funct_1(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s2_funct_1
        & ! [B] : 
            ( r2_hidden(B,f1_s2_funct_1)
           => p1_s2_funct_1(B,k1_funct_1(A,B)) ) ) ),
    file(funct_1,s2_funct_1),
    [interesting(0.00)]).

fof(t44_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)) ) ) ),
    file(relat_1,t44_relat_1),
    [interesting(0.00)]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.00)]).

fof(t25_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k2_relat_1(k5_relat_1(C,B)))
           => r2_hidden(A,k2_relat_1(B)) ) ) ) ),
    file(funct_1,t25_funct_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(d11_borsuk_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => k17_borsuk_1(A,B) = k2_borsuk_1(u1_struct_0(A),B) ) ) ),
    file(borsuk_1,d11_borsuk_1),
    [interesting(0.00)]).

fof(d1_borsuk_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( C = k2_borsuk_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => r2_hidden(D,k8_funct_2(A,B,C,D)) ) ) ) ) ) ),
    file(borsuk_1,d1_borsuk_1),
    [interesting(0.00)]).

fof(t43_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ? [C] : 
          ( v3_relat_2(C)
          & v8_relat_2(C)
          & v1_partfun1(C,A,A)
          & m2_relset_1(C,A,A)
          & B = k7_eqrel_1(A,C) ) ) ),
    file(eqrel_1,t43_eqrel_1),
    [interesting(0.00)]).

fof(t28_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,k6_eqrel_1(A,B,C)) ) ) ),
    file(eqrel_1,t28_eqrel_1),
    [interesting(0.00)]).

fof(d5_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    [interesting(0.00)]).

fof(t32_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C,D] : ~ ( r2_hidden(C,A)
          & r2_hidden(D,A)
          & k6_eqrel_1(A,B,C) != k6_eqrel_1(A,B,D)
          & ~ r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) ) ) ),
    file(eqrel_1,t32_eqrel_1),
    [interesting(0.00)]).

fof(t22_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.00)]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(t181_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)) ) ) ),
    file(relat_1,t181_relat_1),
    [interesting(0.00)]).

fof(t31_borsuk_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => k3_funct_2(A,B,k2_borsuk_1(A,B),C) = k3_tarski(C) ) ) ) ),
    file(borsuk_1,t31_borsuk_1),
    [interesting(0.00)]).

fof(t69_borsuk_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ( r2_hidden(k3_tarski(C),u1_pre_topc(A))
              <=> r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) ) ) ) ) ),
    file(borsuk_1,t69_borsuk_1),
    [interesting(0.00)]).

fof(t1_t_1topsp,theorem,(
    $true ),
    file(t_1topsp,t1_t_1topsp),
    [interesting(0.00)]).

fof(t44_setfam_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,B)
                <=> r2_hidden(D,C) ) )
           => B = C ) ) ) ),
    file(setfam_1,t44_setfam_1),
    [interesting(0.00)]).

fof(t80_zfmisc_1,theorem,(
    ! [A] : r1_tarski(k1_tarski(A),k1_zfmisc_1(A)) ),
    file(zfmisc_1,t80_zfmisc_1),
    [interesting(0.00)]).