% Mizar problem: t16_t_1topsp,t_1topsp,944,22 
fof(t16_t_1topsp,conjecture,(
    ! [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_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc1_eqrel_1,cc1_funct_1,cc1_relset_1,cc2_eqrel_1,cc2_funct_1,d10_borsuk_1,d10_xboole_0,d11_borsuk_1,d12_pre_topc,d13_funct_1,d1_borsuk_1,d1_funct_2,d1_t_1topsp,d1_tarski,d1_xboole_0,d3_tarski,d4_tarski,d5_funct_1,d5_t_1topsp,d6_eqrel_1,d6_t_1topsp,d7_t_1topsp,dt_g1_pre_topc,dt_k10_relat_1,dt_k16_borsuk_1,dt_k17_borsuk_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_t_1topsp,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_borsuk_1,dt_k2_relat_1,dt_k2_t_1topsp,dt_k2_zfmisc_1,dt_k3_t_1topsp,dt_k3_tarski,dt_k4_borsuk_1,dt_k4_relset_1,dt_k4_t_1topsp,dt_k5_pre_topc,dt_k5_relat_1,dt_k5_setfam_1,dt_k5_t_1topsp,dt_k7_funct_2,dt_k8_funct_2,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,fc1_funct_1,fc1_struct_0,fc1_subset_1,fc1_t_1topsp,fc1_xboole_0,fc2_subset_1,fc2_t_1topsp,fc4_borsuk_1,fc4_subset_1,fraenkel_a_1_0_t_1topsp,fraenkel_a_2_4_borsuk_1,fraenkel_a_3_2_t_1topsp,free_g1_pre_topc,rc1_borsuk_1,rc1_funct_1,rc1_partfun1,rc1_pre_topc,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_pre_topc,rc2_subset_1,rc2_t_1topsp,rc2_xboole_0,rc3_funct_1,rc3_struct_0,rc3_t_1topsp,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,redefinition_k1_struct_0,redefinition_k4_borsuk_1,redefinition_k4_relset_1,redefinition_k5_pre_topc,redefinition_k5_setfam_1,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,s2_funct_1__e11_30__t_1topsp,s2_funct_1__e7_30__t_1topsp,symmetry_r1_xboole_0,t10_t_1topsp,t11_relset_1,t12_relset_1,t13_t_1topsp,t14_t_1topsp,t15_t_1topsp,t181_relat_1,t1_subset,t1_xboole_1,t21_funct_1,t22_funct_1,t23_funct_1,t25_funct_1,t2_subset,t2_t_1topsp,t2_tarski,t3_subset,t3_xboole_0,t44_relat_1,t4_subset,t5_subset,t5_t_1topsp,t6_boole,t7_boole,t8_boole,t9_funct_1,t9_t_1topsp]),
    [file(t_1topsp,t16_t_1topsp)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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

fof(cc1_eqrel_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(d10_borsuk_1,axiom,(
    ! [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_4_borsuk_1(A,B) ) ) ) ) ) ),
    file(borsuk_1,d10_borsuk_1),
    []).

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

fof(d11_borsuk_1,axiom,(
    ! [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),
    []).

fof(d12_pre_topc,axiom,(
    ! [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),
    []).

fof(d13_funct_1,axiom,(
    ! [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),
    []).

fof(d1_borsuk_1,axiom,(
    ! [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),
    []).

fof(d1_funct_2,axiom,(
    ! [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),
    []).

fof(d1_t_1topsp,axiom,(
    ! [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),
    []).

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

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

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

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

fof(d5_funct_1,axiom,(
    ! [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),
    []).

fof(d5_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k3_t_1topsp(A) = a_1_0_t_1topsp(A) ) ),
    file(t_1topsp,d5_t_1topsp),
    []).

fof(d6_eqrel_1,axiom,(
    ! [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),
    []).

fof(d6_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k4_t_1topsp(A) = k16_borsuk_1(A,k2_t_1topsp(u1_struct_0(A),k3_t_1topsp(A))) ) ),
    file(t_1topsp,d6_t_1topsp),
    []).

fof(d7_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k5_t_1topsp(A) = k17_borsuk_1(A,k2_t_1topsp(u1_struct_0(A),k3_t_1topsp(A))) ) ),
    file(t_1topsp,d7_t_1topsp),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    []).

fof(dt_k16_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( v1_pre_topc(k16_borsuk_1(A,B))
        & v2_pre_topc(k16_borsuk_1(A,B))
        & l1_pre_topc(k16_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,k16_borsuk_1),
    []).

fof(dt_k17_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k17_borsuk_1(A,B))
        & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)))
        & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B))
        & m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) ) ) ),
    file(borsuk_1,k17_borsuk_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(dt_k1_t_1topsp,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_subset_1(k1_t_1topsp(A,B,C),k1_zfmisc_1(A)) ) ),
    file(t_1topsp,k1_t_1topsp),
    []).

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

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_k2_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,A) )
     => ( v1_funct_1(k2_borsuk_1(A,B))
        & v1_funct_2(k2_borsuk_1(A,B),A,B)
        & m2_relset_1(k2_borsuk_1(A,B),A,B) ) ) ),
    file(borsuk_1,k2_borsuk_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_t_1topsp,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_t_1topsp(B,A)
        & m1_t_1topsp(B,A) )
     => ( ~ v1_xboole_0(k2_t_1topsp(A,B))
        & m1_eqrel_1(k2_t_1topsp(A,B),A) ) ) ),
    file(t_1topsp,k2_t_1topsp),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v1_xboole_0(k3_t_1topsp(A))
        & v1_t_1topsp(k3_t_1topsp(A),u1_struct_0(A))
        & m1_t_1topsp(k3_t_1topsp(A),u1_struct_0(A)) ) ) ),
    file(t_1topsp,k3_t_1topsp),
    []).

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

fof(dt_k4_borsuk_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( v1_funct_1(k4_borsuk_1(A,B,C,D,E))
        & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
        & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C)
        & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ),
    file(borsuk_1,k4_borsuk_1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_pre_topc(k4_t_1topsp(A))
        & l1_pre_topc(k4_t_1topsp(A)) ) ) ),
    file(t_1topsp,k4_t_1topsp),
    []).

fof(dt_k5_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k5_pre_topc),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(dt_k5_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k5_t_1topsp(A))
        & v1_funct_2(k5_t_1topsp(A),u1_struct_0(A),u1_struct_0(k4_t_1topsp(A)))
        & v5_pre_topc(k5_t_1topsp(A),A,k4_t_1topsp(A))
        & m2_relset_1(k5_t_1topsp(A),u1_struct_0(A),u1_struct_0(k4_t_1topsp(A))) ) ) ),
    file(t_1topsp,k5_t_1topsp),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : m1_t_1topsp(B,A) ),
    file(t_1topsp,m1_t_1topsp),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k4_t_1topsp(A))
        & v1_pre_topc(k4_t_1topsp(A))
        & v2_pre_topc(k4_t_1topsp(A)) ) ) ),
    file(t_1topsp,fc1_t_1topsp),
    []).

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

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

fof(fc2_t_1topsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k4_t_1topsp(A))
        & v1_pre_topc(k4_t_1topsp(A))
        & v2_pre_topc(k4_t_1topsp(A))
        & v1_urysohn1(k4_t_1topsp(A)) ) ) ),
    file(t_1topsp,fc2_t_1topsp),
    []).

fof(fc4_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k16_borsuk_1(A,B))
        & v1_pre_topc(k16_borsuk_1(A,B))
        & v2_pre_topc(k16_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,fc4_borsuk_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fraenkel_a_1_0_t_1topsp,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( r2_hidden(A,a_1_0_t_1topsp(B))
      <=> ? [C] : 
            ( m1_eqrel_1(C,u1_struct_0(B))
            & A = C
            & v2_tops_2(C,B) ) ) ) ),
    file(t_1topsp,a_1_0_t_1topsp),
    []).

fof(fraenkel_a_2_4_borsuk_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_eqrel_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_4_borsuk_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(C))
            & A = D
            & r2_hidden(k3_tarski(D),u1_pre_topc(B)) ) ) ) ),
    file(borsuk_1,a_2_4_borsuk_1),
    []).

fof(fraenkel_a_3_2_t_1topsp,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(D,B,C)
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_2_t_1topsp(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k5_pre_topc(B,C,D,k1_struct_0(C,E))
            & r2_hidden(E,k2_relat_1(D)) ) ) ) ),
    file(t_1topsp,a_3_2_t_1topsp),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(rc1_borsuk_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_eqrel_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_setfam_1(B) ) ) ),
    file(borsuk_1,rc1_borsuk_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    []).

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

fof(rc1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_t_1topsp(B,A)
      & v1_t_1topsp(B,A) ) ),
    file(t_1topsp,rc1_t_1topsp),
    []).

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

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    []).

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

fof(rc2_t_1topsp,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_eqrel_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_setfam_1(B) ) ) ),
    file(t_1topsp,rc2_t_1topsp),
    []).

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

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_t_1topsp(B,A)
      & ~ v1_xboole_0(B)
      & v1_t_1topsp(B,A) ) ),
    file(t_1topsp,rc3_t_1topsp),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    []).

fof(rc7_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    []).

fof(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k4_borsuk_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => k4_borsuk_1(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(borsuk_1,k4_borsuk_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k5_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k5_pre_topc(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(pre_topc,k5_pre_topc),
    []).

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(s2_funct_1__e11_30__t_1topsp,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & 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))
        & m1_eqrel_1(D,u1_struct_0(A)) )
     => ( ( ! [E,F,G] : 
              ( ( r2_hidden(E,D)
                & ! [H] : 
                    ( m1_subset_1(H,u1_struct_0(B))
                   => ( ( r2_hidden(H,k2_relat_1(C))
                        & E = k5_pre_topc(A,B,C,k1_struct_0(B,H)) )
                     => F = H ) )
                & ! [I] : 
                    ( m1_subset_1(I,u1_struct_0(B))
                   => ( ( r2_hidden(I,k2_relat_1(C))
                        & E = k5_pre_topc(A,B,C,k1_struct_0(B,I)) )
                     => G = I ) ) )
             => F = G )
          & ! [E] : ~ ( r2_hidden(E,D)
              & ! [F] : ~ ! [J] : 
                    ( m1_subset_1(J,u1_struct_0(B))
                   => ( ( r2_hidden(J,k2_relat_1(C))
                        & E = k5_pre_topc(A,B,C,k1_struct_0(B,J)) )
                     => F = J ) ) ) )
       => ? [E] : 
            ( v1_relat_1(E)
            & v1_funct_1(E)
            & k1_relat_1(E) = D
            & ! [F] : 
                ( r2_hidden(F,D)
               => ! [K] : 
                    ( m1_subset_1(K,u1_struct_0(B))
                   => ( ( r2_hidden(K,k2_relat_1(C))
                        & F = k5_pre_topc(A,B,C,k1_struct_0(B,K)) )
                     => k1_funct_1(E,F) = K ) ) ) ) ) ) ),
    file(t_1topsp,s2_funct_1__e11_30__t_1topsp),
    []).

fof(s2_funct_1__e7_30__t_1topsp,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & 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)) )
     => ( ( ! [D,E,F] : 
              ( ( r2_hidden(D,u1_struct_0(k4_t_1topsp(A)))
                & ! [G] : 
                    ( m1_subset_1(G,u1_struct_0(B))
                   => ( ( r2_hidden(G,k2_relat_1(C))
                        & r1_tarski(D,k5_pre_topc(A,B,C,k1_struct_0(B,G))) )
                     => E = k5_pre_topc(A,B,C,k1_struct_0(B,G)) ) )
                & ! [H] : 
                    ( m1_subset_1(H,u1_struct_0(B))
                   => ( ( r2_hidden(H,k2_relat_1(C))
                        & r1_tarski(D,k5_pre_topc(A,B,C,k1_struct_0(B,H))) )
                     => F = k5_pre_topc(A,B,C,k1_struct_0(B,H)) ) ) )
             => E = F )
          & ! [D] : ~ ( r2_hidden(D,u1_struct_0(k4_t_1topsp(A)))
              & ! [E] : ~ ! [I] : 
                    ( m1_subset_1(I,u1_struct_0(B))
                   => ( ( r2_hidden(I,k2_relat_1(C))
                        & r1_tarski(D,k5_pre_topc(A,B,C,k1_struct_0(B,I))) )
                     => E = k5_pre_topc(A,B,C,k1_struct_0(B,I)) ) ) ) )
       => ? [D] : 
            ( v1_relat_1(D)
            & v1_funct_1(D)
            & k1_relat_1(D) = u1_struct_0(k4_t_1topsp(A))
            & ! [E] : 
                ( r2_hidden(E,u1_struct_0(k4_t_1topsp(A)))
               => ! [J] : 
                    ( m1_subset_1(J,u1_struct_0(B))
                   => ( ( r2_hidden(J,k2_relat_1(C))
                        & r1_tarski(E,k5_pre_topc(A,B,C,k1_struct_0(B,J))) )
                     => k1_funct_1(D,E) = k5_pre_topc(A,B,C,k1_struct_0(B,J)) ) ) ) ) ) ) ),
    file(t_1topsp,s2_funct_1__e7_30__t_1topsp),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t10_t_1topsp,axiom,(
    ! [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) ) ) ) ) ),
    file(t_1topsp,t10_t_1topsp),
    []).

fof(t11_relset_1,axiom,(
    ! [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),
    []).

fof(t12_relset_1,axiom,(
    ! [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),
    []).

fof(t13_t_1topsp,axiom,(
    ! [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_2_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_2_t_1topsp(A,B,C))
                       => v4_pre_topc(D,A) ) ) ) ) ) ) ) ),
    file(t_1topsp,t13_t_1topsp),
    []).

fof(t14_t_1topsp,axiom,(
    ! [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)))) ) ) ) ) ) ) ),
    file(t_1topsp,t14_t_1topsp),
    []).

fof(t15_t_1topsp,axiom,(
    ! [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))) ) ) ) ) ) ) ) ),
    file(t_1topsp,t15_t_1topsp),
    []).

fof(t181_relat_1,axiom,(
    ! [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),
    []).

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

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

fof(t21_funct_1,axiom,(
    ! [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),
    []).

fof(t22_funct_1,axiom,(
    ! [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),
    []).

fof(t23_funct_1,axiom,(
    ! [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),
    []).

fof(t25_funct_1,axiom,(
    ! [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),
    []).

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_t_1topsp,axiom,(
    ! [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) ) ) ) ),
    file(t_1topsp,t2_t_1topsp),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

fof(t3_xboole_0,axiom,(
    ! [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),
    []).

fof(t44_relat_1,axiom,(
    ! [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),
    []).

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(t5_t_1topsp,axiom,(
    ! [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) ) ) ) ) ) ) ),
    file(t_1topsp,t5_t_1topsp),
    []).

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),
    []).

fof(t9_funct_1,axiom,(
    ! [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),
    []).

fof(t9_t_1topsp,axiom,(
    ! [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) ) ) ) ) ) ),
    file(t_1topsp,t9_t_1topsp),
    []).