fof(t13_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k3_t_0topsp(A))
        & v2_pre_topc(k3_t_0topsp(A))
        & v2_t_0topsp(k3_t_0topsp(A))
        & l1_pre_topc(k3_t_0topsp(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[l19_t_0topsp,d7_t_0topsp]),
    [file(t_0topsp,t13_t_0topsp),interesting(1.00)]).

fof(t12_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)) ) ),
    inference(mizar_proof,[status(thm)],[d11_borsuk_1,t5_t_0topsp,t31_borsuk_1,t11_t_0topsp,t33_borsuk_1,d5_pre_topc,t6_t_0topsp,d2_t_0topsp]),
    [file(t_0topsp,t12_t_0topsp),interesting(0.95)]).

fof(l19_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k3_t_0topsp(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_t_0topsp(A)))
             => ~ ( B != C
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_t_0topsp(A))))
                     => ~ ( v3_pre_topc(D,k3_t_0topsp(A))
                          & ( ( r2_hidden(B,D)
                              & ~ r2_hidden(C,D) )
                            | ( r2_hidden(C,D)
                              & ~ r2_hidden(B,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_borsuk_1,t71_borsuk_1,t12_t_0topsp,d2_t_0topsp,t43_funct_2,t115_funct_2,t10_t_0topsp,t43_funct_2,t115_funct_2,t10_t_0topsp,d3_t_0topsp,t9_t_0topsp]),
    [file(t_0topsp,l19_t_0topsp),interesting(0.74)]).

fof(t7_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k3_t_0topsp(A)))
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & B = k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_t_0topsp,t45_eqrel_1,d5_eqrel_1,t5_t_0topsp]),
    [file(t_0topsp,t7_t_0topsp),interesting(0.52)]).

fof(t5_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( u1_struct_0(k3_t_0topsp(A)) = k2_t_0topsp(A)
        & u1_pre_topc(k3_t_0topsp(A)) = a_1_0_t_0topsp(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_borsuk_1]),
    [file(t_0topsp,t5_t_0topsp),interesting(0.50)]).

fof(t11_t_0topsp,theorem,(
    ! [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)))
         => ( v3_pre_topc(B,A)
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,k2_t_0topsp(A))
                 => ( r1_xboole_0(C,B)
                    | r1_tarski(C,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_eqrel_1,t3_xboole_0,t27_eqrel_1,t27_eqrel_1,t12_eqrel_1,t13_eqrel_1,d3_t_0topsp,d3_tarski]),
    [file(t_0topsp,t11_t_0topsp),interesting(0.49)]).

fof(t1_t_0topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_relset_1(C,A,B)
             => ! [D] : 
                  ( m2_relset_1(D,A,B)
                 => ( ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(k4_tarski(E,F),C)
                            <=> r2_hidden(k4_tarski(E,F),D) ) ) )
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t106_zfmisc_1,t106_zfmisc_1,t106_zfmisc_1,d2_relat_1]),
    [file(t_0topsp,t1_t_0topsp),interesting(0.49)]).

fof(t3_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_borsuk_1]),
    [file(t_0topsp,t3_t_0topsp),interesting(0.47)]).

fof(t6_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_t_0topsp(A))))
         => ( v3_pre_topc(B,k3_t_0topsp(A))
          <=> r2_hidden(k3_tarski(B),u1_pre_topc(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_t_0topsp,d5_pre_topc,t69_borsuk_1,t69_borsuk_1,d5_pre_topc]),
    [file(t_0topsp,t6_t_0topsp),interesting(0.46)]).

fof(t4_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( k1_relat_1(k4_t_0topsp(A)) = u1_struct_0(A)
        & r1_tarski(k2_relat_1(k4_t_0topsp(A)),u1_struct_0(k3_t_0topsp(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_tops_2,t12_pre_topc,t51_tops_2,t12_pre_topc]),
    [file(t_0topsp,t4_t_0topsp),interesting(0.45)]).

fof(t8_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B) = k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_t_0topsp,t45_eqrel_1,t3_t_0topsp,t31_eqrel_1]),
    [file(t_0topsp,t8_t_0topsp),interesting(0.42)]).

fof(t9_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)
              <=> r2_hidden(k8_borsuk_1(A,A,C,B),k1_t_0topsp(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_t_0topsp,t8_t_0topsp,t27_eqrel_1,t44_eqrel_1,t8_t_0topsp,t8_t_0topsp]),
    [file(t_0topsp,t9_t_0topsp),interesting(0.36)]).

fof(t2_t_0topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => ( ( r2_hidden(E,D)
                                & k8_funct_2(A,B,C,E) = k8_funct_2(A,B,C,F) )
                             => r2_hidden(F,D) ) ) )
                   => k3_funct_2(A,B,C,k2_funct_2(A,B,C,D)) = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_funct_2,d13_funct_1,t115_funct_2,d3_tarski,d10_xboole_0]),
    [file(t_0topsp,t2_t_0topsp),interesting(0.36)]).

fof(t17_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(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)) )
             => ? [D] : 
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B))
                  & v5_pre_topc(D,k3_t_0topsp(A),B)
                  & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B))
                  & C = k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_t_0topsp,t16_t_0topsp,d1_tarski,s1_funct_2,t7_t_0topsp,t16_t_0topsp,d1_tarski,d4_tarski,d13_funct_1,t7_t_0topsp,t27_eqrel_1,t44_eqrel_1,d1_funct_2,d13_funct_1,d13_funct_1,t7_t_0topsp,t28_eqrel_1,t46_funct_2,d4_tarski,t2_tarski,t55_tops_2,d5_pre_topc,t6_t_0topsp,t55_tops_2,t4_t_0topsp,d5_eqrel_1,t5_t_0topsp,t8_t_0topsp,t23_funct_1,t16_t_0topsp,d1_tarski,t18_funct_2]),
    [file(t_0topsp,t17_t_0topsp),interesting(0.27)]).

fof(t10_t_0topsp,theorem,(
    ! [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)))
         => ( v3_pre_topc(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),D) )
                     => r2_hidden(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_t_0topsp,t8_t_0topsp,t27_eqrel_1,d3_t_0topsp]),
    [file(t_0topsp,t10_t_0topsp),interesting(0.26)]).

fof(t14_t_0topsp,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(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)))
                & m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)))
                & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A))
                & r1_rfinseq(k4_t_0topsp(A),k7_funct_2(u1_struct_0(B),u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(B),C)) )
           => r1_t_0topsp(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_rfinseq,d1_funct_2,d1_funct_2,t11_relset_1,d1_t_0topsp,t12_pre_topc,d5_tops_2,d5_tops_2,t12_t_0topsp,d2_t_0topsp,d5_tops_2,t55_tops_2,t154_funct_1,d4_tops_2,t159_relat_1,t55_tops_2,t21_funct_2,t21_funct_2,t25_funct_2,t10_t_0topsp,t181_relat_1,t2_t_0topsp,t55_tops_2,t63_tops_2,t21_funct_2,t21_funct_2,t25_funct_2,t10_t_0topsp,t12_t_0topsp,d2_t_0topsp,t55_tops_2,t159_relat_1,t68_tops_2,t55_tops_2,t55_relat_1,t55_relat_1,t65_tops_2,d1_funct_2,t23_funct_2,t55_relat_1,t65_tops_2,t23_funct_2,t181_relat_1,t2_t_0topsp,t55_tops_2]),
    [file(t_0topsp,t14_t_0topsp),interesting(0.24)]).

fof(t16_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(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)) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t115_funct_2,t27_eqrel_1,t15_t_0topsp,d1_tarski,d1_tarski,t28_eqrel_1,t43_funct_2,t2_tarski]),
    [file(t_0topsp,t16_t_0topsp),interesting(0.04)]).

fof(t71_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,u1_struct_0(k16_borsuk_1(A,B)))
             => ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                  & k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D) = C ) ) ) ) ),
    file(borsuk_1,t71_borsuk_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(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(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(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(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(t27_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    file(eqrel_1,t27_eqrel_1),
    [interesting(0.00)]).

fof(t12_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(k4_tarski(B,C),D)
       => r2_hidden(k4_tarski(C,B),D) ) ) ),
    file(eqrel_1,t12_eqrel_1),
    [interesting(0.00)]).

fof(t13_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(k4_tarski(B,C),E)
          & r2_hidden(k4_tarski(C,D),E) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t13_eqrel_1),
    [interesting(0.00)]).

fof(d3_t_0topsp,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k1_t_0topsp(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ( v3_pre_topc(E,A)
                           => ( r2_hidden(C,E)
                            <=> r2_hidden(D,E) ) ) ) ) ) ) ) ) ) ),
    file(t_0topsp,d3_t_0topsp),
    [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(t33_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(A))
             => ( ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(A))
                   => ( r2_hidden(D,B)
                     => ( r1_xboole_0(D,C)
                        | r1_tarski(D,C) ) ) )
               => C = k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C)) ) ) ) ) ),
    file(borsuk_1,t33_borsuk_1),
    [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(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(d2_t_0topsp,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)) )
             => ( v1_t_0topsp(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v3_pre_topc(D,A)
                     => v3_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ),
    file(t_0topsp,d2_t_0topsp),
    [interesting(0.00)]).

fof(t43_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( ? [F] : 
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ),
    file(funct_2,t43_funct_2),
    [interesting(0.00)]).

fof(t115_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : ~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
          & ! [F] : ~ ( r2_hidden(F,A)
              & r2_hidden(F,C)
              & E = k1_funct_1(D,F) ) ) ) ),
    file(funct_2,t115_funct_2),
    [interesting(0.00)]).

fof(t70_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,u1_struct_0(A))
             => r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)) ) ) ) ),
    file(borsuk_1,t70_borsuk_1),
    [interesting(0.00)]).

fof(t45_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,B,B)
        & m2_relset_1(C,B,B) )
     => ~ ( r2_hidden(A,k7_eqrel_1(B,C))
          & ! [D] : 
              ( m1_subset_1(D,B)
             => A != k6_eqrel_1(B,C,D) ) ) ) ),
    file(eqrel_1,t45_eqrel_1),
    [interesting(0.00)]).

fof(t31_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(B,k6_eqrel_1(A,C,D))
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    file(eqrel_1,t31_eqrel_1),
    [interesting(0.00)]).

fof(t44_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(k4_tarski(D,B),C)
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    file(eqrel_1,t44_eqrel_1),
    [interesting(0.00)]).

fof(d7_t_0topsp,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v2_t_0topsp(A)
      <=> ( v3_struct_0(A)
          | ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( B != C
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v3_pre_topc(D,A)
                              & ( ( r2_hidden(B,D)
                                  & ~ r2_hidden(C,D) )
                                | ( r2_hidden(C,D)
                                  & ~ r2_hidden(B,D) ) ) ) ) ) ) ) ) ) ) ),
    file(t_0topsp,d7_t_0topsp),
    [interesting(0.00)]).

fof(t3_rfinseq,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_rfinseq(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & k1_relat_1(C) = k1_relat_1(A)
                & k2_relat_1(C) = k1_relat_1(B)
                & v2_funct_1(C)
                & A = k5_relat_1(C,B) ) ) ) ) ),
    file(rfinseq,t3_rfinseq),
    [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(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(d1_t_0topsp,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ( r1_t_0topsp(A,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))
                & v3_tops_2(C,A,B) ) ) ) ) ),
    file(t_0topsp,d1_t_0topsp),
    [interesting(0.00)]).

fof(t12_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,t12_pre_topc),
    [interesting(0.00)]).

fof(d5_tops_2,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)) )
             => ( v3_tops_2(C,A,B)
              <=> ( k1_relat_1(C) = k2_pre_topc(A)
                  & k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C)
                  & v5_pre_topc(C,A,B)
                  & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ),
    file(tops_2,d5_tops_2),
    [interesting(0.00)]).

fof(t55_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(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)))
                   => ( v3_pre_topc(D,B)
                     => v3_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ),
    file(tops_2,t55_tops_2),
    [interesting(0.00)]).

fof(t154_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v2_funct_1(B)
       => k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A) ) ) ),
    file(funct_1,t154_funct_1),
    [interesting(0.00)]).

fof(d4_tops_2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_struct_0(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)) )
             => ( ( k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C) )
               => k2_tops_2(A,B,C) = k2_funct_1(C) ) ) ) ) ),
    file(tops_2,d4_tops_2),
    [interesting(0.00)]).

fof(t159_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)) ) ) ),
    file(relat_1,t159_relat_1),
    [interesting(0.00)]).

fof(t21_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(t25_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => ( v2_funct_1(C)
        <=> ! [D,E] : 
              ( ( r2_hidden(D,A)
                & r2_hidden(E,A)
                & k1_funct_1(C,D) = k1_funct_1(C,E) )
             => D = E ) ) ) ) ),
    file(funct_2,t25_funct_2),
    [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(t50_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(C,A)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) ) ) ) ),
    file(funct_2,t50_funct_2),
    [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(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(t63_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_struct_0(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)) )
             => ( ( k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C) )
               => v2_funct_1(k2_tops_2(A,B,C)) ) ) ) ) ),
    file(tops_2,t63_tops_2),
    [interesting(0.00)]).

fof(t68_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_struct_0(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)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( k2_relat_1(C) = k2_pre_topc(B)
                      & v2_funct_1(C) )
                   => k5_pre_topc(A,B,C,D) = k4_pre_topc(B,A,k2_tops_2(A,B,C),D) ) ) ) ) ) ),
    file(tops_2,t68_tops_2),
    [interesting(0.00)]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_1),
    [interesting(0.00)]).

fof(t65_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_struct_0(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)) )
             => ( ( k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C) )
               => ( k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C))
                  & k5_relat_1(k2_tops_2(A,B,C),C) = k6_relat_1(k2_relat_1(C)) ) ) ) ) ) ),
    file(tops_2,t65_tops_2),
    [interesting(0.00)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.00)]).

fof(t15_t_0topsp,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(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)) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_hidden(k8_borsuk_1(A,A,D,E),k1_t_0topsp(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_t_0topsp,t55_tops_2,d1_funct_2,d1_funct_2,d13_funct_1,d3_t_0topsp]),
    [file(t_0topsp,t15_t_0topsp),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(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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(s1_funct_2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_funct_2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_funct_2)
            & p1_s1_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2)
        & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_funct_2)
           => p1_s1_funct_2(B,k1_funct_1(A,B)) ) ) ),
    file(funct_2,s1_funct_2),
    [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(t46_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( r2_hidden(E,k10_relat_1(D,C))
          <=> ( r2_hidden(E,A)
              & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ),
    file(funct_2,t46_funct_2),
    [interesting(0.00)]).

fof(t51_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(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)) )
             => ( k1_relat_1(C) = k2_pre_topc(A)
                & r1_tarski(k2_relat_1(C),k2_pre_topc(B)) ) ) ) ) ),
    file(tops_2,t51_tops_2),
    [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(t18_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( r2_hidden(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t18_funct_2),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).