fof(t22_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ( v3_compts_1(A)
          & v2_compts_1(A) )
       => v5_compts_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_compts_1,d7_xboole_0,t17_compts_1,t17_compts_1,d3_xboole_0,t50_subset_1,t15_compts_1,d5_pre_topc,d7_xboole_0,s2_wellord2,d3_tarski,d12_funct_1,d3_tarski,d12_funct_1,d4_tarski,d1_compts_1,d1_tops_2,d12_funct_1,d7_compts_1,t146_relat_1,t195_orders_1,d3_tarski,d12_funct_1,t18_tops_2,t26_tops_2,t17_finset_1,d1_tops_2,d12_funct_1,t27_tops_2,d1_compts_1,d1_compts_1,d3_tarski,d4_tarski,d12_funct_1,d12_funct_1,d12_funct_1,t6_setfam_1,d3_xboole_0,d4_tarski,d12_funct_1,d12_funct_1,d1_setfam_1,d3_xboole_0,d7_xboole_0]),
    [file(compts_1,t22_compts_1),interesting(1.00)]).

fof(t18_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v6_compts_1(B,A)
                  & r1_tarski(C,B)
                  & v4_pre_topc(C,A) )
               => v6_compts_1(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_1,t9_compts_1,d10_pre_topc,t12_pre_topc,t34_tops_2,t12_compts_1,t17_compts_1,t11_compts_1]),
    [file(compts_1,t18_compts_1),interesting(0.98)]).

fof(t21_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ( v3_compts_1(A)
          & v2_compts_1(A) )
       => v4_compts_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_compts_1,t17_compts_1,t15_compts_1]),
    [file(compts_1,t21_compts_1),interesting(0.95)]).

fof(t20_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_compts_1(A)
                  & v6_compts_1(B,A)
                  & v6_compts_1(C,A) )
               => v6_compts_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_compts_1,t35_tops_1,t17_xboole_1,t18_compts_1]),
    [file(compts_1,t20_compts_1),interesting(0.93)]).

fof(t10_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v2_compts_1(A)
      <=> v6_compts_1(k2_pre_topc(A),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_compts_1,d1_compts_1,t14_pre_topc,d10_xboole_0,d8_pre_topc,d3_compts_1,d8_pre_topc,d1_compts_1,d3_compts_1,d8_pre_topc,d1_compts_1,d7_compts_1,d1_compts_1,t14_pre_topc,d10_xboole_0,d8_pre_topc]),
    [file(compts_1,t10_compts_1),interesting(0.86)]).

fof(t17_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v2_compts_1(A)
              & v4_pre_topc(B,A) )
           => v6_compts_1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_compts_1,d1_compts_1,t9_xboole_1,t14_pre_topc,t18_pre_topc,d10_xboole_0,t31_zfmisc_1,t96_zfmisc_1,d8_pre_topc,t29_tops_1,d1_tops_2,d2_xboole_0,d1_tarski,d1_tops_2,d3_compts_1,t33_xboole_1,t40_xboole_1,t36_xboole_1,t1_xboole_1,d8_pre_topc,t31_zfmisc_1,t17_pre_topc,t6_tops_2,d1_compts_1,t16_finset_1]),
    [file(compts_1,t17_compts_1),interesting(0.85)]).

fof(t9_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => v6_compts_1(k1_pre_topc(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d7_compts_1,t2_xboole_1,t2_xboole_1,d1_compts_1,t2_xboole_1]),
    [file(compts_1,t9_compts_1),interesting(0.83)]).

fof(t16_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_compts_1(A)
              & v6_compts_1(B,A) )
           => v4_pre_topc(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_tops_1,t15_compts_1,t31_subset_1,t20_tops_1,t1_xboole_1,t57_tops_1,t29_tops_1]),
    [file(compts_1,t16_compts_1),interesting(0.82)]).

fof(t12_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( B = k1_xboole_0
             => ( v6_compts_1(B,A)
              <=> v2_compts_1(k3_pre_topc(A,B)) ) )
            & ( v2_pre_topc(A)
             => ( B = k1_xboole_0
                | ( v6_compts_1(B,A)
                <=> v2_compts_1(k3_pre_topc(A,B)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_pre_topc,t9_compts_1,t10_compts_1,t9_compts_1,t3_xboole_1,d1_struct_0,t10_compts_1,t11_compts_1,d10_pre_topc,t11_compts_1]),
    [file(compts_1,t12_compts_1),interesting(0.75)]).

fof(t11_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,k2_pre_topc(B))
               => ( v6_compts_1(C,A)
                <=> ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                     => ( D = C
                       => v6_compts_1(D,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_pre_topc,t12_pre_topc,t28_xboole_1,d7_compts_1,t49_tops_2,d1_compts_1,t44_tops_2,t1_xboole_1,d1_compts_1,d7_compts_1,t1_tops_2,d10_pre_topc,t12_pre_topc,t40_tops_2,d1_compts_1,t42_tops_2,d1_compts_1,t46_tops_2,t12_pre_topc,d7_compts_1,t50_tops_2,t1_tops_2,d10_pre_topc,t12_pre_topc,d1_compts_1,t42_tops_2,d1_compts_1,d1_tops_2,d3_tops_2,d1_tops_2,d5_pre_topc,d9_pre_topc,d5_pre_topc,d7_compts_1,t195_orders_1,t3_tops_2,d3_tarski,d1_compts_1,d4_tarski,d12_funct_1,d3_xboole_0,d4_tarski,d1_compts_1]),
    [file(compts_1,t11_compts_1),interesting(0.71)]).

fof(t13_compts_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
           => ~ ( v1_compts_1(B)
                & v2_tops_2(B,A)
                & k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_compts_1,t12_tops_2,t17_pre_topc,d8_pre_topc,t16_tops_2,d3_compts_1,d3_tarski,d8_setfam_1,d8_setfam_1,t13_tops_2,t5_tops_2,t11_tops_2,t17_pre_topc,d8_pre_topc,t37_xboole_1,t10_tops_2,d2_compts_1,d3_compts_1,t17_tops_2,t5_tops_2,t11_tops_2,t17_pre_topc,d8_pre_topc,t37_xboole_1,t10_tops_2,d2_compts_1,t1_xboole_1,d3_tarski,d8_setfam_1,d8_setfam_1,t12_tops_2,t17_pre_topc,d8_pre_topc,t13_tops_2]),
    [file(compts_1,t13_compts_1),interesting(0.48)]).

fof(t19_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v6_compts_1(B,A)
                  & v6_compts_1(C,A) )
               => v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_compts_1,d1_compts_1,t7_xboole_1,t1_xboole_1,d1_compts_1,d7_compts_1,t7_xboole_1,t1_xboole_1,d1_compts_1,d7_compts_1,t8_xboole_1,d1_compts_1,t13_xboole_1,t96_zfmisc_1,d1_compts_1,t14_finset_1]),
    [file(compts_1,t19_compts_1),interesting(0.45)]).

fof(t23_compts_1,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)) )
             => ( ( v2_compts_1(A)
                  & v5_pre_topc(C,A,B)
                  & k2_relat_1(C) = k2_pre_topc(B) )
               => v2_compts_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_compts_1,t54_tops_2,t1_tops_2,t30_funct_3,d8_pre_topc,t146_relat_1,t51_tops_2,t51_tops_2,t146_funct_1,t14_pre_topc,d10_xboole_0,d8_pre_topc,t59_tops_2,d3_compts_1,t156_relat_1,t33_funct_3,t145_funct_1,t156_relat_1,t1_xboole_1,t1_xboole_1,t51_tops_2,t1_tops_2,t16_funct_3,d8_pre_topc,t51_tops_2,t146_relat_1,d8_pre_topc,t17_finset_1]),
    [file(compts_1,t23_compts_1),interesting(0.30)]).

fof(t24_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_pre_topc(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
                 => ( ( v5_pre_topc(D,A,C)
                      & k2_relat_1(D) = k2_pre_topc(C)
                      & v6_compts_1(B,A) )
                   => v6_compts_1(k4_pre_topc(A,C,D,B),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_compts_1,t54_tops_2,t1_tops_2,t30_funct_3,d1_compts_1,t178_relat_1,t14_pre_topc,t51_tops_2,t146_funct_1,t1_xboole_1,d1_compts_1,t59_tops_2,d7_compts_1,t156_relat_1,t33_funct_3,t145_funct_1,t156_relat_1,t1_xboole_1,t1_xboole_1,t51_tops_2,t1_tops_2,t16_funct_3,d1_compts_1,t156_relat_1,d1_compts_1,t17_finset_1]),
    [file(compts_1,t24_compts_1),interesting(0.30)]).

fof(t25_compts_1,theorem,(
    ! [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))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v2_compts_1(A)
                  & v3_compts_1(B)
                  & k2_relat_1(C) = k2_pre_topc(B)
                  & v5_pre_topc(C,A,B) )
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v4_pre_topc(D,A)
                     => v4_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_compts_1,t24_compts_1,t16_compts_1]),
    [file(compts_1,t25_compts_1),interesting(0.28)]).

fof(t15_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_compts_1(A)
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v6_compts_1(B,A)
             => ( B = k1_xboole_0
                | ! [C] : 
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B))
                        & ! [D] : 
                            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                           => ! [E] : 
                                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                               => ~ ( v3_pre_topc(D,A)
                                    & v3_pre_topc(E,A)
                                    & r2_hidden(C,D)
                                    & r1_tarski(B,E)
                                    & r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_subset_1,d4_compts_1,d5_pre_topc,d7_xboole_0,s2_wellord2,d3_tarski,d12_funct_1,d3_tarski,d12_funct_1,d4_tarski,d1_compts_1,d1_tops_2,d12_funct_1,d7_compts_1,t146_relat_1,t195_orders_1,d3_tarski,d12_funct_1,t17_finset_1,d1_tops_2,d12_funct_1,t27_tops_2,t18_tops_2,t26_tops_2,d1_compts_1,d3_tarski,d4_tarski,d12_funct_1,d12_funct_1,d12_funct_1,d1_setfam_1,d1_compts_1,d3_xboole_0,d4_tarski,d12_funct_1,d12_funct_1,d1_setfam_1,d3_xboole_0,d7_xboole_0]),
    [file(compts_1,t15_compts_1),interesting(0.18)]).

fof(t26_compts_1,theorem,(
    ! [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))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v2_compts_1(A)
                  & v3_compts_1(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) )
               => v3_tops_2(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_compts_1,d12_pre_topc,t152_funct_1,t51_tops_2,t14_pre_topc,t146_funct_1,d10_xboole_0,t72_tops_2]),
    [file(compts_1,t26_compts_1),interesting(0.16)]).

fof(d2_compts_1,definition,(
    ! [A] : 
      ( v1_compts_1(A)
    <=> ( A != k1_xboole_0
        & ! [B] : ~ ( B != k1_xboole_0
            & r1_tarski(B,A)
            & v1_finset_1(B)
            & k1_setfam_1(B) = k1_xboole_0 ) ) ) ),
    file(compts_1,d2_compts_1),
    [interesting(0.00)]).

fof(t12_tops_2,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B)) ) ) ),
    file(tops_2,t12_tops_2),
    [interesting(0.00)]).

fof(t17_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_subset_1(u1_struct_0(A),B) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) ) ) ),
    file(pre_topc,t17_pre_topc),
    [interesting(0.00)]).

fof(d8_pre_topc,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( r1_pre_topc(A,B)
          <=> k2_pre_topc(A) = k5_setfam_1(u1_struct_0(A),B) ) ) ) ),
    file(pre_topc,d8_pre_topc),
    [interesting(0.00)]).

fof(t16_tops_2,theorem,(
    ! [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)
          <=> v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_2,t16_tops_2),
    [interesting(0.00)]).

fof(d3_compts_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v2_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
           => ~ ( r1_pre_topc(A,B)
                & v1_tops_2(B,A)
                & ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                   => ~ ( r1_tarski(C,B)
                        & r1_pre_topc(A,C)
                        & v1_finset_1(C) ) ) ) ) ) ) ),
    file(compts_1,d3_compts_1),
    [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(d8_setfam_1,definition,(
    ! [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)))
         => ( C = k7_setfam_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> r2_hidden(k3_subset_1(A,D),B) ) ) ) ) ) ),
    file(setfam_1,d8_setfam_1),
    [interesting(0.00)]).

fof(t13_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_finset_1(k7_setfam_1(u1_struct_0(A),B))
          <=> v1_finset_1(B) ) ) ) ),
    file(tops_2,t13_tops_2),
    [interesting(0.00)]).

fof(t5_tops_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ~ ( r1_pre_topc(A,B)
              & B = k1_xboole_0 ) ) ) ),
    file(tops_2,t5_tops_2),
    [interesting(0.00)]).

fof(t11_tops_2,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B)) ) ) ),
    file(tops_2,t11_tops_2),
    [interesting(0.00)]).

fof(t37_xboole_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    [interesting(0.00)]).

fof(t10_tops_2,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ~ ( B != k1_xboole_0
            & k7_setfam_1(A,B) = k1_xboole_0 )
        & ~ ( k7_setfam_1(A,B) != k1_xboole_0
            & B = k1_xboole_0 ) ) ) ),
    file(tops_2,t10_tops_2),
    [interesting(0.00)]).

fof(t17_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tops_2(B,A)
          <=> v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_2,t17_tops_2),
    [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(t14_compts_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
           => ~ ( B != k1_xboole_0
                & v2_tops_2(B,A)
                & k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0
                & ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                   => ~ ( C != k1_xboole_0
                        & r1_tarski(C,B)
                        & v1_finset_1(C)
                        & k6_setfam_1(u1_struct_0(A),C) = k1_xboole_0 ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_compts_1,d2_compts_1,t1_xboole_1,d2_compts_1,d2_compts_1,t13_compts_1]),
    [file(compts_1,t14_compts_1),interesting(0.00)]).

fof(d7_compts_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_compts_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
               => ~ ( r1_compts_1(A,C,B)
                    & v1_tops_2(C,A)
                    & ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                       => ~ ( r1_tarski(D,C)
                            & r1_compts_1(A,D,B)
                            & v1_finset_1(D) ) ) ) ) ) ) ) ),
    file(compts_1,d7_compts_1),
    [interesting(0.00)]).

fof(d1_compts_1,definition,(
    ! [A] : 
      ( l1_struct_0(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)))
             => ( r1_compts_1(A,B,C)
              <=> r1_tarski(C,k5_setfam_1(u1_struct_0(A),B)) ) ) ) ) ),
    file(compts_1,d1_compts_1),
    [interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(t96_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) ),
    file(zfmisc_1,t96_zfmisc_1),
    [interesting(0.00)]).

fof(t14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,t14_finset_1),
    [interesting(0.00)]).

fof(t1_compts_1,theorem,(
    $true ),
    file(compts_1,t1_compts_1),
    [interesting(0.00)]).

fof(t22_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k1_pre_topc(A),A) ) ),
    file(tops_1,t22_tops_1),
    [interesting(0.00)]).

fof(t54_subset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ~ ( r2_hidden(B,k3_subset_1(A,C))
          & r2_hidden(B,C) ) ) ),
    file(subset_1,t54_subset_1),
    [interesting(0.00)]).

fof(d4_compts_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_compts_1(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)))
                       => ! [E] : 
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v3_pre_topc(D,A)
                                & v3_pre_topc(E,A)
                                & r2_hidden(B,D)
                                & r2_hidden(C,E)
                                & r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ),
    file(compts_1,d4_compts_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(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(s2_wellord2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s2_wellord2)
        & ! [B,C] : ~ ( r2_hidden(B,f2_s2_wellord2)
            & r2_hidden(C,f3_s2_wellord2)
            & p1_s2_wellord2(A,B,C) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & k1_relat_1(A) = f1_s2_wellord2
            & k1_relat_1(B) = f1_s2_wellord2
            & ! [C] : 
                ( r2_hidden(C,f1_s2_wellord2)
               => p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ),
    file(wellord2,s2_wellord2),
    [interesting(0.00)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [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(d1_tops_2,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tops_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v3_pre_topc(C,A) ) ) ) ) ) ),
    file(tops_2,d1_tops_2),
    [interesting(0.00)]).

fof(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.00)]).

fof(t195_orders_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : ~ ( v1_finset_1(B)
          & r1_tarski(B,k2_relat_1(A))
          & ! [C] : ~ ( r1_tarski(C,k1_relat_1(A))
              & v1_finset_1(C)
              & k9_relat_1(A,C) = B ) ) ) ),
    file(orders_1,t195_orders_1),
    [interesting(0.00)]).

fof(t17_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_finset_1(A)
       => v1_finset_1(k9_relat_1(B,A)) ) ) ),
    file(finset_1,t17_finset_1),
    [interesting(0.00)]).

fof(t27_tops_2,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))))
         => ( ( v1_tops_2(B,A)
              & v1_finset_1(B) )
           => v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_2,t27_tops_2),
    [interesting(0.00)]).

fof(t18_tops_2,theorem,(
    ! [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(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( r1_tarski(B,C)
                  & v1_tops_2(C,A) )
               => v1_tops_2(B,A) ) ) ) ) ),
    file(tops_2,t18_tops_2),
    [interesting(0.00)]).

fof(t26_tops_2,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))))
         => ( v1_tops_2(B,A)
           => v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_2,t26_tops_2),
    [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(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t31_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(B,C)
          <=> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) ) ) ) ),
    file(subset_1,t31_subset_1),
    [interesting(0.00)]).

fof(t20_tops_1,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
              <=> r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ),
    file(tops_1,t20_tops_1),
    [interesting(0.00)]).

fof(t57_tops_1,theorem,(
    ! [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] : 
                ( r2_hidden(C,B)
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & v3_pre_topc(D,A)
                    & r1_tarski(D,B)
                    & r2_hidden(C,D) ) ) ) ) ) ),
    file(tops_1,t57_tops_1),
    [interesting(0.00)]).

fof(t29_tops_1,theorem,(
    ! [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(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_1,t29_tops_1),
    [interesting(0.00)]).

fof(t35_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  & v4_pre_topc(C,A) )
               => v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    file(tops_1,t35_tops_1),
    [interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

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

fof(d10_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v1_pre_topc(C)
                & m1_pre_topc(C,A) )
             => ( C = k3_pre_topc(A,B)
              <=> k2_pre_topc(C) = B ) ) ) ) ),
    file(pre_topc,d10_pre_topc),
    [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(t34_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_pre_topc(C,A)
             => ( v4_pre_topc(B,A)
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                   => ( D = B
                     => v4_pre_topc(D,C) ) ) ) ) ) ) ),
    file(tops_2,t34_tops_2),
    [interesting(0.00)]).

fof(t14_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k2_pre_topc(A)) ) ) ),
    file(pre_topc,t14_pre_topc),
    [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(d1_struct_0,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_struct_0(A)
      <=> v1_xboole_0(u1_struct_0(A)) ) ) ),
    file(struct_0,d1_struct_0),
    [interesting(0.00)]).

fof(d9_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ( m1_pre_topc(B,A)
          <=> ( r1_tarski(k2_pre_topc(B),k2_pre_topc(A))
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
                 => ( r2_hidden(C,u1_pre_topc(B))
                  <=> ? [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                        & r2_hidden(D,u1_pre_topc(A))
                        & C = k3_xboole_0(D,k2_pre_topc(B)) ) ) ) ) ) ) ) ),
    file(pre_topc,d9_pre_topc),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(t49_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
             => ~ ( v1_tops_2(C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                     => ~ ( v1_tops_2(D,A)
                          & ! [E] : 
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ( E = k2_pre_topc(B)
                               => C = k1_tops_2(A,E,D) ) ) ) ) ) ) ) ) ),
    file(tops_2,t49_tops_2),
    [interesting(0.00)]).

fof(t44_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => r1_tarski(k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)),k5_setfam_1(u1_struct_0(A),C)) ) ) ) ),
    file(tops_2,t44_tops_2),
    [interesting(0.00)]).

fof(t1_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => r1_tarski(B,k1_zfmisc_1(k2_pre_topc(A))) ) ) ),
    file(tops_2,t1_tops_2),
    [interesting(0.00)]).

fof(t40_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k1_tops_2(A,B,C),k1_tops_2(A,B,D)) ) ) ) ) ) ),
    file(tops_2,t40_tops_2),
    [interesting(0.00)]).

fof(t42_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                 => ( r1_tarski(B,k5_setfam_1(u1_struct_0(A),D))
                   => r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k5_setfam_1(u1_struct_0(k3_pre_topc(A,C)),k1_tops_2(A,C,D))) ) ) ) ) ) ),
    file(tops_2,t42_tops_2),
    [interesting(0.00)]).

fof(t46_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( v1_finset_1(C)
               => v1_finset_1(k1_tops_2(A,B,C)) ) ) ) ) ),
    file(tops_2,t46_tops_2),
    [interesting(0.00)]).

fof(t50_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & k1_relat_1(D) = C
                  & k2_relat_1(D) = k1_tops_2(A,B,C)
                  & ! [E] : 
                      ( r2_hidden(E,C)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( F = E
                           => k1_funct_1(D,E) = k5_subset_1(u1_struct_0(A),F,B) ) ) ) ) ) ) ) ),
    file(tops_2,t50_tops_2),
    [interesting(0.00)]).

fof(d3_tops_2,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))))
                 => ( D = k1_tops_2(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))
                       => ( r2_hidden(E,D)
                        <=> ? [F] : 
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                              & r2_hidden(F,C)
                              & k5_subset_1(u1_struct_0(A),F,B) = E ) ) ) ) ) ) ) ) ),
    file(tops_2,d3_tops_2),
    [interesting(0.00)]).

fof(t3_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] : 
              ( r1_tarski(C,B)
             => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ),
    file(tops_2,t3_tops_2),
    [interesting(0.00)]).

fof(t9_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) ),
    file(xboole_1,t9_xboole_1),
    [interesting(0.00)]).

fof(t18_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A) ) ) ),
    file(pre_topc,t18_pre_topc),
    [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(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [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(t33_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ),
    file(xboole_1,t33_xboole_1),
    [interesting(0.00)]).

fof(t40_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_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(t6_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ),
    file(tops_2,t6_tops_2),
    [interesting(0.00)]).

fof(t16_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,t16_finset_1),
    [interesting(0.00)]).

fof(d5_compts_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v4_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != k1_xboole_0
                    & v4_pre_topc(C,A)
                    & r2_hidden(B,k3_subset_1(u1_struct_0(A),C))
                    & ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ! [E] : 
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v3_pre_topc(D,A)
                                & v3_pre_topc(E,A)
                                & r2_hidden(B,D)
                                & r1_tarski(C,E)
                                & r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ),
    file(compts_1,d5_compts_1),
    [interesting(0.00)]).

fof(d6_compts_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v5_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( B != k1_xboole_0
                    & C != k1_xboole_0
                    & v4_pre_topc(B,A)
                    & v4_pre_topc(C,A)
                    & r1_xboole_0(B,C)
                    & ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ! [E] : 
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( v3_pre_topc(D,A)
                                & v3_pre_topc(E,A)
                                & r1_tarski(B,D)
                                & r1_tarski(C,E)
                                & r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ),
    file(compts_1,d6_compts_1),
    [interesting(0.00)]).

fof(t50_subset_1,theorem,(
    ! [A] : 
      ( A != k1_xboole_0
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ( ~ r2_hidden(C,B)
               => r2_hidden(C,k3_subset_1(A,B)) ) ) ) ) ),
    file(subset_1,t50_subset_1),
    [interesting(0.00)]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    [interesting(0.00)]).

fof(t54_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)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                 => m1_subset_1(k9_relat_1(k3_funct_3(C),D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ) ),
    file(tops_2,t54_tops_2),
    [interesting(0.00)]).

fof(t30_funct_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k1_zfmisc_1(k2_relat_1(B)))
       => k3_tarski(k9_relat_1(k3_funct_3(B),A)) = k10_relat_1(B,k3_tarski(A)) ) ) ),
    file(funct_3,t30_funct_3),
    [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(t146_funct_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A))) ) ) ),
    file(funct_1,t146_funct_1),
    [interesting(0.00)]).

fof(t59_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)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                 => ( ( v5_pre_topc(C,A,B)
                      & v1_tops_2(D,B) )
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                       => ( E = k9_relat_1(k3_funct_3(C),D)
                         => v1_tops_2(E,A) ) ) ) ) ) ) ) ),
    file(tops_2,t59_tops_2),
    [interesting(0.00)]).

fof(t156_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ),
    file(relat_1,t156_relat_1),
    [interesting(0.00)]).

fof(t33_funct_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k9_relat_1(k3_funct_3(B),A),k10_relat_1(k1_funct_3(B),A)) ) ),
    file(funct_3,t33_funct_3),
    [interesting(0.00)]).

fof(t145_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A) ) ),
    file(funct_1,t145_funct_1),
    [interesting(0.00)]).

fof(t16_funct_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k1_zfmisc_1(k1_relat_1(B)))
       => k9_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k1_funct_3(B),A)) ) ) ),
    file(funct_3,t16_funct_3),
    [interesting(0.00)]).

fof(t178_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) ) ) ),
    file(relat_1,t178_relat_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(t152_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v2_funct_1(B)
       => r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A) ) ) ),
    file(funct_1,t152_funct_1),
    [interesting(0.00)]).

fof(t72_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)) )
             => ( 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)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ( v4_pre_topc(D,A)
                      <=> v4_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ) ),
    file(tops_2,t72_tops_2),
    [interesting(0.00)]).

fof(t2_compts_1,theorem,(
    $true ),
    file(compts_1,t2_compts_1),
    [interesting(0.00)]).

fof(t3_compts_1,theorem,(
    $true ),
    file(compts_1,t3_compts_1),
    [interesting(0.00)]).

fof(t4_compts_1,theorem,(
    $true ),
    file(compts_1,t4_compts_1),
    [interesting(0.00)]).

fof(t5_compts_1,theorem,(
    $true ),
    file(compts_1,t5_compts_1),
    [interesting(0.00)]).

fof(t6_compts_1,theorem,(
    $true ),
    file(compts_1,t6_compts_1),
    [interesting(0.00)]).

fof(t7_compts_1,theorem,(
    $true ),
    file(compts_1,t7_compts_1),
    [interesting(0.00)]).

fof(t8_compts_1,theorem,(
    $true ),
    file(compts_1,t8_compts_1),
    [interesting(0.00)]).