fof(t60_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => v4_compts_1(A) ) ),
    inference(mizar_proof,[status(thm)],[t55_tops_1,d1_connsp_2,d6_group_1,t37_topgrp_1,t19_group_1,t54_topgrp_1,t4_connsp_2,t38_tops_1,t55_tops_1,d1_connsp_2,d3_tarski,t50_topgrp_1,d5_group_1,t33_group_2,d13_pre_topc,t4_xboole_0,d3_xboole_0,t33_group_2,t17_xboole_1,t9_topgrp_1,t8_topgrp_1,t4_topgrp_1,t1_xboole_1,d5_group_1,d6_group_1,d4_group_1,t17_xboole_1,t5_group_2,t12_group_2,t36_topgrp_1]),
    [file(topgrp_1,t60_topgrp_1),interesting(1.00)]).

fof(t2_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => k2_tops_2(A,A,k7_grcat_1(A)) = k7_grcat_1(A) ) ),
    inference(mizar_proof,[status(thm)],[t1_topgrp_1,t51_tops_2,d4_tops_2,d11_grcat_1,t67_funct_1,d11_grcat_1]),
    [file(topgrp_1,t2_topgrp_1),interesting(0.77)]).

fof(t1_topgrp_1,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_relat_1(k7_grcat_1(A)) = k2_pre_topc(A) ) ),
    inference(mizar_proof,[status(thm)],[d11_grcat_1,t71_relat_1]),
    [file(topgrp_1,t1_topgrp_1),interesting(0.74)]).

fof(t20_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => v3_tops_2(k7_grcat_1(A),A,A) ) ),
    inference(mizar_proof,[status(thm)],[t1_topgrp_1,t51_tops_2,d5_tops_2]),
    [file(topgrp_1,t20_topgrp_1),interesting(0.74)]).

fof(t33_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => k3_topgrp_1(A) = k2_group_1(k4_topgrp_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d4_topgrp_1,d4_topgrp_1,d4_topgrp_1,t93_tmap_1,d4_topgrp_1,t93_tmap_1,t10_group_1]),
    [file(topgrp_1,t33_topgrp_1),interesting(0.74)]).

fof(t30_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_topgrp_1(B,A)
         => m1_topgrp_1(k2_tops_2(A,A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_topgrp_1]),
    [file(topgrp_1,t30_topgrp_1),interesting(0.67)]).

fof(t14_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_funct_2(u1_struct_0(A),k4_group_1(A)) = k4_group_1(A) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d1_funct_2,d7_group_1,t19_group_1,d7_group_1,t54_funct_1,t9_funct_1]),
    [file(topgrp_1,t14_topgrp_1),interesting(0.67)]).

fof(t12_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v2_funct_1(k4_group_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d8_funct_1,d1_funct_2,d7_group_1,t17_group_1]),
    [file(topgrp_1,t12_topgrp_1),interesting(0.66)]).

fof(t31_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_topgrp_1(B,A)
         => ! [C] : 
              ( m1_topgrp_1(C,A)
             => m1_topgrp_1(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_tops_2,d3_topgrp_1]),
    [file(topgrp_1,t31_topgrp_1),interesting(0.63)]).

fof(t3_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_pre_topc(A,A,k7_grcat_1(A),B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t2_topgrp_1,t1_topgrp_1,t51_tops_2,t67_tops_2,t3_waybel15]),
    [file(topgrp_1,t3_topgrp_1),interesting(0.63)]).

fof(t54_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_connsp_2(C,A,B)
             => m1_connsp_2(k1_group_2(A,C),A,k3_group_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_connsp_2,t54_tops_1,t9_topgrp_1,t51_topgrp_1,t5_group_2,t54_tops_1,d1_connsp_2]),
    [file(topgrp_1,t54_topgrp_1),interesting(0.63)]).

fof(t45_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => m1_topgrp_1(k5_topgrp_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d3_funct_2,d5_tops_2,d3_topgrp_1,d6_topgrp_1,t14_topgrp_1,d4_tops_2,d6_topgrp_1]),
    [file(topgrp_1,t45_topgrp_1),interesting(0.62)]).

fof(t18_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_tops_2(A,A,k1_topgrp_1(A,B)) = k1_topgrp_1(A,k3_group_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d3_funct_2,d1_funct_2,d1_topgrp_1,d1_topgrp_1,d4_group_1,d6_group_1,d5_group_1,t57_funct_1,d4_tops_2,d8_funct_1,t9_funct_1]),
    [file(topgrp_1,t18_topgrp_1),interesting(0.61)]).

fof(t19_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_tops_2(A,A,k2_topgrp_1(A,B)) = k2_topgrp_1(A,k3_group_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d3_funct_2,d1_funct_2,d2_topgrp_1,d2_topgrp_1,d4_group_1,d6_group_1,d5_group_1,t57_funct_1,d4_tops_2,d8_funct_1,t9_funct_1]),
    [file(topgrp_1,t19_topgrp_1),interesting(0.61)]).

fof(t17_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_pre_topc(A,A,k2_topgrp_1(A,C),B) = k4_group_2(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d12_funct_1,d2_topgrp_1,t34_group_2,d3_tarski,d10_xboole_0,d3_tarski,t34_group_2,d2_topgrp_1,d12_funct_1]),
    [file(topgrp_1,t17_topgrp_1),interesting(0.60)]).

fof(t16_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_pre_topc(A,A,k1_topgrp_1(A,C),B) = k3_group_2(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d12_funct_1,d1_topgrp_1,t33_group_2,d3_tarski,d10_xboole_0,d3_tarski,t33_group_2,d1_topgrp_1,d12_funct_1]),
    [file(topgrp_1,t16_topgrp_1),interesting(0.60)]).

fof(t5_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_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)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_tarski(B,C)
                   => r1_tarski(k4_group_2(A,D,B),k4_group_2(A,D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t34_group_2,t34_group_2]),
    [file(topgrp_1,t5_topgrp_1),interesting(0.59)]).

fof(t8_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_group_2(A,k1_group_2(A,B)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_group_2,d1_group_2,t19_group_1,d3_tarski,d10_xboole_0,d3_tarski,t19_group_1]),
    [file(topgrp_1,t8_topgrp_1),interesting(0.59)]).

fof(t13_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k2_relat_1(k4_group_1(A)) = u1_struct_0(A) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,d10_xboole_0,d3_tarski,d7_group_1,t19_group_1,d1_funct_2,d5_funct_1]),
    [file(topgrp_1,t13_topgrp_1),interesting(0.57)]).

fof(t21_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_connsp_2(k2_pre_topc(A),A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_tops_1,d1_connsp_2]),
    [file(topgrp_1,t21_topgrp_1),interesting(0.57)]).

fof(t59_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_yellow_8(B,A,k2_group_1(A))
         => ! [C] : 
              ( ( v1_tops_1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => m1_cantor_1(a_3_0_topgrp_1(A,B,C),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_tarski,t21_yellow_8,t49_topgrp_1,d5_pre_topc,t49_topgrp_1,t16_group_1,d5_group_1,d6_group_1,t34_group_2,t5_connsp_2,t55_topgrp_1,t6_connsp_2,t22_yellow_8,t21_yellow_8,t80_tops_1,t4_xboole_0,d3_xboole_0,t33_group_2,d5_group_1,d6_group_1,d4_group_1,d4_group_1,d6_group_1,d5_group_1,t7_topgrp_1,d6_group_1,t34_group_2,d5_group_1,t34_group_2,t40_group_2,d3_tarski,t34_group_2,t5_group_2,t12_group_2,t1_xboole_1,t5_topgrp_1,t40_group_2,d6_group_1,t43_group_2,t40_group_2,t32_yellow_9]),
    [file(topgrp_1,t59_topgrp_1),interesting(0.57)]).

fof(t51_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v3_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v3_pre_topc(k1_group_2(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_topgrp_1,t25_topgrp_1]),
    [file(topgrp_1,t51_topgrp_1),interesting(0.57)]).

fof(t49_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v3_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v3_pre_topc(k4_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_topgrp_1,t25_topgrp_1]),
    [file(topgrp_1,t49_topgrp_1),interesting(0.55)]).

fof(t50_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v3_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v3_pre_topc(k3_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_topgrp_1,t25_topgrp_1]),
    [file(topgrp_1,t50_topgrp_1),interesting(0.55)]).

fof(t11_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_pre_topc(A,A,k4_group_1(A),B) = k1_group_2(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d13_funct_1,t5_group_2,d7_group_1,t19_group_1,d3_tarski,d10_xboole_0,d3_tarski,t5_group_2,d7_group_1,t19_group_1,d13_funct_1]),
    [file(topgrp_1,t11_topgrp_1),interesting(0.55)]).

fof(t9_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_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)))
             => ( r1_tarski(B,C)
              <=> r1_tarski(k1_group_2(A,B),k1_group_2(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_group_2,d1_group_2,d3_tarski,t8_topgrp_1,d1_group_2,d1_group_2,d3_tarski]),
    [file(topgrp_1,t9_topgrp_1),interesting(0.55)]).

fof(t38_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_topgrp_1(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_connsp_2(D,A,k1_group_1(A,B,C))
                   => ? [E] : 
                        ( m1_connsp_2(E,A,B)
                        & ? [F] : 
                            ( m1_connsp_2(F,A,C)
                            & r1_tarski(k2_group_2(A,E,F),D) ) ) ) ) )
       => v4_topgrp_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_topgrp_1,t50_borsuk_1,t15_topgrp_1,d2_borsuk_1]),
    [file(topgrp_1,t38_topgrp_1),interesting(0.54)]).

fof(t43_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_topgrp_1(k1_topgrp_1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d3_funct_2,d5_tops_2,d3_topgrp_1,t18_topgrp_1]),
    [file(topgrp_1,t43_topgrp_1),interesting(0.54)]).

fof(t44_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_topgrp_1(k2_topgrp_1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d3_funct_2,d5_tops_2,d3_topgrp_1,t19_topgrp_1]),
    [file(topgrp_1,t44_topgrp_1),interesting(0.54)]).

fof(t34_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_topgrp_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k4_topgrp_1(A)))
             => ( B = C
               => k3_group_1(k4_topgrp_1(A),C) = k2_tops_2(A,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_topgrp_1,d4_topgrp_1,d5_tops_2,d4_topgrp_1,t65_tops_2,d11_grcat_1,t33_topgrp_1,d4_topgrp_1,t65_tops_2,d11_grcat_1,t33_topgrp_1,t12_group_1]),
    [file(topgrp_1,t34_topgrp_1),interesting(0.53)]).

fof(t10_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_pre_topc(A,A,k4_group_1(A),B) = k1_group_2(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_group_2,t115_funct_2,d7_group_1,d3_tarski,d10_xboole_0,d3_tarski,d7_group_1,t43_funct_2]),
    [file(topgrp_1,t10_topgrp_1),interesting(0.53)]).

fof(t7_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k1_group_2(A,B))
              <=> r2_hidden(k3_group_1(A,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_group_2,t19_group_1,t19_group_1]),
    [file(topgrp_1,t7_topgrp_1),interesting(0.52)]).

fof(t35_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_topgrp_1(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & v4_pre_topc(k1_struct_0(A,B),A) )
       => v1_urysohn1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_topgrp_1,d1_funct_2,t117_funct_1,t72_tops_2,t27_urysohn1]),
    [file(topgrp_1,t35_topgrp_1),interesting(0.50)]).

fof(t40_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & l1_topgrp_1(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_connsp_2(C,A,k3_group_1(A,B))
               => ? [D] : 
                    ( m1_connsp_2(D,A,B)
                    & r1_tarski(k1_group_2(A,D),C) ) ) )
       => v3_topgrp_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_group_1,t10_topgrp_1,d2_borsuk_1,d6_topgrp_1]),
    [file(topgrp_1,t40_topgrp_1),interesting(0.48)]).

fof(t37_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_connsp_2(D,A,k1_group_1(A,B,C))
                 => ? [E] : 
                      ( v3_pre_topc(E,A)
                      & m1_connsp_2(E,A,B)
                      & ? [F] : 
                          ( v3_pre_topc(F,A)
                          & m1_connsp_2(F,A,C)
                          & r1_tarski(k2_group_2(A,E,F),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_borsuk_1,d7_topgrp_1,d2_borsuk_1,d1_connsp_2,t45_borsuk_1,d4_tarski,t106_zfmisc_1,t55_tops_1,d1_connsp_2,d1_connsp_2,d2_group_2,d3_tarski,t106_zfmisc_1,d4_tarski,t44_tops_1,t43_funct_2]),
    [file(topgrp_1,t37_topgrp_1),interesting(0.48)]).

fof(t6_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_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)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_tarski(B,C)
                   => r1_tarski(k3_group_2(A,D,B),k3_group_2(A,D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t33_group_2,t33_group_2]),
    [file(topgrp_1,t6_topgrp_1),interesting(0.47)]).

fof(t36_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_topgrp_1(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( v3_pre_topc(C,A)
                    & r2_hidden(B,C)
                    & ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r2_hidden(B,D)
                            & v3_pre_topc(D,A)
                            & r1_tarski(k6_pre_topc(A,D),C) ) ) ) ) )
       => v4_compts_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_topgrp_1,d1_funct_2,d5_tops_2,t54_funct_1,t54_funct_1,d13_funct_1,t55_tops_2,t25_topgrp_1,d12_funct_1,t156_relat_1,t74_tops_2,t147_funct_1,t29_urysohn1]),
    [file(topgrp_1,t36_topgrp_1),interesting(0.46)]).

fof(t56_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v1_tops_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v1_tops_1(k1_group_2(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_topgrp_1,t29_topgrp_1]),
    [file(topgrp_1,t56_topgrp_1),interesting(0.44)]).

fof(t52_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_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)))
             => ( v3_pre_topc(C,A)
               => v3_pre_topc(k2_group_2(A,C,B),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_tops_1,d10_xboole_0,d3_tarski,t12_group_2,t49_topgrp_1,d3_tarski,t34_group_2,t12_group_2,t34_group_2,t54_tops_1]),
    [file(topgrp_1,t52_topgrp_1),interesting(0.43)]).

fof(t53_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_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)))
             => ( v3_pre_topc(C,A)
               => v3_pre_topc(k2_group_2(A,B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_tops_1,d10_xboole_0,d3_tarski,t12_group_2,t50_topgrp_1,d3_tarski,t33_group_2,t12_group_2,t33_group_2,t54_tops_1]),
    [file(topgrp_1,t53_topgrp_1),interesting(0.43)]).

fof(t39_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_connsp_2(C,A,k3_group_1(A,B))
             => ? [D] : 
                  ( v3_pre_topc(D,A)
                  & m1_connsp_2(D,A,B)
                  & r1_tarski(k1_group_2(A,D),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_group_1,d6_topgrp_1,d2_borsuk_1,d1_connsp_2,t45_tops_1,d1_connsp_2,d1_group_2,d3_tarski,t44_tops_1,d7_group_1,t43_funct_2]),
    [file(topgrp_1,t39_topgrp_1),interesting(0.43)]).

fof(t57_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v1_tops_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v1_tops_1(k3_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_topgrp_1,t28_topgrp_1]),
    [file(topgrp_1,t57_topgrp_1),interesting(0.41)]).

fof(t58_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v1_tops_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v1_tops_1(k4_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_topgrp_1,t28_topgrp_1]),
    [file(topgrp_1,t58_topgrp_1),interesting(0.41)]).

fof(t48_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v4_pre_topc(k1_group_2(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_topgrp_1,t72_tops_2]),
    [file(topgrp_1,t48_topgrp_1),interesting(0.39)]).

fof(t28_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_tops_1(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( v3_tops_2(C,A,B)
                   => v1_tops_1(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tops_1,d5_tops_2,t74_tops_2,t45_funct_2,d3_tops_1]),
    [file(topgrp_1,t28_topgrp_1),interesting(0.39)]).

fof(t55_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_connsp_2(C,A,k1_group_1(A,B,k3_group_1(A,B)))
             => ? [D] : 
                  ( v3_pre_topc(D,A)
                  & m1_connsp_2(D,A,B)
                  & r1_tarski(k2_group_2(A,D,k1_group_2(A,D)),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_topgrp_1,t4_connsp_2,t38_tops_1,d3_tarski,t12_group_2,t7_topgrp_1,d3_xboole_0,t7_topgrp_1,d3_xboole_0,t12_group_2]),
    [file(topgrp_1,t55_topgrp_1),interesting(0.39)]).

fof(t29_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_tops_1(D,B)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( v3_tops_2(C,A,B)
                   => v1_tops_1(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tops_1,t73_tops_2,t52_tops_2,d3_tops_1]),
    [file(topgrp_1,t29_topgrp_1),interesting(0.38)]).

fof(t46_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v4_pre_topc(k4_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_topgrp_1,t72_tops_2]),
    [file(topgrp_1,t46_topgrp_1),interesting(0.37)]).

fof(t47_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => v4_pre_topc(k3_group_2(A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_topgrp_1,t72_tops_2]),
    [file(topgrp_1,t47_topgrp_1),interesting(0.37)]).

fof(t41_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & v3_topgrp_1(A)
        & v4_topgrp_1(A)
        & l1_topgrp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_connsp_2(D,A,k1_group_1(A,B,k3_group_1(A,C)))
                 => ? [E] : 
                      ( v3_pre_topc(E,A)
                      & m1_connsp_2(E,A,B)
                      & ? [F] : 
                          ( v3_pre_topc(F,A)
                          & m1_connsp_2(F,A,C)
                          & r1_tarski(k2_group_2(A,E,k1_group_2(A,F)),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_topgrp_1,t39_topgrp_1,d2_group_2,d2_group_2,d1_group_2,d3_tarski]),
    [file(topgrp_1,t41_topgrp_1),interesting(0.26)]).

fof(t25_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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)))
                     => ( v3_pre_topc(D,A)
                      <=> v3_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_tops_2,d5_tops_2,d5_tops_2,d4_tops_2,t154_funct_1,t55_tops_2,t55_tops_2,t152_funct_1,t146_funct_1,d10_xboole_0,t147_funct_1,t55_tops_2,d4_tops_2,t154_funct_1,t55_tops_2,d5_tops_2]),
    [file(topgrp_1,t25_topgrp_1),interesting(0.19)]).

fof(t27_topgrp_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)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_tops_1,t178_relat_1,t48_tops_1,t55_tops_2,t55_tops_1,t55_tops_1,d10_xboole_0,t44_tops_1,t55_tops_2]),
    [file(topgrp_1,t27_topgrp_1),interesting(0.18)]).

fof(t42_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v2_pre_topc(A)
        & l1_topgrp_1(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_connsp_2(D,A,k1_group_1(A,B,k3_group_1(A,C)))
                   => ? [E] : 
                        ( m1_connsp_2(E,A,B)
                        & ? [F] : 
                            ( m1_connsp_2(F,A,C)
                            & r1_tarski(k2_group_2(A,E,k1_group_2(A,F)),D) ) ) ) ) )
       => ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v2_pre_topc(A)
          & v3_topgrp_1(A)
          & v4_topgrp_1(A)
          & l1_topgrp_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_group_1,d3_tarski,t5_group_2,t6_connsp_2,t12_group_2,d5_group_1,t19_group_1,d3_tarski,t12_group_2,t5_group_2,t7_topgrp_1,t12_group_2,t38_topgrp_1,t40_topgrp_1]),
    [file(topgrp_1,t42_topgrp_1),interesting(0.13)]).

fof(t23_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( ( v3_pre_topc(E,A)
                          & m1_connsp_2(E,A,D) )
                       => ? [F] : 
                            ( m1_connsp_2(F,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D))
                            & r1_tarski(F,k4_pre_topc(A,B,C,E)) ) ) )
               => v1_t_0topsp(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_t_0topsp,d12_funct_1,t5_connsp_2,t156_relat_1,t44_tops_1,t1_xboole_1,t1_xboole_1,d1_connsp_2,t57_tops_1]),
    [file(topgrp_1,t23_topgrp_1),interesting(0.09)]).

fof(t22_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_t_0topsp(C,A,B)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_connsp_2(E,A,D)
                       => ? [F] : 
                            ( v3_pre_topc(F,B)
                            & m1_connsp_2(F,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D))
                            & r1_tarski(F,k4_pre_topc(A,B,C,E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_t_0topsp,d1_connsp_2,t43_funct_2,t5_connsp_2,t44_tops_1,t156_relat_1]),
    [file(topgrp_1,t22_topgrp_1),interesting(0.08)]).

fof(t26_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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(B)))
                     => ( v3_pre_topc(D,B)
                      <=> v3_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_tops_2,d5_tops_2,t55_tops_2,t25_topgrp_1,t147_funct_1,d5_tops_2,t55_tops_2,t67_tops_2,d8_funct_1,t2_t_0topsp,t55_tops_2]),
    [file(topgrp_1,t26_topgrp_1),interesting(0.02)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [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(d7_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k4_group_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k3_group_1(A,C) ) ) ) ) ),
    file(group_1,d7_group_1),
    [interesting(0.00)]).

fof(t17_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_group_1(A,B) = k3_group_1(A,C)
               => B = C ) ) ) ) ),
    file(group_1,t17_group_1),
    [interesting(0.00)]).

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

fof(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(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(t19_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_group_1(A,k3_group_1(A,B)) = B ) ) ),
    file(group_1,t19_group_1),
    [interesting(0.00)]).

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

fof(d11_grcat_1,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)) ) ),
    file(grcat_1,d11_grcat_1),
    [interesting(0.00)]).

fof(t71_relat_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    [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(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(t43_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) ),
    file(tops_1,t43_tops_1),
    [interesting(0.00)]).

fof(d1_connsp_2,definition,(
    ! [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,k1_zfmisc_1(u1_struct_0(A)))
             => ( m1_connsp_2(C,A,B)
              <=> r2_hidden(B,k1_tops_1(A,C)) ) ) ) ) ),
    file(connsp_2,d1_connsp_2),
    [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(t5_connsp_2,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)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v3_pre_topc(B,A)
                  & r2_hidden(C,B) )
               => m1_connsp_2(B,A,C) ) ) ) ) ),
    file(connsp_2,t5_connsp_2),
    [interesting(0.00)]).

fof(t44_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k1_tops_1(A,B),B) ) ) ),
    file(tops_1,t44_tops_1),
    [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(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(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(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(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(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(t147_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k2_relat_1(B))
       => k9_relat_1(B,k10_relat_1(B,A)) = A ) ) ),
    file(funct_1,t147_funct_1),
    [interesting(0.00)]).

fof(t67_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(A)))
                 => ( ( k2_relat_1(C) = k2_pre_topc(B)
                      & v2_funct_1(C) )
                   => k4_pre_topc(A,B,C,D) = k5_pre_topc(B,A,k2_tops_2(A,B,C),D) ) ) ) ) ) ),
    file(tops_2,t67_tops_2),
    [interesting(0.00)]).

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 ) ) ) ) ) ),
    file(t_0topsp,t2_t_0topsp),
    [interesting(0.00)]).

fof(t24_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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(B)))
                     => ( v4_pre_topc(D,B)
                      <=> v4_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_tops_2,d5_tops_2,d12_pre_topc,t72_tops_2,t147_funct_1,d5_tops_2,d12_pre_topc,d12_pre_topc,t67_tops_2,d8_funct_1,t2_t_0topsp]),
    [file(topgrp_1,t24_topgrp_1),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(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(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(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(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(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(t48_tops_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)))
             => ( r1_tarski(B,C)
               => r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C)) ) ) ) ) ),
    file(tops_1,t48_tops_1),
    [interesting(0.00)]).

fof(t55_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( v3_pre_topc(D,B)
                     => k1_tops_1(B,D) = D )
                    & ( k1_tops_1(A,C) = C
                     => v3_pre_topc(C,A) ) ) ) ) ) ) ),
    file(tops_1,t55_tops_1),
    [interesting(0.00)]).

fof(d3_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( m1_topgrp_1(B,A)
          <=> v3_tops_2(B,A,A) ) ) ) ),
    file(topgrp_1,d3_topgrp_1),
    [interesting(0.00)]).

fof(t71_tops_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [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(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v3_tops_2(D,A,B)
                          & v3_tops_2(E,B,C) )
                       => v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ),
    file(tops_2,t71_tops_2),
    [interesting(0.00)]).

fof(d4_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & l1_group_1(B) )
         => ( B = k4_topgrp_1(A)
          <=> ! [C] : 
                ( ( r2_hidden(C,u1_struct_0(B))
                 => m1_topgrp_1(C,A) )
                & ( m1_topgrp_1(C,A)
                 => r2_hidden(C,u1_struct_0(B)) )
                & ! [D] : 
                    ( m1_topgrp_1(D,A)
                   => ! [E] : 
                        ( m1_topgrp_1(E,A)
                       => k1_binop_1(u1_group_1(B),D,E) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,E) ) ) ) ) ) ) ),
    file(topgrp_1,d4_topgrp_1),
    [interesting(0.00)]).

fof(t32_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_topgrp_1(B,A)
         => ! [C] : 
              ( m1_topgrp_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k4_topgrp_1(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k4_topgrp_1(A)))
                     => ( ( B = D
                          & C = E )
                       => k1_group_1(k4_topgrp_1(A),D,E) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_topgrp_1]),
    [file(topgrp_1,t32_topgrp_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(t93_tmap_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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)) )
             => ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) = C
                & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) = C ) ) ) ) ),
    file(tmap_1,t93_tmap_1),
    [interesting(0.00)]).

fof(t10_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k1_group_1(A,C,B) = C
                  & k1_group_1(A,B,C) = C ) )
           => B = k2_group_1(A) ) ) ) ),
    file(group_1,t10_group_1),
    [interesting(0.00)]).

fof(t12_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( k1_group_1(A,B,C) = k2_group_1(A)
                  & k1_group_1(A,C,B) = k2_group_1(A) )
               => C = k3_group_1(A,B) ) ) ) ) ),
    file(group_1,t12_group_1),
    [interesting(0.00)]).

fof(d5_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( v1_topgrp_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_topgrp_1(D,A)
                    & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = C ) ) ) ) ) ),
    file(topgrp_1,d5_topgrp_1),
    [interesting(0.00)]).

fof(t117_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t117_funct_1),
    [interesting(0.00)]).

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

fof(t67_funct_1,theorem,(
    ! [A] : k2_funct_1(k6_relat_1(A)) = k6_relat_1(A) ),
    file(funct_1,t67_funct_1),
    [interesting(0.00)]).

fof(t3_waybel15,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_pre_topc(A,A,k7_grcat_1(A),B) = B ) ) ),
    file(waybel15,t3_waybel15),
    [interesting(0.00)]).

fof(d5_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v2_group_1(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k2_group_1(A)
            <=> ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k1_group_1(A,C,B) = C
                    & k1_group_1(A,B,C) = C ) ) ) ) ) ) ),
    file(group_1,d5_group_1),
    [interesting(0.00)]).

fof(t5_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ( r2_hidden(A,k1_group_2(B,C))
          <=> ? [D] : 
                ( m1_subset_1(D,u1_struct_0(B))
                & A = k3_group_1(B,D)
                & r2_hidden(D,C) ) ) ) ) ),
    file(group_2,t5_group_2),
    [interesting(0.00)]).

fof(t6_connsp_2,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)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( m1_connsp_2(B,A,C)
               => r2_hidden(C,B) ) ) ) ) ),
    file(connsp_2,t6_connsp_2),
    [interesting(0.00)]).

fof(t12_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(A,k2_group_2(B,C,D))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] : 
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r2_hidden(E,C)
                        & r2_hidden(F,D) ) ) ) ) ) ) ),
    file(group_2,t12_group_2),
    [interesting(0.00)]).

fof(d1_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_group_2(A,B) = a_2_0_group_2(A,B) ) ) ),
    file(group_2,d1_group_2),
    [interesting(0.00)]).

fof(d7_topgrp_1,definition,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_topgrp_1(A) )
     => ( v4_topgrp_1(A)
      <=> ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A))
              & m2_relset_1(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A)) )
           => ( B = u1_group_1(A)
             => v5_pre_topc(B,k6_borsuk_1(A,A),A) ) ) ) ) ),
    file(topgrp_1,d7_topgrp_1),
    [interesting(0.00)]).

fof(t50_borsuk_1,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] : 
              ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B)))
             => ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                      & C = k8_borsuk_1(A,B,D,E) ) ) ) ) ) ),
    file(borsuk_1,t50_borsuk_1),
    [interesting(0.00)]).

fof(d2_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_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)))
             => k2_group_2(A,B,C) = a_3_0_group_2(A,B,C) ) ) ) ),
    file(group_2,d2_group_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(d2_zfmisc_1,definition,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    [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(t15_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_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)))
             => k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_group_1(A),k2_zfmisc_1(B,C)) = k2_group_2(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_group_2,t115_funct_2,d2_zfmisc_1,d3_tarski,d10_xboole_0,d3_tarski,t106_zfmisc_1,t43_funct_2]),
    [file(topgrp_1,t15_topgrp_1),interesting(0.00)]).

fof(d2_borsuk_1,definition,(
    ! [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))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D))
                       => ? [F] : 
                            ( m1_connsp_2(F,A,D)
                            & r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ),
    file(borsuk_1,d2_borsuk_1),
    [interesting(0.00)]).

fof(d6_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_topgrp_1(A) )
     => ( v3_topgrp_1(A)
      <=> v5_pre_topc(k5_topgrp_1(A),A,A) ) ) ),
    file(topgrp_1,d6_topgrp_1),
    [interesting(0.00)]).

fof(d3_funct_2,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> k2_relat_1(C) = B ) ) ),
    file(funct_2,d3_funct_2),
    [interesting(0.00)]).

fof(d1_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k1_topgrp_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_group_1(A,B,D) ) ) ) ) ) ),
    file(topgrp_1,d1_topgrp_1),
    [interesting(0.00)]).

fof(d4_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v4_group_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)) ) ) ) ) ) ),
    file(group_1,d4_group_1),
    [interesting(0.00)]).

fof(d6_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C = k3_group_1(A,B)
              <=> ( k1_group_1(A,B,C) = k2_group_1(A)
                  & k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ) ),
    file(group_1,d6_group_1),
    [interesting(0.00)]).

fof(t57_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k2_relat_1(B)) )
       => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))
          & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ),
    file(funct_1,t57_funct_1),
    [interesting(0.00)]).

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

fof(d2_topgrp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k2_topgrp_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_group_1(A,D,B) ) ) ) ) ) ),
    file(topgrp_1,d2_topgrp_1),
    [interesting(0.00)]).

fof(t54_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( B = k2_funct_1(A)
            <=> ( k1_relat_1(B) = k2_relat_1(A)
                & ! [C,D] : 
                    ( ( ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) )
                     => ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) ) )
                    & ( ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) )
                     => ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ),
    file(funct_1,t54_funct_1),
    [interesting(0.00)]).

fof(t34_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k4_group_2(B,D,C))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,E,D)
                    & r2_hidden(E,C) ) ) ) ) ) ),
    file(group_2,t34_group_2),
    [interesting(0.00)]).

fof(t33_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k3_group_2(B,D,C))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,D,E)
                    & r2_hidden(E,C) ) ) ) ) ) ),
    file(group_2,t33_group_2),
    [interesting(0.00)]).

fof(t54_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B,C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k1_tops_1(A,C))
          <=> ? [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                & v3_pre_topc(D,A)
                & r1_tarski(D,C)
                & r2_hidden(B,D) ) ) ) ) ),
    file(tops_1,t54_tops_1),
    [interesting(0.00)]).

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

fof(d3_tops_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_1(B,A)
          <=> k6_pre_topc(A,B) = k2_pre_topc(A) ) ) ) ),
    file(tops_1,d3_tops_1),
    [interesting(0.00)]).

fof(t73_tops_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [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)) )
             => ( 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(B)))
                     => k5_pre_topc(A,B,C,k6_pre_topc(B,D)) = k6_pre_topc(A,k5_pre_topc(A,B,C,D)) ) ) ) ) ) ) ),
    file(tops_2,t73_tops_2),
    [interesting(0.00)]).

fof(t52_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)) )
             => k5_pre_topc(A,B,C,k2_pre_topc(B)) = k2_pre_topc(A) ) ) ) ),
    file(tops_2,t52_tops_2),
    [interesting(0.00)]).

fof(t74_tops_2,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)) )
             => ( 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)))
                     => k4_pre_topc(A,B,C,k6_pre_topc(A,D)) = k6_pre_topc(B,k4_pre_topc(A,B,C,D)) ) ) ) ) ) ) ),
    file(tops_2,t74_tops_2),
    [interesting(0.00)]).

fof(t45_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 )
       => k2_funct_2(A,B,C,A) = k2_relat_1(C) ) ) ),
    file(funct_2,t45_funct_2),
    [interesting(0.00)]).

fof(t21_yellow_8,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_yellow_8(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(D,C)
                   => ( v3_pre_topc(D,A)
                      & r2_hidden(B,D) ) ) ) ) ) ) ),
    file(yellow_8,t21_yellow_8),
    [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(t16_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k3_group_1(A,k2_group_1(A)) = k2_group_1(A) ) ),
    file(group_1,t16_group_1),
    [interesting(0.00)]).

fof(d5_borsuk_1,definition,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_pre_topc(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ( C = k6_borsuk_1(A,B)
              <=> ( u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))
                  & u1_pre_topc(C) = a_3_0_borsuk_1(A,B,C) ) ) ) ) ) ),
    file(borsuk_1,d5_borsuk_1),
    [interesting(0.00)]).

fof(t45_borsuk_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ( v3_pre_topc(C,k6_borsuk_1(A,B))
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
                    & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D)
                    & ! [E] : ~ ( r2_hidden(E,D)
                        & ! [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                           => ! [G] : 
                                ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
                               => ~ ( E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G)
                                    & v3_pre_topc(F,A)
                                    & v3_pre_topc(G,B) ) ) ) ) ) ) ) ) ) ),
    file(borsuk_1,t45_borsuk_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(t45_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B) ) ) ),
    file(tops_1,t45_tops_1),
    [interesting(0.00)]).

fof(t4_connsp_2,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( m1_connsp_2(C,A,B)
                      & m1_connsp_2(D,A,B) )
                  <=> m1_connsp_2(k5_subset_1(u1_struct_0(A),C,D),A,B) ) ) ) ) ) ),
    file(connsp_2,t4_connsp_2),
    [interesting(0.00)]).

fof(t38_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)))
             => ( ( v3_pre_topc(B,A)
                  & v3_pre_topc(C,A) )
               => v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    file(tops_1,t38_tops_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(t22_yellow_8,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_yellow_8(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r2_hidden(B,D)
                      & v3_pre_topc(D,A)
                      & ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r2_hidden(E,C)
                              & r1_tarski(E,D) ) ) ) ) ) ) ) ),
    file(yellow_8,t22_yellow_8),
    [interesting(0.00)]).

fof(t80_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != k1_xboole_0
                    & v3_pre_topc(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) ) ),
    file(tops_1,t80_tops_1),
    [interesting(0.00)]).

fof(t4_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) )
      & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B))
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t4_xboole_0),
    [interesting(0.00)]).

fof(t40_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( v4_group_1(A)
                   => k4_group_2(A,D,k4_group_2(A,C,B)) = k4_group_2(A,k1_group_1(A,C,D),B) ) ) ) ) ) ),
    file(group_2,t40_group_2),
    [interesting(0.00)]).

fof(t43_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( k3_group_2(A,k2_group_1(A),B) = B
            & k4_group_2(A,k2_group_1(A),B) = B ) ) ) ),
    file(group_2,t43_group_2),
    [interesting(0.00)]).

fof(t32_yellow_9,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))))
         => ( ( r1_tarski(B,u1_pre_topc(A))
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v3_pre_topc(C,A)
                   => ! [D] : 
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( r2_hidden(D,C)
                            & ! [E] : 
                                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                               => ~ ( r2_hidden(E,B)
                                    & r2_hidden(D,E)
                                    & r1_tarski(E,C) ) ) ) ) ) ) )
           => m1_cantor_1(B,A) ) ) ) ),
    file(yellow_9,t32_yellow_9),
    [interesting(0.00)]).

fof(d13_pre_topc,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(u1_struct_0(A)))
             => ( C = k6_pre_topc(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( v3_pre_topc(E,A)
                              & r2_hidden(D,E)
                              & r1_xboole_0(B,E) ) ) ) ) ) ) ) ) ),
    file(pre_topc,d13_pre_topc),
    [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(t4_topgrp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_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)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,C)
                          & r1_tarski(D,E) )
                       => r1_tarski(k2_group_2(A,B,D),k2_group_2(A,C,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t12_group_2,t12_group_2]),
    [file(topgrp_1,t4_topgrp_1),interesting(0.00)]).

fof(t29_urysohn1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_compts_1(A)
      <=> ! [B] : 
            ( ( v3_pre_topc(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] : 
                        ( ( v3_pre_topc(D,A)
                          & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                       => ~ ( r2_hidden(C,D)
                            & r1_tarski(k6_pre_topc(A,D),B) ) ) ) ) ) ) ) ),
    file(urysohn1,t29_urysohn1),
    [interesting(0.00)]).