fof(t41_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_connsp_1(k1_connsp_1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_connsp_1,t33_connsp_1,d1_setfam_1,t27_connsp_1]),
    [file(connsp_1,t41_connsp_1),interesting(1.00)]).

fof(t28_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_connsp_1(k2_pre_topc(A),A)
      <=> v1_connsp_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_pre_topc,d3_connsp_1,t14_pre_topc,t16_pre_topc,t16_pre_topc,t7_connsp_1,d2_connsp_1,d2_connsp_1,t39_pre_topc,t39_pre_topc,t6_connsp_1,d2_connsp_1,d2_connsp_1,d3_connsp_1]),
    [file(connsp_1,t28_connsp_1),interesting(0.94)]).

fof(t30_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
       => v1_connsp_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_connsp_1,s3_subset_1,t14_pre_topc,d4_tarski,d3_tarski,d10_xboole_0,t29_connsp_1,d1_tarski,d1_setfam_1,t27_connsp_1,t28_connsp_1]),
    [file(connsp_1,t30_connsp_1),interesting(0.90)]).

fof(t32_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
       => v1_connsp_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_connsp_1,t30_connsp_1]),
    [file(connsp_1,t32_connsp_1),interesting(0.88)]).

fof(t20_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_connsp_1(B,A)
           => v2_connsp_1(k6_pre_topc(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_pre_topc,t19_connsp_1]),
    [file(connsp_1,t20_connsp_1),interesting(0.87)]).

fof(t40_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(B,k1_connsp_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_connsp_1,t33_connsp_1,d1_setfam_1,t3_setfam_1]),
    [file(connsp_1,t40_connsp_1),interesting(0.84)]).

fof(t43_connsp_1,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)))
         => ( r3_connsp_1(A,B)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & B = k1_connsp_1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_connsp_1,t34_connsp_1,t41_pre_topc,d7_connsp_1,t92_zfmisc_1,t41_connsp_1,d5_connsp_1,t41_connsp_1,t42_connsp_1,d5_connsp_1]),
    [file(connsp_1,t43_connsp_1),interesting(0.84)]).

fof(t35_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r3_connsp_1(A,B)
           => v4_pre_topc(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_pre_topc,d5_connsp_1,t20_connsp_1,d5_connsp_1,t52_pre_topc]),
    [file(connsp_1,t35_connsp_1),interesting(0.83)]).

fof(t31_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_connsp_1,d4_connsp_1,d3_xboole_0,d7_xboole_0,t2_connsp_1,t18_connsp_1,d2_xboole_0,d4_connsp_1]),
    [file(connsp_1,t31_connsp_1),interesting(0.82)]).

fof(t29_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_connsp_1(k1_struct_0(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_connsp_1,t2_connsp_1,d7_xboole_0,t44_zfmisc_1]),
    [file(connsp_1,t29_connsp_1),interesting(0.80)]).

fof(t44_connsp_1,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))
             => ( ( r3_connsp_1(A,B)
                  & r2_hidden(C,B) )
               => B = k1_connsp_1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_connsp_1,d3_xboole_0,d7_xboole_0,t43_connsp_1,t36_connsp_1,t2_connsp_1]),
    [file(connsp_1,t44_connsp_1),interesting(0.76)]).

fof(t24_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => ( v2_connsp_1(C,A)
                    <=> v2_connsp_1(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_pre_topc,t12_pre_topc,t12_pre_topc,d3_connsp_1,t11_connsp_1,t43_pre_topc,t43_pre_topc,t17_xboole_1,t16_pre_topc,t43_pre_topc,t17_xboole_1,t27_xboole_1,t17_xboole_1,t17_xboole_1,t14_pre_topc,t7_xboole_1,t1_xboole_1,t19_xboole_1,t19_xboole_1,d10_xboole_0,t43_pre_topc,t17_xboole_1,t16_pre_topc,t43_pre_topc,t17_xboole_1,t27_xboole_1,t17_xboole_1,t17_xboole_1,t14_pre_topc,t7_xboole_1,t1_xboole_1,t19_xboole_1,t19_xboole_1,d10_xboole_0,t43_pre_topc,t11_connsp_1,d3_connsp_1,d3_connsp_1,t11_connsp_1,t43_pre_topc,t43_pre_topc,t43_pre_topc,t43_pre_topc,t15_pre_topc,t16_xboole_1,t43_pre_topc,t15_pre_topc,t16_xboole_1,t43_pre_topc,t11_connsp_1,d3_connsp_1]),
    [file(connsp_1,t24_connsp_1),interesting(0.75)]).

fof(t2_connsp_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_connsp_1(A,B,C)
               => r1_xboole_0(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_connsp_1,t48_pre_topc,t27_xboole_1,t3_xboole_1,d7_xboole_0]),
    [file(connsp_1,t2_connsp_1),interesting(0.74)]).

fof(t46_connsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                <=> r3_connsp_1(A,C) ) )
           => r1_pre_topc(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_pre_topc,t43_connsp_1,t92_zfmisc_1,t40_connsp_1,d3_tarski,d10_xboole_0,d8_pre_topc]),
    [file(connsp_1,t46_connsp_1),interesting(0.74)]).

fof(t34_connsp_1,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)))
         => ~ ( r3_connsp_1(A,B)
              & B = k1_pre_topc(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_connsp_1,t2_xboole_1,d5_connsp_1]),
    [file(connsp_1,t34_connsp_1),interesting(0.71)]).

fof(t36_connsp_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)))
             => ~ ( r3_connsp_1(A,B)
                  & r3_connsp_1(A,C)
                  & B != C
                  & ~ r1_connsp_1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_connsp_1,t18_connsp_1,t7_xboole_1,d5_connsp_1]),
    [file(connsp_1,t36_connsp_1),interesting(0.71)]).

fof(t39_connsp_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)))
             => ( ( v1_connsp_1(A)
                  & v2_connsp_1(B,A)
                  & r4_connsp_1(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),C) )
               => v2_connsp_1(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_connsp_1,d5_connsp_1,t14_pre_topc,d10_pre_topc,t31_subset_1,t17_pre_topc,t22_pre_topc,t17_pre_topc,t2_connsp_1,t7_xboole_1,t43_subset_1,d7_xboole_0,t24_connsp_1,t26_subset_1,t43_subset_1,t27_xboole_1,d7_xboole_0,t23_xboole_1,t3_xboole_1,d7_xboole_0,t43_subset_1,t17_pre_topc,d10_pre_topc,t16_pre_topc,t21_connsp_1,t24_connsp_1,t26_subset_1,t7_xboole_1,d5_connsp_1,t7_xboole_1,t19_xboole_1,t17_pre_topc,d7_xboole_0,t3_xboole_1,t26_subset_1,t43_subset_1,t27_xboole_1,d7_xboole_0,t23_xboole_1,t3_xboole_1,d7_xboole_0,t43_subset_1,t17_pre_topc,d10_pre_topc,t16_pre_topc,t21_connsp_1,t24_connsp_1,t7_xboole_1,d5_connsp_1,t7_xboole_1,t26_subset_1,t7_xboole_1,t19_xboole_1,t17_pre_topc,d7_xboole_0,t3_xboole_1,t17_connsp_1,t16_connsp_1]),
    [file(connsp_1,t39_connsp_1),interesting(0.67)]).

fof(t19_connsp_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)))
             => ( ( v2_connsp_1(B,A)
                  & r1_tarski(B,C)
                  & r1_tarski(C,k6_pre_topc(A,B)) )
               => v2_connsp_1(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_connsp_1,d1_connsp_1,d7_xboole_0,t49_pre_topc,t27_xboole_1,t3_xboole_1,t27_xboole_1,t3_xboole_1,t21_xboole_1,t49_pre_topc,t27_xboole_1,t3_xboole_1,t27_xboole_1,t3_xboole_1,t21_xboole_1,t17_connsp_1]),
    [file(connsp_1,t19_connsp_1),interesting(0.66)]).

fof(t18_connsp_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)))
             => ( ( v2_connsp_1(B,A)
                  & v2_connsp_1(C,A) )
               => ( r1_connsp_1(A,B,C)
                  | v2_connsp_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_connsp_1,t2_connsp_1,d7_xboole_0,t7_xboole_1,t7_xboole_1,t8_xboole_1,d10_xboole_0,t7_xboole_1,t28_xboole_1,t8_connsp_1,t8_connsp_1,t7_xboole_1,t8_xboole_1,d10_xboole_0,t7_xboole_1,t28_xboole_1,t17_connsp_1]),
    [file(connsp_1,t18_connsp_1),interesting(0.65)]).

fof(t25_connsp_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)
                  & v2_connsp_1(k4_subset_1(u1_struct_0(A),B,C),A)
                  & v2_connsp_1(k5_subset_1(u1_struct_0(A),B,C),A) )
               => ( v2_connsp_1(B,A)
                  & v2_connsp_1(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_connsp_1,d10_pre_topc,t7_xboole_1,t16_pre_topc,t16_pre_topc,t55_xboole_1,t51_xboole_1,t51_xboole_1,t28_xboole_1,t28_xboole_1,t43_pre_topc,t10_connsp_1,t24_connsp_1,t21_connsp_1,t24_connsp_1]),
    [file(connsp_1,t25_connsp_1),interesting(0.61)]).

fof(t37_connsp_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)))
             => ~ ( r3_connsp_1(A,B)
                  & r3_connsp_1(A,C)
                  & B != C
                  & ~ r1_xboole_0(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_connsp_1,t2_connsp_1]),
    [file(connsp_1,t37_connsp_1),interesting(0.60)]).

fof(t42_connsp_1,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))
             => ( ( v2_connsp_1(B,A)
                  & r1_tarski(k1_connsp_1(A,C),B) )
               => B = k1_connsp_1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_connsp_1,t40_connsp_1,t92_zfmisc_1,d10_xboole_0]),
    [file(connsp_1,t42_connsp_1),interesting(0.55)]).

fof(t38_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_connsp_1(B,A)
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( r3_connsp_1(A,C)
                    & ~ r1_xboole_0(B,C)
                    & ~ r1_tarski(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_connsp_1,d5_connsp_1,t18_connsp_1,t7_xboole_1,d5_connsp_1,t7_xboole_1]),
    [file(connsp_1,t38_connsp_1),interesting(0.53)]).

fof(t14_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_connsp_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ~ ( v3_pre_topc(B,A)
                & v4_pre_topc(B,A)
                & B != k1_pre_topc(A)
                & B != k2_pre_topc(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_pre_topc,t53_pre_topc,t26_subset_1,t17_pre_topc,d7_xboole_0,d7_xboole_0,t13_connsp_1,d2_connsp_1,t5_connsp_1,t2_connsp_1,t25_pre_topc,t23_pre_topc]),
    [file(connsp_1,t14_connsp_1),interesting(0.43)]).

fof(t27_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v2_connsp_1(C,A) ) )
           => ( k6_setfam_1(u1_struct_0(A),B) = k1_pre_topc(A)
              | v2_connsp_1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_pre_topc,t3_setfam_1,d4_tarski,t48_pre_topc,d1_setfam_1,d3_xboole_0,d7_xboole_0,d1_connsp_1,t26_connsp_1]),
    [file(connsp_1,t27_connsp_1),interesting(0.43)]).

fof(t13_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_connsp_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ~ ( B != k1_pre_topc(A)
                & B != k2_pre_topc(A)
                & r1_xboole_0(k6_pre_topc(A,B),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t23_pre_topc,t48_pre_topc,t27_xboole_1,t3_xboole_1,d7_xboole_0,t48_pre_topc,t27_xboole_1,t3_xboole_1,d7_xboole_0,d1_connsp_1,t18_pre_topc,t17_pre_topc,d2_connsp_1,t11_connsp_1,t25_pre_topc,t52_pre_topc,t23_pre_topc]),
    [file(connsp_1,t13_connsp_1),interesting(0.38)]).

fof(t5_connsp_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)))
             => ( ( k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                  & r1_connsp_1(A,B,C) )
               => ( v3_pre_topc(B,A)
                  & v4_pre_topc(B,A)
                  & v3_pre_topc(C,A)
                  & v4_pre_topc(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_connsp_1,t25_pre_topc,t48_pre_topc,t52_pre_topc,t50_pre_topc,t7_xboole_1,t73_xboole_1,d10_xboole_0,t7_xboole_1,t73_xboole_1,d10_xboole_0,t25_pre_topc,d1_connsp_1,t52_pre_topc,t53_pre_topc]),
    [file(connsp_1,t5_connsp_1),interesting(0.37)]).

fof(t4_connsp_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)))
             => ( ( k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                  & v3_pre_topc(B,A)
                  & v3_pre_topc(C,A)
                  & r1_xboole_0(B,C) )
               => r1_connsp_1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t53_pre_topc,t25_pre_topc,t52_pre_topc,t3_connsp_1]),
    [file(connsp_1,t4_connsp_1),interesting(0.34)]).

fof(t16_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_connsp_1(B,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)))
                   => ~ ( B = k4_subset_1(u1_struct_0(A),C,D)
                        & r1_connsp_1(A,C,D)
                        & C != k1_pre_topc(A)
                        & D != k1_pre_topc(A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_pre_topc,t7_xboole_1,t16_pre_topc,t16_pre_topc,t7_connsp_1,d2_connsp_1,d3_connsp_1,d3_connsp_1,d2_connsp_1,t39_pre_topc,t39_pre_topc,t6_connsp_1]),
    [file(connsp_1,t16_connsp_1),interesting(0.34)]).

fof(t26_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v2_connsp_1(C,A) ) )
           => ( ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( C != k1_pre_topc(A)
                      & r2_hidden(C,B)
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r2_hidden(D,B)
                              & D != C
                              & r1_connsp_1(A,C,D) ) ) ) )
              | v2_connsp_1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_connsp_1,d7_xboole_0,t92_zfmisc_1,t92_zfmisc_1,t17_connsp_1,t8_connsp_1,t94_zfmisc_1,t7_xboole_1,d10_xboole_0,t7_xboole_1,t28_xboole_1,t92_zfmisc_1,t17_connsp_1,t8_connsp_1,t94_zfmisc_1,t7_xboole_1,d10_xboole_0,t7_xboole_1,t28_xboole_1,t17_connsp_1,t16_connsp_1]),
    [file(connsp_1,t26_connsp_1),interesting(0.26)]).

fof(t11_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_connsp_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_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                    & B != k1_pre_topc(A)
                    & C != k1_pre_topc(A)
                    & v4_pre_topc(B,A)
                    & v4_pre_topc(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_connsp_1,d2_connsp_1,d2_connsp_1,t5_connsp_1,t2_connsp_1]),
    [file(connsp_1,t11_connsp_1),interesting(0.25)]).

fof(t23_connsp_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)))
             => ~ ( v2_connsp_1(B,A)
                  & ~ r1_xboole_0(B,C)
                  & k6_subset_1(u1_struct_0(A),B,C) != k1_pre_topc(A)
                  & r1_xboole_0(B,k2_tops_1(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t32_subset_1,t15_pre_topc,t18_pre_topc,t23_xboole_1,t17_xboole_1,t49_pre_topc,t48_pre_topc,t48_pre_topc,t17_xboole_1,t49_pre_topc,t16_connsp_1,d1_connsp_1,d7_xboole_0,t15_xboole_1,t16_xboole_1,t16_xboole_1,t16_xboole_1,t23_xboole_1,t27_xboole_1,t27_xboole_1,t8_xboole_1,t27_xboole_1,d2_tops_1,t3_xboole_1,d7_xboole_0]),
    [file(connsp_1,t23_connsp_1),interesting(0.23)]).

fof(t7_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,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(B)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( C = E
                              & D = F
                              & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),k2_pre_topc(B))
                              & r1_connsp_1(A,C,D) )
                           => r1_connsp_1(B,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_connsp_1,t7_xboole_1,t1_xboole_1,t16_pre_topc,t47_pre_topc,t16_xboole_1,t15_pre_topc,t47_pre_topc,t16_xboole_1,t15_pre_topc,d7_xboole_0,d1_connsp_1]),
    [file(connsp_1,t7_connsp_1),interesting(0.22)]).

fof(t21_connsp_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)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_connsp_1(A)
                      & v2_connsp_1(B,A)
                      & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k4_subset_1(u1_struct_0(A),C,D)
                      & r1_connsp_1(A,C,D) )
                   => ( v2_connsp_1(k4_subset_1(u1_struct_0(A),B,C),A)
                      & v2_connsp_1(k4_subset_1(u1_struct_0(A),B,D),A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_pre_topc,t4_xboole_1,t7_xboole_1,t8_connsp_1,t2_connsp_1,t7_xboole_1,t73_xboole_1,t8_connsp_1,t9_connsp_1,t4_xboole_1,d2_connsp_1,t15_xboole_1,t8_connsp_1,t2_connsp_1,t7_xboole_1,t73_xboole_1,t8_connsp_1,t9_connsp_1,t4_xboole_1,d2_connsp_1,t15_xboole_1,t17_connsp_1,t16_connsp_1]),
    [file(connsp_1,t21_connsp_1),interesting(0.21)]).

fof(t15_connsp_1,theorem,(
    ! [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)) )
             => ( ( v5_pre_topc(C,A,B)
                  & k4_pre_topc(A,B,C,k2_pre_topc(A)) = k2_pre_topc(B)
                  & v1_connsp_1(A) )
               => v1_connsp_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_pre_topc,t12_pre_topc,t11_connsp_1,d7_xboole_0,t3_xboole_1,t12_pre_topc,t48_funct_2,t12_pre_topc,t175_relat_1,t137_funct_1,t171_relat_1,d7_xboole_0,d12_pre_topc,t45_funct_2,t174_relat_1,t11_connsp_1]),
    [file(connsp_1,t15_connsp_1),interesting(0.17)]).

fof(t12_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_connsp_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_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                    & B != k1_pre_topc(A)
                    & C != k1_pre_topc(A)
                    & v3_pre_topc(B,A)
                    & v3_pre_topc(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_connsp_1,d2_connsp_1,d2_connsp_1,t5_connsp_1,t2_connsp_1]),
    [file(connsp_1,t12_connsp_1),interesting(0.04)]).

fof(t53_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
             => k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) )
            & ( ( v2_pre_topc(A)
                & k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) )
             => v3_pre_topc(B,A) ) ) ) ) ),
    file(pre_topc,t53_pre_topc),
    [interesting(0.00)]).

fof(t25_pre_topc,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)))
             => ( ( k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                  & r1_xboole_0(B,C) )
               => C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) ) ) ) ) ),
    file(pre_topc,t25_pre_topc),
    [interesting(0.00)]).

fof(t52_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
             => k6_pre_topc(A,B) = B )
            & ( ( v2_pre_topc(A)
                & k6_pre_topc(A,B) = B )
             => v4_pre_topc(B,A) ) ) ) ) ),
    file(pre_topc,t52_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(d1_connsp_1,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)))
             => ( r1_connsp_1(A,B,C)
              <=> ( r1_xboole_0(k6_pre_topc(A,B),C)
                  & r1_xboole_0(B,k6_pre_topc(A,C)) ) ) ) ) ) ),
    file(connsp_1,d1_connsp_1),
    [interesting(0.00)]).

fof(t3_connsp_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)))
             => ( ( k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                  & v4_pre_topc(B,A)
                  & v4_pre_topc(C,A)
                  & r1_xboole_0(B,C) )
               => r1_connsp_1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t52_pre_topc,d7_xboole_0,d1_connsp_1]),
    [file(connsp_1,t3_connsp_1),interesting(0.00)]).

fof(d2_connsp_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_connsp_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_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)
                    & r1_connsp_1(A,B,C)
                    & B != k1_pre_topc(A)
                    & C != k1_pre_topc(A) ) ) ) ) ) ),
    file(connsp_1,d2_connsp_1),
    [interesting(0.00)]).

fof(t48_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k6_pre_topc(A,B)) ) ) ),
    file(pre_topc,t48_pre_topc),
    [interesting(0.00)]).

fof(t27_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ),
    file(xboole_1,t27_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(t50_pre_topc,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)))
             => k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ),
    file(pre_topc,t50_pre_topc),
    [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(t73_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,k2_xboole_0(B,C))
        & r1_xboole_0(A,C) )
     => r1_tarski(A,B) ) ),
    file(xboole_1,t73_xboole_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(t26_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => r1_xboole_0(B,k3_subset_1(A,B)) ) ),
    file(subset_1,t26_subset_1),
    [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(t23_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ ( B != k2_pre_topc(A)
                & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k1_xboole_0 )
            & ~ ( k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0
                & B = k2_pre_topc(A) ) ) ) ) ),
    file(pre_topc,t23_pre_topc),
    [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(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(t48_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 )
       => k3_funct_2(A,B,C,B) = A ) ) ),
    file(funct_2,t48_funct_2),
    [interesting(0.00)]).

fof(t175_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) ),
    file(relat_1,t175_relat_1),
    [interesting(0.00)]).

fof(t137_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) ),
    file(funct_1,t137_funct_1),
    [interesting(0.00)]).

fof(t171_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(relat_1,t171_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(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(t174_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ~ ( A != k1_xboole_0
          & r1_tarski(A,k2_relat_1(B))
          & k10_relat_1(B,A) = k1_xboole_0 ) ) ),
    file(relat_1,t174_relat_1),
    [interesting(0.00)]).

fof(t1_connsp_1,theorem,(
    $true ),
    file(connsp_1,t1_connsp_1),
    [interesting(0.00)]).

fof(t24_pre_topc,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)))
             => ( k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C
               => k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C) ) ) ) ) ),
    file(pre_topc,t24_pre_topc),
    [interesting(0.00)]).

fof(t15_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = B ) ) ),
    file(pre_topc,t15_pre_topc),
    [interesting(0.00)]).

fof(t24_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) ),
    file(xboole_1,t24_xboole_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(t23_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    [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(t22_connsp_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)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k4_subset_1(u1_struct_0(A),C,D)
                      & r1_connsp_1(A,C,D)
                      & v4_pre_topc(B,A) )
                   => ( v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)
                      & v4_pre_topc(k4_subset_1(u1_struct_0(A),B,D),A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_pre_topc,t24_pre_topc,t48_pre_topc,d1_connsp_1,d7_xboole_0,t50_pre_topc,t15_pre_topc,t24_xboole_1,t4_xboole_1,t24_xboole_1,t23_xboole_1,t28_xboole_1,t52_pre_topc]),
    [file(connsp_1,t22_connsp_1),interesting(0.00)]).

fof(t32_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)) ) ) ),
    file(subset_1,t32_subset_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(t49_pre_topc,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(k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ),
    file(pre_topc,t49_pre_topc),
    [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(t16_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( r1_tarski(B,k2_pre_topc(A))
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(pre_topc,t16_pre_topc),
    [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(t47_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => k6_pre_topc(B,D) = k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) ) ) ) ) ) ),
    file(pre_topc,t47_pre_topc),
    [interesting(0.00)]).

fof(t16_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ),
    file(xboole_1,t16_xboole_1),
    [interesting(0.00)]).

fof(d3_connsp_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_connsp_1(B,A)
          <=> v1_connsp_1(k3_pre_topc(A,B)) ) ) ) ),
    file(connsp_1,d3_connsp_1),
    [interesting(0.00)]).

fof(t39_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ),
    file(pre_topc,t39_pre_topc),
    [interesting(0.00)]).

fof(t6_connsp_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,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(B)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( E = C
                              & F = D
                              & r1_connsp_1(B,E,F) )
                           => r1_connsp_1(A,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_connsp_1,t39_pre_topc,t47_pre_topc,t16_xboole_1,t15_pre_topc,t47_pre_topc,t16_xboole_1,t15_pre_topc,d7_xboole_0,d1_connsp_1]),
    [file(connsp_1,t6_connsp_1),interesting(0.00)]).

fof(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_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(d2_tops_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) ),
    file(tops_1,d2_tops_1),
    [interesting(0.00)]).

fof(t55_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) ),
    file(xboole_1,t55_xboole_1),
    [interesting(0.00)]).

fof(t51_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A ),
    file(xboole_1,t51_xboole_1),
    [interesting(0.00)]).

fof(t43_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v4_pre_topc(C,B)
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & v4_pre_topc(D,A)
                    & k3_xboole_0(D,k2_pre_topc(B)) = C ) ) ) ) ) ),
    file(pre_topc,t43_pre_topc),
    [interesting(0.00)]).

fof(t51_pre_topc,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(k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))) ) ) ) ),
    file(pre_topc,t51_pre_topc),
    [interesting(0.00)]).

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

fof(t22_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = B ) ) ),
    file(pre_topc,t22_pre_topc),
    [interesting(0.00)]).

fof(t10_connsp_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)))
             => ( ( ( v4_pre_topc(B,A)
                    & v4_pre_topc(C,A) )
                  | ( v3_pre_topc(B,A)
                    & v3_pre_topc(C,A) ) )
               => r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_subset_1,t51_pre_topc,t27_xboole_1,t51_pre_topc,t27_xboole_1,t53_pre_topc,t17_pre_topc,t53_pre_topc,t26_subset_1,d7_xboole_0,t17_xboole_1,t27_xboole_1,t1_xboole_1,t17_xboole_1,t27_xboole_1,t1_xboole_1,t3_xboole_1,d7_xboole_0,d1_connsp_1,d6_pre_topc,t17_pre_topc,t32_subset_1,t17_pre_topc,t22_pre_topc,t32_subset_1,t32_subset_1,t17_pre_topc,t22_pre_topc,t32_subset_1]),
    [file(connsp_1,t10_connsp_1),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(t19_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    [interesting(0.00)]).

fof(t8_connsp_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)))
             => ! [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_connsp_1(A,B,C)
                          & r1_tarski(D,B)
                          & r1_tarski(E,C) )
                       => r1_connsp_1(A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_connsp_1,t49_pre_topc,t27_xboole_1,t3_xboole_1,d7_xboole_0,d1_connsp_1]),
    [file(connsp_1,t8_connsp_1),interesting(0.00)]).

fof(t9_connsp_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)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r1_connsp_1(A,B,C)
                      & r1_connsp_1(A,B,D) )
                   => r1_connsp_1(A,B,k4_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_connsp_1,d7_xboole_0,t23_xboole_1,d7_xboole_0,t50_pre_topc,t23_xboole_1,d7_xboole_0,d1_connsp_1]),
    [file(connsp_1,t9_connsp_1),interesting(0.00)]).

fof(t17_connsp_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)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( v2_connsp_1(B,A)
                      & r1_tarski(B,k4_subset_1(u1_struct_0(A),C,D))
                      & r1_connsp_1(A,C,D)
                      & ~ r1_tarski(B,C)
                      & ~ r1_tarski(B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t73_xboole_1,d7_xboole_0,t17_xboole_1,t8_connsp_1,t23_xboole_1,t28_xboole_1,t16_connsp_1]),
    [file(connsp_1,t17_connsp_1),interesting(0.00)]).

fof(d4_connsp_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_connsp_1(A,B,C)
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & v2_connsp_1(D,A)
                    & r2_hidden(B,D)
                    & r2_hidden(C,D) ) ) ) ) ) ),
    file(connsp_1,d4_connsp_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(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(s3_subset_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1))
      & ! [B] : 
          ( m1_subset_1(B,f1_s3_subset_1)
         => ( r2_hidden(B,A)
          <=> p1_s3_subset_1(B) ) ) ) ),
    file(subset_1,s3_subset_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(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(t44_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( k1_tarski(A) = k2_xboole_0(B,C)
      & B != C
      & B != k1_xboole_0
      & C != k1_xboole_0 ) ),
    file(zfmisc_1,t44_zfmisc_1),
    [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(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(t41_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( B != k1_pre_topc(A)
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ r2_hidden(C,B) ) ) ) ) ),
    file(pre_topc,t41_pre_topc),
    [interesting(0.00)]).

fof(t3_setfam_1,theorem,(
    ! [A] : r1_tarski(k1_setfam_1(A),k3_tarski(A)) ),
    file(setfam_1,t3_setfam_1),
    [interesting(0.00)]).

fof(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [interesting(0.00)]).

fof(t94_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(C,B) )
     => r1_tarski(k3_tarski(A),B) ) ),
    file(zfmisc_1,t94_zfmisc_1),
    [interesting(0.00)]).

fof(d5_connsp_1,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r3_connsp_1(A,B)
          <=> ( v2_connsp_1(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v2_connsp_1(C,A)
                      & r1_tarski(B,C) )
                   => B = C ) ) ) ) ) ) ),
    file(connsp_1,d5_connsp_1),
    [interesting(0.00)]).

fof(t21_xboole_1,theorem,(
    ! [A,B] : k3_xboole_0(A,k2_xboole_0(A,B)) = A ),
    file(xboole_1,t21_xboole_1),
    [interesting(0.00)]).

fof(d6_connsp_1,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)))
             => ( r4_connsp_1(A,B,C)
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))
                    & D = C
                    & r3_connsp_1(k3_pre_topc(A,B),D) ) ) ) ) ) ),
    file(connsp_1,d6_connsp_1),
    [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(t43_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_xboole_0(B,C)
          <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) ),
    file(subset_1,t43_subset_1),
    [interesting(0.00)]).

fof(d7_connsp_1,definition,(
    ! [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)))
             => ( C = k1_connsp_1(A,B)
              <=> ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                    & ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( r2_hidden(E,D)
                        <=> ( v2_connsp_1(E,A)
                            & r2_hidden(B,E) ) ) )
                    & k5_setfam_1(u1_struct_0(A),D) = C ) ) ) ) ) ),
    file(connsp_1,d7_connsp_1),
    [interesting(0.00)]).

fof(t33_connsp_1,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(k1_zfmisc_1(u1_struct_0(A))))
             => ~ ( ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ( r2_hidden(D,C)
                      <=> ( v2_connsp_1(D,A)
                          & r2_hidden(B,D) ) ) )
                  & C = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_connsp_1,d1_tarski]),
    [file(connsp_1,t33_connsp_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(t45_connsp_1,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))
             => ( B = k1_connsp_1(A,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,B)
                     => k1_connsp_1(A,D) = B ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_connsp_1,t37_connsp_1,d7_xboole_0,t40_connsp_1,d3_xboole_0]),
    [file(connsp_1,t45_connsp_1),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)]).