% Mizar ND problem: t4_borsuk_3,borsuk_3,137,77 
fof(dh_c1_12__borsuk_3,definition,
    ( ( ( v2_pre_topc(c1_12__borsuk_3)
        & l1_pre_topc(c1_12__borsuk_3) )
     => ! [A] : 
          ( ( v3_struct_0(A)
            & v2_pre_topc(A)
            & l1_pre_topc(A) )
         => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,A))
            & v3_struct_0(k6_borsuk_1(A,c1_12__borsuk_3)) ) ) )
   => ! [B] : 
        ( ( v2_pre_topc(B)
          & l1_pre_topc(B) )
       => ! [C] : 
            ( ( v3_struct_0(C)
              & v2_pre_topc(C)
              & l1_pre_topc(C) )
           => ( v3_struct_0(k6_borsuk_1(B,C))
              & v3_struct_0(k6_borsuk_1(C,B)) ) ) ) ),
    introduced(definition,[new_symbol(c1_12__borsuk_3),file(borsuk_3,c1_12__borsuk_3)]),
    [interesting(0.8),axiom,file(borsuk_3,c1_12__borsuk_3)]).

fof(dh_c2_12__borsuk_3,definition,
    ( ( ( v3_struct_0(c2_12__borsuk_3)
        & v2_pre_topc(c2_12__borsuk_3)
        & l1_pre_topc(c2_12__borsuk_3) )
     => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,c2_12__borsuk_3))
        & v3_struct_0(k6_borsuk_1(c2_12__borsuk_3,c1_12__borsuk_3)) ) )
   => ! [A] : 
        ( ( v3_struct_0(A)
          & v2_pre_topc(A)
          & l1_pre_topc(A) )
       => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,A))
          & v3_struct_0(k6_borsuk_1(A,c1_12__borsuk_3)) ) ) ),
    introduced(definition,[new_symbol(c2_12__borsuk_3),file(borsuk_3,c2_12__borsuk_3)]),
    [interesting(0.8),axiom,file(borsuk_3,c2_12__borsuk_3)]).

fof(rc4_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A) ) ) ),
    file(tops_1,rc4_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc4_tops_1)]).

fof(rc5_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_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A)
          & v3_tops_1(B,A) ) ) ),
    file(tops_1,rc5_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc5_tops_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(cc4_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_tops_1(B,A)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc4_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc4_tops_1)]).

fof(cc5_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v2_tops_1(B,A) )
           => ( v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc5_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc5_tops_1)]).

fof(cc6_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)
              & v3_tops_1(B,A) )
           => ( v1_xboole_0(B)
              & v3_pre_topc(B,A)
              & v4_pre_topc(B,A)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc6_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc6_tops_1)]).

fof(rc1_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) ) ) ),
    file(tops_1,rc1_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc1_tops_1)]).

fof(rc2_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)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc2_tops_1)]).

fof(rc3_tops_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)))
          & ~ v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc3_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc3_tops_1)]).

fof(rc6_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc6_pre_topc)]).

fof(rc7_pre_topc,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)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc7_pre_topc)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc1_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_xboole_0(B)
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) ),
    file(tops_1,cc1_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc1_tops_1)]).

fof(cc1_waybel12,theorem,(
    ! [A] : 
      ( ( v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
            & v1_finset_1(B) ) ) ) ),
    file(waybel12,cc1_waybel12),
    [interesting(0.9),axiom,file(waybel12,cc1_waybel12)]).

fof(cc2_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc2_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc2_tops_1)]).

fof(cc3_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_xboole_0(B)
           => v3_tops_1(B,A) ) ) ) ),
    file(tops_1,cc3_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc3_tops_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc3_waybel12,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_card_4(B) ) ) ),
    file(waybel12,rc3_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc3_waybel12)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(rc7_waybel12,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_card_4(B) ) ) ),
    file(waybel12,rc7_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc7_waybel12)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(free_g1_pre_topc,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,u1_pre_topc)]).

fof(fc4_borsuk_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v2_t_0topsp(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & v2_t_0topsp(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_2,fc4_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,fc4_borsuk_2)]).

fof(rc1_borsuk_3,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_t_0topsp(A) ) ),
    file(borsuk_3,rc1_borsuk_3),
    [interesting(0.9),axiom,file(borsuk_3,rc1_borsuk_3)]).

fof(rc2_waybel12,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc2_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc2_waybel12)]).

fof(rc4_waybel12,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc4_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc4_waybel12)]).

fof(rc6_waybel12,theorem,(
    ? [A] : 
      ( ~ v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc6_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc6_waybel12)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(abstractness_v1_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,v1_pre_topc)]).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(cc2_waybel12,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => v1_card_4(A) ) ),
    file(waybel12,cc2_waybel12),
    [interesting(0.9),axiom,file(waybel12,cc2_waybel12)]).

fof(cc4_borsuk_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_struct_0(A)
       => v2_t_0topsp(A) ) ) ),
    file(borsuk_2,cc4_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc4_borsuk_2)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(fc2_borsuk_1,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,fc2_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,fc2_borsuk_1)]).

fof(rc1_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc1_pre_topc)]).

fof(rc2_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc2_pre_topc)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k6_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & l1_pre_topc(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,k6_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k6_borsuk_1)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_12__borsuk_3,assumption,
    ( v2_pre_topc(c1_12__borsuk_3)
    & l1_pre_topc(c1_12__borsuk_3) ),
    introduced(assumption,[file(borsuk_3,c1_12__borsuk_3)]),
    [interesting(0.8),axiom,file(borsuk_3,c1_12__borsuk_3)]).

fof(dt_c2_12__borsuk_3,assumption,
    ( v3_struct_0(c2_12__borsuk_3)
    & v2_pre_topc(c2_12__borsuk_3)
    & l1_pre_topc(c2_12__borsuk_3) ),
    introduced(assumption,[file(borsuk_3,c2_12__borsuk_3)]),
    [interesting(0.8),axiom,file(borsuk_3,c2_12__borsuk_3)]).

fof(fc1_borsuk_3,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(borsuk_3,fc1_borsuk_3),
    [interesting(0.9),axiom,file(borsuk_3,fc1_borsuk_3)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(fc1_waybel12,theorem,(
    ! [A] : 
      ( ( v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v1_xboole_0(u1_struct_0(A))
        & v1_finset_1(u1_struct_0(A)) ) ) ),
    file(waybel12,fc1_waybel12),
    [interesting(0.9),axiom,file(waybel12,fc1_waybel12)]).

fof(fc2_borsuk_3,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(A)
     => v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(borsuk_3,fc2_borsuk_3),
    [interesting(0.9),axiom,file(borsuk_3,fc2_borsuk_3)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_waybel12,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & v3_struct_0(A) ) ),
    file(waybel12,rc1_waybel12),
    [interesting(0.9),axiom,file(waybel12,rc1_waybel12)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(redefinition_k12_mcart_1,definition,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ),
    file(mcart_1,k12_mcart_1),
    [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]).

fof(dt_k12_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(mcart_1,k12_mcart_1),
    [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(redefinition_k5_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(fraenkel_a_2_1_borsuk_1,definition,(
    ! [A,B,C] : 
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & v2_pre_topc(C)
        & l1_pre_topc(C) )
     => ( r2_hidden(A,a_2_1_borsuk_1(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E)
            & r2_hidden(D,u1_pre_topc(B))
            & r2_hidden(E,u1_pre_topc(C)) ) ) ) ),
    file(borsuk_1,a_2_1_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,a_2_1_borsuk_1)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_3_0_borsuk_1,definition,(
    ! [A,B,C,D] : 
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_pre_topc(D)
        & v2_pre_topc(D)
        & l1_pre_topc(D) )
     => ( r2_hidden(A,a_3_0_borsuk_1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D))))
            & A = k5_setfam_1(u1_struct_0(D),E)
            & r1_tarski(E,a_2_1_borsuk_1(B,C)) ) ) ) ),
    file(borsuk_1,a_3_0_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,a_3_0_borsuk_1)]).

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(0.9),axiom,file(borsuk_1,d5_borsuk_1)]).

fof(e1_12__borsuk_3,plain,
    ( u1_struct_0(k6_borsuk_1(c1_12__borsuk_3,c2_12__borsuk_3)) = k2_zfmisc_1(u1_struct_0(c1_12__borsuk_3),u1_struct_0(c2_12__borsuk_3))
    & u1_struct_0(k6_borsuk_1(c2_12__borsuk_3,c1_12__borsuk_3)) = k2_zfmisc_1(u1_struct_0(c2_12__borsuk_3),u1_struct_0(c1_12__borsuk_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_12__borsuk_3,dt_c2_12__borsuk_3])],[rc4_tops_1,rc5_tops_1,dt_k1_xboole_0,cc4_tops_1,cc5_tops_1,cc6_tops_1,fc1_xboole_0,rc1_tops_1,rc2_tops_1,rc2_waybel12,rc3_tops_1,rc3_waybel12,rc4_waybel12,rc6_pre_topc,rc6_waybel12,rc7_pre_topc,rc7_waybel12,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k3_tarski,cc1_tops_1,cc2_tops_1,cc2_waybel12,cc3_tops_1,fc1_borsuk_3,fc2_borsuk_3,fc4_borsuk_2,fc4_subset_1,rc1_borsuk_3,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_subset_1,redefinition_k5_setfam_1,dt_g1_pre_topc,dt_k1_zfmisc_1,dt_k5_setfam_1,dt_l1_struct_0,dt_m1_subset_1,cc1_relset_1,cc1_waybel12,cc4_borsuk_2,fc1_struct_0,fc1_subset_1,fc1_waybel12,fc2_borsuk_1,rc1_waybel12,rc2_pre_topc,rc3_struct_0,t1_subset,t3_subset,t4_subset,t7_boole,fraenkel_a_2_1_borsuk_1,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_k2_zfmisc_1,dt_k6_borsuk_1,dt_l1_pre_topc,dt_u1_pre_topc,dt_u1_struct_0,dt_c1_12__borsuk_3,dt_c2_12__borsuk_3,rc1_pre_topc,t2_tarski,fraenkel_a_3_0_borsuk_1,d5_borsuk_1]),
    [interesting(0.8),file(borsuk_3,e1_12__borsuk_3),[file(borsuk_3,e1_12__borsuk_3)]]).

fof(d1_struct_0,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_struct_0(A)
      <=> v1_xboole_0(u1_struct_0(A)) ) ) ),
    file(struct_0,d1_struct_0),
    [interesting(0.9),axiom,file(struct_0,d1_struct_0)]).

fof(e2_12__borsuk_3,plain,
    ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,c2_12__borsuk_3))
    & v3_struct_0(k6_borsuk_1(c2_12__borsuk_3,c1_12__borsuk_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_12__borsuk_3,dt_c2_12__borsuk_3])],[rc4_tops_1,rc5_tops_1,reflexivity_r1_tarski,cc4_tops_1,cc5_tops_1,cc6_tops_1,rc1_tops_1,rc2_tops_1,rc3_tops_1,rc6_pre_topc,rc7_pre_topc,dt_k1_zfmisc_1,cc1_relset_1,cc1_tops_1,cc1_waybel12,cc2_tops_1,cc3_tops_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_waybel12,rc5_struct_0,rc7_waybel12,t3_subset,t4_subset,t5_subset,free_g1_pre_topc,existence_m1_subset_1,dt_g1_pre_topc,dt_m1_subset_1,dt_u1_pre_topc,fc4_borsuk_2,rc1_borsuk_3,rc2_waybel12,rc4_waybel12,rc6_waybel12,t2_subset,antisymmetry_r2_hidden,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_k1_xboole_0,dt_l1_pre_topc,cc2_waybel12,cc4_borsuk_2,fc1_xboole_0,fc2_borsuk_1,rc1_pre_topc,rc2_pre_topc,t1_subset,existence_l1_struct_0,dt_k2_zfmisc_1,dt_k6_borsuk_1,dt_l1_struct_0,dt_u1_struct_0,dt_c1_12__borsuk_3,dt_c2_12__borsuk_3,fc1_borsuk_3,fc1_struct_0,fc1_waybel12,fc2_borsuk_3,fc4_subset_1,rc1_waybel12,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t6_boole,t7_boole,t8_boole,e1_12__borsuk_3,d1_struct_0]),
    [interesting(0.8),file(borsuk_3,e2_12__borsuk_3),[file(borsuk_3,e2_12__borsuk_3)]]).

fof(i3_12__borsuk_3,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_3,i3_12__borsuk_3)]),
    [interesting(0.8),trivial,file(borsuk_3,i3_12__borsuk_3)]).

fof(i2_12__borsuk_3,plain,
    ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,c2_12__borsuk_3))
    & v3_struct_0(k6_borsuk_1(c2_12__borsuk_3,c1_12__borsuk_3)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_12__borsuk_3,dt_c2_12__borsuk_3])],[e2_12__borsuk_3,i3_12__borsuk_3]),
    [interesting(0.8),file(borsuk_3,i2_12__borsuk_3),[file(borsuk_3,i2_12__borsuk_3)]]).

fof(i2_12_tmp__borsuk_3,plain,
    ( ( v3_struct_0(c2_12__borsuk_3)
      & v2_pre_topc(c2_12__borsuk_3)
      & l1_pre_topc(c2_12__borsuk_3) )
   => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,c2_12__borsuk_3))
      & v3_struct_0(k6_borsuk_1(c2_12__borsuk_3,c1_12__borsuk_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_12__borsuk_3]),discharge_asm(discharge,[dt_c2_12__borsuk_3])],[dt_c2_12__borsuk_3,i2_12__borsuk_3]),
    [interesting(0.8),i1_12__borsuk_3]).

fof(i1_12__borsuk_3,plain,(
    ! [A] : 
      ( ( v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,A))
        & v3_struct_0(k6_borsuk_1(A,c1_12__borsuk_3)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_12__borsuk_3])],[i2_12_tmp__borsuk_3,dh_c2_12__borsuk_3]),
    [interesting(0.8),file(borsuk_3,i1_12__borsuk_3),[file(borsuk_3,i1_12__borsuk_3)]]).

fof(i1_12_tmp__borsuk_3,plain,
    ( ( v2_pre_topc(c1_12__borsuk_3)
      & l1_pre_topc(c1_12__borsuk_3) )
   => ! [A] : 
        ( ( v3_struct_0(A)
          & v2_pre_topc(A)
          & l1_pre_topc(A) )
       => ( v3_struct_0(k6_borsuk_1(c1_12__borsuk_3,A))
          & v3_struct_0(k6_borsuk_1(A,c1_12__borsuk_3)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_12__borsuk_3])],[dt_c1_12__borsuk_3,i1_12__borsuk_3]),
    [interesting(1),t4_borsuk_3]).

fof(t4_borsuk_3,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( v3_struct_0(k6_borsuk_1(A,B))
            & v3_struct_0(k6_borsuk_1(B,A)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_12_tmp__borsuk_3,dh_c1_12__borsuk_3]),
    [interesting(1),file(borsuk_3,t4_borsuk_3),[file(borsuk_3,t4_borsuk_3)]]).