% Mizar ND problem: t6_borsuk_6,borsuk_6,113,27 
fof(dh_c1_4__borsuk_6,definition,
    ( ( m1_subset_1(c1_4__borsuk_6,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(c1_4__borsuk_6,k6_real_1(1,2))
       => m1_subset_1(k3_xcmplx_0(2,c1_4__borsuk_6),u1_struct_0(k5_topmetr)) ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k5_topmetr))
       => ( r1_xreal_0(A,k6_real_1(1,2))
         => m1_subset_1(k3_xcmplx_0(2,A),u1_struct_0(k5_topmetr)) ) ) ),
    introduced(definition,[new_symbol(c1_4__borsuk_6),file(borsuk_6,c1_4__borsuk_6)]),
    [interesting(0.8),axiom,file(borsuk_6,c1_4__borsuk_6)]).

fof(e1_4__borsuk_6,assumption,(
    r1_xreal_0(c1_4__borsuk_6,k6_real_1(1,2)) ),
    introduced(assumption,[file(borsuk_6,e1_4__borsuk_6)]),
    [interesting(0.8),axiom,file(borsuk_6,e1_4__borsuk_6)]).

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

fof(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc2_xcmplx_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,cc2_xcmplx_0)]).

fof(cc3_borsuk_5,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_5,cc3_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,cc3_borsuk_5)]).

fof(fc10_borsuk_5,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & ~ v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(borsuk_5,fc10_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc10_borsuk_5)]).

fof(fc11_borsuk_5,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & v1_xcmplx_0(k3_xcmplx_0(B,A))
        & ~ v1_rat_1(k3_xcmplx_0(B,A)) ) ) ),
    file(borsuk_5,fc11_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc11_borsuk_5)]).

fof(fc12_borsuk_5,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & v1_xcmplx_0(k7_xcmplx_0(A,B))
        & ~ v1_rat_1(k7_xcmplx_0(A,B)) ) ) ),
    file(borsuk_5,fc12_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc12_borsuk_5)]).

fof(fc13_borsuk_5,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & v1_xcmplx_0(k7_xcmplx_0(B,A))
        & ~ v1_rat_1(k7_xcmplx_0(B,A)) ) ) ),
    file(borsuk_5,fc13_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc13_borsuk_5)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(rc2_borsuk_5,theorem,(
    ? [A] : 
      ( v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & ~ v1_rat_1(A) ) ),
    file(borsuk_5,rc2_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,rc2_borsuk_5)]).

fof(rc3_borsuk_5,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & v1_rat_1(A) ) ),
    file(borsuk_5,rc3_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,rc3_borsuk_5)]).

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_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_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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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(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(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_borsuk_3,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v3_struct_0(A)
          & v2_pre_topc(A) )
       => ( v2_pre_topc(A)
          & v2_compts_1(A) ) ) ) ),
    file(borsuk_3,cc1_borsuk_3),
    [interesting(0.9),axiom,file(borsuk_3,cc1_borsuk_3)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc1_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v2_pre_topc(B) ) ) ),
    file(pre_topc,cc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,cc1_pre_topc)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(cc3_borsuk_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_borsuk_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_connsp_1(A) ) ) ) ),
    file(borsuk_2,cc3_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc3_borsuk_2)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

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(fc21_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc21_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc21_xreal_0)]).

fof(fc22_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc22_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc22_xreal_0)]).

fof(fc24_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc24_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc24_xreal_0)]).

fof(fc27_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc27_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]).

fof(fc28_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc28_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]).

fof(fc29_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc29_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

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(rc1_borsuk_5,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_connsp_1(A) ) ),
    file(borsuk_5,rc1_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,rc1_borsuk_5)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_borsuk_2,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_borsuk_2(A) ) ),
    file(borsuk_2,rc3_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,rc3_borsuk_2)]).

fof(rc3_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc3_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc3_pre_topc)]).

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(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_pre_topc,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc4_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc4_pre_topc)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(rc5_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B) ) ) ),
    file(pre_topc,rc5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc5_pre_topc)]).

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(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

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_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

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(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

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_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(existence_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k22_borsuk_1,axiom,(
    l1_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,k22_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k22_borsuk_1)]).

fof(dt_k3_topmetr,axiom,
    ( v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & l1_pre_topc(k3_topmetr) ),
    file(topmetr,k3_topmetr),
    [interesting(0.9),axiom,file(topmetr,k3_topmetr)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_xcmplx_0,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,cc1_xcmplx_0)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(fc18_borsuk_5,theorem,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1)
    & v1_connsp_1(k22_borsuk_1)
    & v2_t_0topsp(k22_borsuk_1)
    & v2_compts_1(k22_borsuk_1)
    & v3_compts_1(k22_borsuk_1)
    & v3_yellow_8(k22_borsuk_1)
    & v1_borsuk_2(k22_borsuk_1)
    & v1_urysohn1(k22_borsuk_1) ),
    file(borsuk_5,fc18_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc18_borsuk_5)]).

fof(fc1_borsuk_5,theorem,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v1_connsp_1(k3_topmetr)
    & v2_t_0topsp(k3_topmetr)
    & v3_compts_1(k3_topmetr)
    & v1_borsuk_2(k3_topmetr)
    & v1_urysohn1(k3_topmetr) ),
    file(borsuk_5,fc1_borsuk_5),
    [interesting(0.9),axiom,file(borsuk_5,fc1_borsuk_5)]).

fof(fc23_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc23_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc23_xreal_0)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(fc30_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc30_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]).

fof(fc3_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,fc3_xcmplx_0)]).

fof(fc5_borsuk_1,theorem,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,fc5_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,fc5_borsuk_1)]).

fof(fc5_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc5_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,fc5_xcmplx_0)]).

fof(fc7_borsuk_2,theorem,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1)
    & v2_t_0topsp(k22_borsuk_1)
    & v2_compts_1(k22_borsuk_1)
    & v3_compts_1(k22_borsuk_1)
    & v3_yellow_8(k22_borsuk_1) ),
    file(borsuk_2,fc7_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,fc7_borsuk_2)]).

fof(fc8_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & ~ v1_xboole_0(B)
        & v1_xcmplx_0(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xcmplx_0,fc8_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,fc8_xcmplx_0)]).

fof(fc9_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & ~ v1_xboole_0(B)
        & v1_xcmplx_0(B) )
     => ( ~ v1_xboole_0(k7_xcmplx_0(A,B))
        & v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xcmplx_0,fc9_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,fc9_xcmplx_0)]).

fof(rc1_xcmplx_0,theorem,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,rc1_xcmplx_0)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_xcmplx_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,rc2_xcmplx_0)]).

fof(spc4_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ),
    file(arithm,spc4_arithm),
    [interesting(0.9),axiom,file(arithm,spc4_arithm)]).

fof(spc7_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t2_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    [interesting(0.9),axiom,file(arithm,t2_arithm)]).

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(t3_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    [interesting(0.9),axiom,file(arithm,t3_arithm)]).

fof(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(0,A) = 0 ) ),
    file(arithm,t5_arithm),
    [interesting(0.9),axiom,file(arithm,t5_arithm)]).

fof(t6_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    [interesting(0.9),axiom,file(arithm,t6_arithm)]).

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(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(commutativity_k3_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(commutativity_k4_real_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k4_real_1(B,A) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

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(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(redefinition_k4_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(redefinition_k5_topmetr,definition,(
    k5_topmetr = k22_borsuk_1 ),
    file(topmetr,k5_topmetr),
    [interesting(0.9),axiom,file(topmetr,k5_topmetr)]).

fof(redefinition_k6_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ),
    file(real_1,k6_real_1),
    [interesting(0.9),axiom,file(real_1,k6_real_1)]).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(dt_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(dt_k5_topmetr,axiom,
    ( v1_pre_topc(k5_topmetr)
    & m1_pre_topc(k5_topmetr,k3_topmetr) ),
    file(topmetr,k5_topmetr),
    [interesting(0.9),axiom,file(topmetr,k5_topmetr)]).

fof(dt_k6_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ),
    file(real_1,k6_real_1),
    [interesting(0.9),axiom,file(real_1,k6_real_1)]).

fof(dt_k7_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k7_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]).

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_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_4__borsuk_6,assumption,(
    m1_subset_1(c1_4__borsuk_6,u1_struct_0(k5_topmetr)) ),
    introduced(assumption,[file(borsuk_6,c1_4__borsuk_6)]),
    [interesting(0.8),axiom,file(borsuk_6,c1_4__borsuk_6)]).

fof(cc1_borsuk_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_2,cc1_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc1_borsuk_2)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(fc1_borsuk_4,theorem,
    ( ~ v1_xboole_0(u1_struct_0(k5_topmetr))
    & v1_membered(u1_struct_0(k5_topmetr))
    & v2_membered(u1_struct_0(k5_topmetr)) ),
    file(borsuk_4,fc1_borsuk_4),
    [interesting(0.9),axiom,file(borsuk_4,fc1_borsuk_4)]).

fof(fc4_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc4_xreal_0)]).

fof(fc6_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn1d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r0,theorem,(
    ~ r1_xreal_0(2,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,(
    ~ r1_xreal_0(2,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn1d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,(
    k7_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,(
    k7_xcmplx_0(0,2) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,theorem,(
    k7_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,(
    k7_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,(
    k7_xcmplx_0(2,1) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,(
    k7_xcmplx_0(2,2) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]).

fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,(
    k3_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,(
    k3_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,theorem,(
    k3_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]).

fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,(
    k3_xcmplx_0(1,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,(
    k3_xcmplx_0(2,1) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]).

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(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(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(spc2_numerals,theorem,
    ( v2_xreal_0(2)
    & m2_subset_1(2,k1_numbers,k5_numbers)
    & m1_subset_1(2,k5_numbers)
    & m1_subset_1(2,k1_numbers) ),
    file(numerals,spc2_numerals),
    [interesting(0.9),axiom,file(numerals,spc2_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(spc2_boole,theorem,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    [interesting(0.9),axiom,file(boole,spc2_boole)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,(
    r1_xreal_0(1,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]).

fof(t2_jordan5a,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(0,A)
          & r1_xreal_0(A,1) )
      <=> r2_hidden(A,u1_struct_0(k5_topmetr)) ) ) ),
    file(jordan5a,t2_jordan5a),
    [interesting(0.9),axiom,file(jordan5a,t2_jordan5a)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(e3_4__borsuk_6,plain,(
    r1_xreal_0(0,c1_4__borsuk_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_6])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc3_borsuk_5,rc1_arytm_3,rc2_borsuk_5,rc3_borsuk_5,free_g1_pre_topc,existence_l1_pre_topc,dt_g1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_3,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_arytm_3,cc3_borsuk_2,cc3_membered,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_borsuk_3,rc1_borsuk_5,rc1_membered,rc1_pre_topc,rc2_pre_topc,rc2_xreal_0,rc3_borsuk_2,rc3_pre_topc,rc3_struct_0,rc3_xreal_0,rc4_pre_topc,rc4_xreal_0,rc5_pre_topc,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,abstractness_v1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k22_borsuk_1,dt_k3_topmetr,dt_k5_numbers,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_borsuk_2,cc1_funct_1,cc1_xcmplx_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc18_borsuk_5,fc1_borsuk_5,fc2_membered,fc5_borsuk_1,fc7_borsuk_2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k5_topmetr,dt_k5_topmetr,dt_u1_struct_0,dt_c1_4__borsuk_6,cc2_xreal_0,fc1_borsuk_4,rqLessOrEqual__r1_xreal_0__r1_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t2_jordan5a,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(borsuk_6,e3_4__borsuk_6),[file(borsuk_6,e3_4__borsuk_6)]]).

fof(t66_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(0,C) )
               => r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t66_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t66_xreal_1)]).

fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,(
    k3_xcmplx_0(2,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,(
    k3_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]).

fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,(
    k3_xcmplx_0(1,2) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]).

fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,(
    k3_xcmplx_0(0,2) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r2,theorem,(
    r1_xreal_0(0,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,(
    r1_xreal_0(2,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]).

fof(e4_4__borsuk_6,plain,(
    r1_xreal_0(k4_real_1(2,0),k3_xcmplx_0(2,c1_4__borsuk_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_6])],[free_g1_pre_topc,reflexivity_r1_tarski,existence_l1_pre_topc,dt_g1_pre_topc,dt_l1_pre_topc,dt_u1_pre_topc,cc1_arytm_3,cc1_borsuk_3,cc1_pre_topc,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc3_borsuk_2,cc3_borsuk_5,cc4_borsuk_2,fc10_borsuk_5,fc11_borsuk_5,fc1_struct_0,rc1_arytm_3,rc1_borsuk_3,rc1_borsuk_5,rc1_pre_topc,rc2_borsuk_5,rc2_pre_topc,rc3_borsuk_2,rc3_borsuk_5,rc3_pre_topc,rc3_struct_0,rc4_pre_topc,rc5_pre_topc,rc5_struct_0,antisymmetry_r2_hidden,abstractness_v1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k3_topmetr,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc18_borsuk_5,fc1_borsuk_5,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_borsuk_1,fc5_membered,fc6_membered,fc7_borsuk_2,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k5_topmetr,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_topmetr,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,cc1_borsuk_2,cc1_funct_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_borsuk_4,fc23_xreal_0,fc2_membered,fc3_xcmplx_0,fc8_xcmplx_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_c1_4__borsuk_6,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e3_4__borsuk_6,t66_xreal_1,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.8),file(borsuk_6,e4_4__borsuk_6),[file(borsuk_6,e4_4__borsuk_6)]]).

fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(1,2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,(
    k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),2) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn1d2,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2)]).

fof(e2_4__borsuk_6,plain,(
    r1_xreal_0(k3_xcmplx_0(2,c1_4__borsuk_6),k4_real_1(2,k6_real_1(1,2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_6,e1_4__borsuk_6])],[free_g1_pre_topc,reflexivity_r1_tarski,existence_l1_pre_topc,dt_g1_pre_topc,dt_l1_pre_topc,dt_u1_pre_topc,cc1_arytm_3,cc1_borsuk_3,cc1_pre_topc,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc3_borsuk_2,cc3_borsuk_5,cc4_borsuk_2,fc10_borsuk_5,fc11_borsuk_5,fc12_borsuk_5,fc13_borsuk_5,fc1_struct_0,rc1_arytm_3,rc1_borsuk_3,rc1_borsuk_5,rc1_pre_topc,rc2_borsuk_5,rc2_pre_topc,rc3_borsuk_2,rc3_borsuk_5,rc3_pre_topc,rc3_struct_0,rc4_pre_topc,rc5_pre_topc,rc5_struct_0,antisymmetry_r2_hidden,abstractness_v1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k3_topmetr,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc18_borsuk_5,fc1_borsuk_5,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_borsuk_1,fc5_membered,fc6_membered,fc7_borsuk_2,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k5_topmetr,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k5_topmetr,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,cc1_borsuk_2,cc1_funct_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_borsuk_4,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc3_xcmplx_0,fc5_xcmplx_0,fc8_xcmplx_0,fc9_xcmplx_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,spc4_arithm,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_real_1,redefinition_k6_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k6_real_1,dt_k7_xcmplx_0,dt_c1_4__borsuk_6,cc2_xreal_0,fc4_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e1_4__borsuk_6,t66_xreal_1,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.8),file(borsuk_6,e2_4__borsuk_6),[file(borsuk_6,e2_4__borsuk_6)]]).

fof(e5_4__borsuk_6,plain,(
    m1_subset_1(k3_xcmplx_0(2,c1_4__borsuk_6),u1_struct_0(k5_topmetr)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__borsuk_6,e1_4__borsuk_6])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc3_borsuk_5,fc10_borsuk_5,fc11_borsuk_5,fc12_borsuk_5,fc13_borsuk_5,rc1_arytm_3,rc2_borsuk_5,rc3_borsuk_5,free_g1_pre_topc,existence_l1_pre_topc,dt_g1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_3,cc1_membered,cc1_pre_topc,cc20_membered,cc2_membered,cc3_arytm_3,cc3_borsuk_2,cc3_membered,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_struct_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,rc1_borsuk_3,rc1_borsuk_5,rc1_membered,rc1_pre_topc,rc2_pre_topc,rc2_xreal_0,rc3_borsuk_2,rc3_pre_topc,rc3_struct_0,rc3_xreal_0,rc4_pre_topc,rc4_xreal_0,rc5_pre_topc,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,abstractness_v1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k22_borsuk_1,dt_k3_topmetr,dt_k5_numbers,dt_l1_struct_0,dt_m1_pre_topc,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_funct_1,cc1_xcmplx_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc18_borsuk_5,fc1_borsuk_5,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc3_xcmplx_0,fc5_borsuk_1,fc5_xcmplx_0,fc7_borsuk_2,fc8_xcmplx_0,fc9_xcmplx_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,spc4_arithm,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_real_1,redefinition_k5_topmetr,redefinition_k6_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k5_topmetr,dt_k6_real_1,dt_k7_xcmplx_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__borsuk_6,cc1_borsuk_2,cc2_xreal_0,fc1_borsuk_4,fc4_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_rn1d2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e4_4__borsuk_6,e2_4__borsuk_6,t2_jordan5a,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2]),
    [interesting(0.8),file(borsuk_6,e5_4__borsuk_6),[file(borsuk_6,e5_4__borsuk_6)]]).

fof(i3_4__borsuk_6,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_6,i3_4__borsuk_6)]),
    [interesting(0.8),trivial,file(borsuk_6,i3_4__borsuk_6)]).

fof(i2_4__borsuk_6,plain,(
    m1_subset_1(k3_xcmplx_0(2,c1_4__borsuk_6),u1_struct_0(k5_topmetr)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__borsuk_6,e1_4__borsuk_6])],[e5_4__borsuk_6,i3_4__borsuk_6]),
    [interesting(0.8),file(borsuk_6,i2_4__borsuk_6),[file(borsuk_6,i2_4__borsuk_6)]]).

fof(i1_4__borsuk_6,plain,
    ( r1_xreal_0(c1_4__borsuk_6,k6_real_1(1,2))
   => m1_subset_1(k3_xcmplx_0(2,c1_4__borsuk_6),u1_struct_0(k5_topmetr)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__borsuk_6]),discharge_asm(discharge,[e1_4__borsuk_6])],[e1_4__borsuk_6,i2_4__borsuk_6]),
    [interesting(0.8),file(borsuk_6,i1_4__borsuk_6),[file(borsuk_6,i1_4__borsuk_6)]]).

fof(i1_4_tmp__borsuk_6,plain,
    ( m1_subset_1(c1_4__borsuk_6,u1_struct_0(k5_topmetr))
   => ( r1_xreal_0(c1_4__borsuk_6,k6_real_1(1,2))
     => m1_subset_1(k3_xcmplx_0(2,c1_4__borsuk_6),u1_struct_0(k5_topmetr)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__borsuk_6])],[dt_c1_4__borsuk_6,i1_4__borsuk_6]),
    [interesting(1),t6_borsuk_6]).

fof(t6_borsuk_6,theorem,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(A,k6_real_1(1,2))
       => m1_subset_1(k3_xcmplx_0(2,A),u1_struct_0(k5_topmetr)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__borsuk_6,dh_c1_4__borsuk_6]),
    [interesting(1),file(borsuk_6,t6_borsuk_6),[file(borsuk_6,t6_borsuk_6)]]).