% Mizar problem: t52_rcomp_3,rcomp_3,1764,35 
fof(t52_rcomp_3,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( A = B
           => ( v2_connsp_1(A,k3_topalg_2)
            <=> v1_jct_misc(B) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_membered,cc10_yellow13,cc11_membered,cc11_topreal6,cc11_yellow13,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_6,cc1_finseq_1,cc1_membered,cc1_pre_topc,cc1_topreal6,cc1_tops_1,cc1_xreal_0,cc20_membered,cc2_borsuk_6,cc2_membered,cc2_pscomp_1,cc2_topreal6,cc2_tops_1,cc2_xreal_0,cc3_borsuk_5,cc3_int_1,cc3_membered,cc3_nat_1,cc3_sprect_1,cc3_topalg_2,cc3_tops_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_sprect_1,cc4_topalg_2,cc4_tops_1,cc4_xreal_0,cc4_yellow13,cc5_topalg_2,cc5_tops_1,cc5_xreal_0,cc5_yellow13,cc6_membered,cc6_tops_1,cc6_xreal_0,cc6_yellow13,cc7_xreal_0,cc7_yellow13,cc8_xreal_0,cc8_yellow13,cc9_yellow13,connectedness_r1_xreal_0,d3_connsp_1,d3_jct_misc,d3_toprealb,d4_subset_1,dt_g1_pre_topc,dt_k12_prob_1,dt_k1_numbers,dt_k1_rcomp_1,dt_k1_rcomp_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_limfunc1,dt_k2_rcomp_1,dt_k2_rcomp_2,dt_k2_subset_1,dt_k3_limfunc1,dt_k3_pre_topc,dt_k3_topalg_2,dt_k3_topmetr,dt_k4_limfunc1,dt_k5_toprealb,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,fc10_pscomp_1,fc10_rcomp_3,fc10_toprealb,fc11_rcomp_3,fc11_toprealb,fc12_rcomp_3,fc12_toprealb,fc13_rcomp_3,fc13_toprealb,fc14_borsuk_5,fc14_rcomp_3,fc14_toprealb,fc15_borsuk_5,fc15_rcomp_3,fc16_borsuk_5,fc16_rcomp_3,fc17_borsuk_5,fc1_borsuk_5,fc1_fcont_3,fc1_pscomp_1,fc1_rcomp_1,fc1_rcomp_3,fc1_struct_0,fc1_subset_1,fc1_topreal6,fc1_yellow13,fc2_finseq_1,fc2_membered,fc2_rcomp_1,fc2_rcomp_3,fc3_fcont_3,fc3_pre_topc,fc3_rcomp_3,fc4_fcont_3,fc4_pre_topc,fc4_rcomp_3,fc5_fcont_3,fc5_rcomp_3,fc6_fcont_3,fc6_membered,fc6_rcomp_3,fc7_borsuk_6,fc7_rcomp_3,fc7_topreal6,fc8_rcomp_3,fc8_topreal6,fc9_rcomp_3,fc9_sprect_1,free_g1_pre_topc,rc10_pscomp_1,rc1_borsuk_5,rc1_borsuk_6,rc1_finseq_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_rcomp_1,rc1_rcomp_3,rc1_subset_1,rc1_topreal6,rc1_tops_1,rc1_xreal_0,rc2_borsuk_5,rc2_borsuk_6,rc2_int_1,rc2_pre_topc,rc2_pscomp_1,rc2_rcomp_3,rc2_subset_1,rc2_tops_1,rc2_waybel_7,rc2_xreal_0,rc3_borsuk_5,rc3_borsuk_6,rc3_finseq_1,rc3_pre_topc,rc3_pscomp_1,rc3_rcomp_3,rc3_sprect_1,rc3_struct_0,rc3_topalg_2,rc3_tops_1,rc3_waybel_7,rc3_xreal_0,rc4_pre_topc,rc4_pscomp_1,rc4_topalg_2,rc4_tops_1,rc4_xreal_0,rc5_pre_topc,rc5_pscomp_1,rc5_struct_0,rc5_tops_1,rc6_finseq_1,rc6_pre_topc,rc7_finseq_1,rc7_pre_topc,rc8_finseq_1,rc9_pscomp_1,redefinition_k3_topalg_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,t10_topalg_2,t111_borsuk_5,t11_topalg_2,t15_rcomp_1,t1_real,t1_subset,t2_real,t2_subset,t3_rcomp_2,t3_real,t3_subset,t41_rcomp_3,t4_rcomp_2,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,t8_topalg_2,t9_topalg_2]),
    [file(rcomp_3,t52_rcomp_3)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [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),
    []).

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

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

fof(cc10_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v3_compts_1(A) )
       => ( v2_pre_topc(A)
          & v1_urysohn1(A) ) ) ) ),
    file(yellow13,cc10_yellow13),
    []).

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

fof(cc11_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_finset_1(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v1_rcomp_1(A) ) ) ) ),
    file(topreal6,cc11_topreal6),
    []).

fof(cc11_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_urysohn1(A) )
       => ( v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(yellow13,cc11_yellow13),
    []).

fof(cc12_membered,axiom,(
    ! [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),
    []).

fof(cc13_membered,axiom,(
    ! [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),
    []).

fof(cc14_membered,axiom,(
    ! [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),
    []).

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

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

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

fof(cc18_membered,axiom,(
    ! [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),
    []).

fof(cc19_membered,axiom,(
    ! [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),
    []).

fof(cc1_borsuk_6,axiom,(
    ! [A] : 
      ( ( v1_borsuk_6(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(borsuk_6,cc1_borsuk_6),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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

fof(cc1_pre_topc,axiom,(
    ! [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),
    []).

fof(cc1_topreal6,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_connsp_1(B,A) ) ) ) ),
    file(topreal6,cc1_topreal6),
    []).

fof(cc1_tops_1,axiom,(
    ! [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),
    []).

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

fof(cc20_membered,axiom,(
    ! [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),
    []).

fof(cc2_borsuk_6,axiom,(
    ! [A] : 
      ( ( v1_borsuk_6(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v1_borsuk_6(B) ) ) ),
    file(borsuk_6,cc2_borsuk_6),
    []).

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

fof(cc2_pscomp_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v10_pscomp_1(A) ) ) ) ),
    file(pscomp_1,cc2_pscomp_1),
    []).

fof(cc2_topreal6,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
           => v6_compts_1(B,A) ) ) ) ),
    file(topreal6,cc2_topreal6),
    []).

fof(cc2_tops_1,axiom,(
    ! [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),
    []).

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

fof(cc3_borsuk_5,axiom,(
    ! [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),
    []).

fof(cc3_int_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    []).

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

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc3_sprect_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v3_seq_4(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v1_seq_4(A)
          & v2_seq_4(A) ) ) ) ),
    file(sprect_1,cc3_sprect_1),
    []).

fof(cc3_topalg_2,axiom,(
    ! [A] : 
      ( m1_pre_topc(A,k3_topmetr)
     => ( v2_pre_topc(A)
        & v1_borsuk_6(A) ) ) ),
    file(topalg_2,cc3_topalg_2),
    []).

fof(cc3_tops_1,axiom,(
    ! [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),
    []).

fof(cc3_xreal_0,axiom,(
    ! [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),
    []).

fof(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

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

fof(cc4_sprect_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( ( v1_seq_4(A)
          & v2_seq_4(A) )
       => ( v1_membered(A)
          & v2_membered(A)
          & v3_seq_4(A) ) ) ) ),
    file(sprect_1,cc4_sprect_1),
    []).

fof(cc4_topalg_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( v1_xboole_0(A)
       => v2_topalg_2(A) ) ) ),
    file(topalg_2,cc4_topalg_2),
    []).

fof(cc4_tops_1,axiom,(
    ! [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),
    []).

fof(cc4_xreal_0,axiom,(
    ! [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),
    []).

fof(cc4_yellow13,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
           => v4_pre_topc(B,A) ) ) ) ),
    file(yellow13,cc4_yellow13),
    []).

fof(cc5_topalg_2,axiom,(
    ! [A] : 
      ( m1_pre_topc(A,k3_topalg_2)
     => ( ( ~ v3_struct_0(A)
          & v3_topalg_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_borsuk_2(A)
          & v1_borsuk_6(A)
          & v1_connsp_1(A) ) ) ) ),
    file(topalg_2,cc5_topalg_2),
    []).

fof(cc5_tops_1,axiom,(
    ! [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),
    []).

fof(cc5_xreal_0,axiom,(
    ! [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),
    []).

fof(cc5_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v6_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A) ) ) ) ),
    file(yellow13,cc5_yellow13),
    []).

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

fof(cc6_tops_1,axiom,(
    ! [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),
    []).

fof(cc6_xreal_0,axiom,(
    ! [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),
    []).

fof(cc6_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v6_group_1(A) )
       => ( v2_pre_topc(A)
          & v2_compts_1(A) ) ) ) ),
    file(yellow13,cc6_yellow13),
    []).

fof(cc7_xreal_0,axiom,(
    ! [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),
    []).

fof(cc7_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v1_urysohn1(A)
          & v3_compts_1(A)
          & v4_compts_1(A)
          & v5_compts_1(A) ) ) ) ),
    file(yellow13,cc7_yellow13),
    []).

fof(cc8_xreal_0,axiom,(
    ! [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),
    []).

fof(cc8_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v5_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v4_compts_1(A) ) ) ) ),
    file(yellow13,cc8_yellow13),
    []).

fof(cc9_yellow13,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_urysohn1(A)
          & v4_compts_1(A) )
       => ( v2_pre_topc(A)
          & v3_compts_1(A) ) ) ) ),
    file(yellow13,cc9_yellow13),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [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),
    []).

fof(d3_connsp_1,axiom,(
    ! [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),
    []).

fof(d3_jct_misc,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_jct_misc(A)
      <=> ! [B] : 
            ( v1_xreal_0(B)
           => ! [C] : 
                ( v1_xreal_0(C)
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) ) ),
    file(jct_misc,d3_jct_misc),
    []).

fof(d3_toprealb,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k5_toprealb(A) = A ) ),
    file(toprealb,d3_toprealb),
    []).

fof(d4_subset_1,axiom,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_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),
    []).

fof(dt_k12_prob_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k12_prob_1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(prob_1,k12_prob_1),
    []).

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

fof(dt_k1_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_1,k1_rcomp_1),
    []).

fof(dt_k1_rcomp_2,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_2,k1_rcomp_2),
    []).

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

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

fof(dt_k2_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k2_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k2_limfunc1),
    []).

fof(dt_k2_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_1,k2_rcomp_1),
    []).

fof(dt_k2_rcomp_2,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_rcomp_2(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_2,k2_rcomp_2),
    []).

fof(dt_k2_subset_1,axiom,(
    ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) ),
    file(subset_1,k2_subset_1),
    []).

fof(dt_k3_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k3_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k3_limfunc1),
    []).

fof(dt_k3_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & m1_pre_topc(k3_pre_topc(A,B),A) ) ) ),
    file(pre_topc,k3_pre_topc),
    []).

fof(dt_k3_topalg_2,axiom,
    ( v1_pre_topc(k3_topalg_2)
    & v3_topalg_2(k3_topalg_2)
    & m1_pre_topc(k3_topalg_2,k3_topmetr) ),
    file(topalg_2,k3_topalg_2),
    []).

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

fof(dt_k4_limfunc1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_subset_1(k4_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(limfunc1,k4_limfunc1),
    []).

fof(dt_k5_toprealb,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k5_toprealb(A),k1_zfmisc_1(u1_struct_0(k3_topalg_2))) ) ),
    file(toprealb,k5_toprealb),
    []).

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

fof(dt_l1_struct_0,axiom,(
    $true ),
    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),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    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),
    []).

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

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

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    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),
    []).

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

fof(fc10_pscomp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & v6_compts_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_pre_topc(A,B))
        & v1_pre_topc(k3_pre_topc(A,B))
        & v2_pre_topc(k3_pre_topc(A,B))
        & v2_compts_1(k3_pre_topc(A,B)) ) ) ),
    file(pscomp_1,fc10_pscomp_1),
    []).

fof(fc10_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k2_limfunc1(A))
        & v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A))
        & v1_seq_4(k2_limfunc1(A))
        & ~ v2_seq_4(k2_limfunc1(A))
        & v2_rcomp_1(k2_limfunc1(A))
        & v1_jct_misc(k2_limfunc1(A)) ) ) ),
    file(rcomp_3,fc10_rcomp_3),
    []).

fof(fc10_toprealb,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ v1_xboole_0(k5_toprealb(A)) ) ),
    file(toprealb,fc10_toprealb),
    []).

fof(fc11_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k12_prob_1(A))
        & v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A))
        & v1_seq_4(k12_prob_1(A))
        & ~ v2_seq_4(k12_prob_1(A))
        & v3_rcomp_1(k12_prob_1(A))
        & v1_jct_misc(k12_prob_1(A)) ) ) ),
    file(rcomp_3,fc11_rcomp_3),
    []).

fof(fc11_toprealb,axiom,(
    ! [A] : 
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => v3_pre_topc(k5_toprealb(A),k3_topalg_2) ) ),
    file(toprealb,fc11_toprealb),
    []).

fof(fc12_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k3_limfunc1(A))
        & v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A))
        & ~ v1_seq_4(k3_limfunc1(A))
        & v2_seq_4(k3_limfunc1(A))
        & v2_rcomp_1(k3_limfunc1(A))
        & v1_jct_misc(k3_limfunc1(A)) ) ) ),
    file(rcomp_3,fc12_rcomp_3),
    []).

fof(fc12_toprealb,axiom,(
    ! [A] : 
      ( ( v2_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => v4_pre_topc(k5_toprealb(A),k3_topalg_2) ) ),
    file(toprealb,fc12_toprealb),
    []).

fof(fc13_rcomp_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k4_limfunc1(A))
        & v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A))
        & ~ v1_seq_4(k4_limfunc1(A))
        & v2_seq_4(k4_limfunc1(A))
        & v3_rcomp_1(k4_limfunc1(A))
        & v1_jct_misc(k4_limfunc1(A)) ) ) ),
    file(rcomp_3,fc13_rcomp_3),
    []).

fof(fc13_toprealb,axiom,(
    ! [A] : 
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v2_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v1_tsep_1(k3_pre_topc(k3_topalg_2,k5_toprealb(A)),k3_topalg_2)
        & v1_borsuk_6(k3_pre_topc(k3_topalg_2,k5_toprealb(A))) ) ) ),
    file(toprealb,fc13_toprealb),
    []).

fof(fc14_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k4_limfunc1(A))
        & v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A)) ) ) ),
    file(borsuk_5,fc14_borsuk_5),
    []).

fof(fc14_rcomp_3,axiom,
    ( ~ v1_xboole_0(k2_subset_1(k1_numbers))
    & v1_membered(k2_subset_1(k1_numbers))
    & v2_membered(k2_subset_1(k1_numbers))
    & ~ v1_seq_4(k2_subset_1(k1_numbers))
    & ~ v2_seq_4(k2_subset_1(k1_numbers))
    & v2_rcomp_1(k2_subset_1(k1_numbers))
    & v3_rcomp_1(k2_subset_1(k1_numbers))
    & v1_jct_misc(k2_subset_1(k1_numbers)) ),
    file(rcomp_3,fc14_rcomp_3),
    []).

fof(fc14_toprealb,axiom,(
    ! [A] : 
      ( ( v2_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v2_pre_topc(k3_pre_topc(k3_topalg_2,k5_toprealb(A)))
        & v1_borsuk_1(k3_pre_topc(k3_topalg_2,k5_toprealb(A)),k3_topalg_2)
        & v1_borsuk_6(k3_pre_topc(k3_topalg_2,k5_toprealb(A))) ) ) ),
    file(toprealb,fc14_toprealb),
    []).

fof(fc15_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k2_limfunc1(A))
        & v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A)) ) ) ),
    file(borsuk_5,fc15_borsuk_5),
    []).

fof(fc15_rcomp_3,axiom,(
    ! [A] : 
      ( ( v2_topalg_2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topalg_2))) )
     => ( v1_pre_topc(k3_pre_topc(k3_topalg_2,A))
        & v2_pre_topc(k3_pre_topc(k3_topalg_2,A))
        & v1_borsuk_6(k3_pre_topc(k3_topalg_2,A))
        & v3_topalg_2(k3_pre_topc(k3_topalg_2,A)) ) ) ),
    file(rcomp_3,fc15_rcomp_3),
    []).

fof(fc16_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k12_prob_1(A))
        & v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A)) ) ) ),
    file(borsuk_5,fc16_borsuk_5),
    []).

fof(fc16_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_membered(k5_toprealb(A))
        & v2_membered(k5_toprealb(A))
        & v2_topalg_2(k5_toprealb(A)) ) ) ),
    file(rcomp_3,fc16_rcomp_3),
    []).

fof(fc17_borsuk_5,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k3_limfunc1(A))
        & v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A)) ) ) ),
    file(borsuk_5,fc17_borsuk_5),
    []).

fof(fc1_borsuk_5,axiom,
    ( ~ 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),
    []).

fof(fc1_fcont_3,axiom,
    ( v1_membered(k2_subset_1(k1_numbers))
    & v2_membered(k2_subset_1(k1_numbers))
    & v2_rcomp_1(k2_subset_1(k1_numbers))
    & v3_rcomp_1(k2_subset_1(k1_numbers)) ),
    file(fcont_3,fc1_fcont_3),
    []).

fof(fc1_pscomp_1,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers)
    & ~ v1_setfam_1(k1_numbers) ),
    file(pscomp_1,fc1_pscomp_1),
    []).

fof(fc1_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_1,fc1_rcomp_1),
    []).

fof(fc1_rcomp_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_subset_1(A)) ) ),
    file(rcomp_3,fc1_rcomp_3),
    []).

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

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

fof(fc1_topreal6,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & v6_group_1(k3_pre_topc(A,B)) ) ) ),
    file(topreal6,fc1_topreal6),
    []).

fof(fc1_yellow13,axiom,(
    ! [A] : 
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => v1_finset_1(u1_struct_0(A)) ) ),
    file(yellow13,fc1_yellow13),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

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

fof(fc2_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) ),
    file(rcomp_1,fc2_rcomp_1),
    []).

fof(fc2_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_borsuk_6(A)
        & l1_struct_0(A) )
     => ( v1_membered(u1_struct_0(A))
        & v2_membered(u1_struct_0(A)) ) ) ),
    file(rcomp_3,fc2_rcomp_3),
    []).

fof(fc3_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A))
        & v3_rcomp_1(k4_limfunc1(A)) ) ) ),
    file(fcont_3,fc3_fcont_3),
    []).

fof(fc3_pre_topc,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_pre_topc(A,B))
        & v1_pre_topc(k3_pre_topc(A,B)) ) ) ),
    file(pre_topc,fc3_pre_topc),
    []).

fof(fc3_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_2(A,B))
        & v2_membered(k1_rcomp_2(A,B))
        & v1_seq_4(k1_rcomp_2(A,B))
        & v2_seq_4(k1_rcomp_2(A,B))
        & v3_seq_4(k1_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc3_rcomp_3),
    []).

fof(fc4_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A))
        & v3_rcomp_1(k12_prob_1(A)) ) ) ),
    file(fcont_3,fc4_fcont_3),
    []).

fof(fc4_pre_topc,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & v2_pre_topc(k3_pre_topc(A,B)) ) ) ),
    file(pre_topc,fc4_pre_topc),
    []).

fof(fc4_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_2(A,B))
        & v2_membered(k2_rcomp_2(A,B))
        & v1_seq_4(k2_rcomp_2(A,B))
        & v2_seq_4(k2_rcomp_2(A,B))
        & v3_seq_4(k2_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc4_rcomp_3),
    []).

fof(fc5_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A))
        & v2_rcomp_1(k3_limfunc1(A)) ) ) ),
    file(fcont_3,fc5_fcont_3),
    []).

fof(fc5_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v1_seq_4(k2_rcomp_1(A,B))
        & v2_seq_4(k2_rcomp_1(A,B))
        & v3_seq_4(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc5_rcomp_3),
    []).

fof(fc6_fcont_3,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A))
        & v2_rcomp_1(k2_limfunc1(A)) ) ) ),
    file(fcont_3,fc6_fcont_3),
    []).

fof(fc6_membered,axiom,
    ( 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),
    []).

fof(fc6_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B))
        & v1_jct_misc(k1_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc6_rcomp_3),
    []).

fof(fc7_borsuk_6,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v1_connsp_1(k3_topmetr)
    & v3_compts_1(k3_topmetr)
    & v1_urysohn1(k3_topmetr)
    & v1_borsuk_2(k3_topmetr)
    & v2_t_0topsp(k3_topmetr)
    & v1_borsuk_6(k3_topmetr) ),
    file(borsuk_6,fc7_borsuk_6),
    []).

fof(fc7_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_2(A,B))
        & v2_membered(k1_rcomp_2(A,B))
        & v1_seq_4(k1_rcomp_2(A,B))
        & v2_seq_4(k1_rcomp_2(A,B))
        & v3_seq_4(k1_rcomp_2(A,B))
        & v1_jct_misc(k1_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc7_rcomp_3),
    []).

fof(fc7_topreal6,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v3_compts_1(k3_topmetr) ),
    file(topreal6,fc7_topreal6),
    []).

fof(fc8_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_2(A,B))
        & v2_membered(k2_rcomp_2(A,B))
        & v1_seq_4(k2_rcomp_2(A,B))
        & v2_seq_4(k2_rcomp_2(A,B))
        & v3_seq_4(k2_rcomp_2(A,B))
        & v1_jct_misc(k2_rcomp_2(A,B)) ) ) ),
    file(rcomp_3,fc8_rcomp_3),
    []).

fof(fc8_topreal6,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) ),
    file(topreal6,fc8_topreal6),
    []).

fof(fc9_rcomp_3,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_rcomp_1(A,B))
        & v2_membered(k2_rcomp_1(A,B))
        & v1_seq_4(k2_rcomp_1(A,B))
        & v2_seq_4(k2_rcomp_1(A,B))
        & v3_seq_4(k2_rcomp_1(A,B))
        & v3_rcomp_1(k2_rcomp_1(A,B))
        & v1_jct_misc(k2_rcomp_1(A,B)) ) ) ),
    file(rcomp_3,fc9_rcomp_3),
    []).

fof(fc9_sprect_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B)) ) ) ),
    file(sprect_1,fc9_sprect_1),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [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),
    []).

fof(rc10_pscomp_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v10_pscomp_1(A) ) ),
    file(pscomp_1,rc10_pscomp_1),
    []).

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

fof(rc1_borsuk_6,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A)
      & v1_borsuk_6(A) ) ),
    file(borsuk_6,rc1_borsuk_6),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_int_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    []).

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

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

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

fof(rc1_pscomp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc1_pscomp_1),
    []).

fof(rc1_rcomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & v1_membered(A)
      & v2_membered(A)
      & v3_rcomp_1(A) ) ),
    file(rcomp_1,rc1_rcomp_1),
    []).

fof(rc1_rcomp_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A) ) ),
    file(rcomp_3,rc1_rcomp_3),
    []).

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

fof(rc1_topreal6,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v6_group_1(A)
      & v10_pscomp_1(A) ) ),
    file(topreal6,rc1_topreal6),
    []).

fof(rc1_tops_1,axiom,(
    ! [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),
    []).

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

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

fof(rc2_borsuk_6,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_borsuk_6(A) ) ),
    file(borsuk_6,rc2_borsuk_6),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

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

fof(rc2_pscomp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc2_pscomp_1),
    []).

fof(rc2_rcomp_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A)
      & v3_seq_4(A)
      & v3_rcomp_1(A)
      & v1_jct_misc(A) ) ),
    file(rcomp_3,rc2_rcomp_3),
    []).

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

fof(rc2_tops_1,axiom,(
    ! [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),
    []).

fof(rc2_waybel_7,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(waybel_7,rc2_waybel_7),
    []).

fof(rc2_xreal_0,axiom,(
    ? [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),
    []).

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

fof(rc3_borsuk_6,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_funct_1(B)
          & v1_xboole_0(B)
          & v6_compts_1(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B) ) ) ),
    file(borsuk_6,rc3_borsuk_6),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

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

fof(rc3_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc3_pscomp_1),
    []).

fof(rc3_rcomp_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v3_seq_4(A)
      & v2_rcomp_1(A)
      & v3_rcomp_1(A)
      & v1_jct_misc(A) ) ),
    file(rcomp_3,rc3_rcomp_3),
    []).

fof(rc3_sprect_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A) ) ),
    file(sprect_1,rc3_sprect_1),
    []).

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

fof(rc3_topalg_2,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
      & ~ v1_xboole_0(A)
      & v2_topalg_2(A) ) ),
    file(topalg_2,rc3_topalg_2),
    []).

fof(rc3_tops_1,axiom,(
    ! [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),
    []).

fof(rc3_waybel_7,axiom,(
    ! [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) ) ) ),
    file(waybel_7,rc3_waybel_7),
    []).

fof(rc3_xreal_0,axiom,(
    ? [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),
    []).

fof(rc4_pre_topc,axiom,(
    ! [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),
    []).

fof(rc4_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc4_pscomp_1),
    []).

fof(rc4_topalg_2,axiom,(
    ? [A] : 
      ( m1_pre_topc(A,k3_topmetr)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_borsuk_6(A)
      & v3_topalg_2(A) ) ),
    file(topalg_2,rc4_topalg_2),
    []).

fof(rc4_tops_1,axiom,(
    ! [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),
    []).

fof(rc4_xreal_0,axiom,(
    ? [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),
    []).

fof(rc5_pre_topc,axiom,(
    ! [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),
    []).

fof(rc5_pscomp_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_seq_4(A)
      & v2_rcomp_1(A) ) ),
    file(pscomp_1,rc5_pscomp_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [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),
    []).

fof(rc5_tops_1,axiom,(
    ! [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),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc6_pre_topc,axiom,(
    ! [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),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc7_pre_topc,axiom,(
    ! [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),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(rc9_pscomp_1,axiom,(
    ! [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)
          & v6_compts_1(B,A) ) ) ),
    file(pscomp_1,rc9_pscomp_1),
    []).

fof(redefinition_k3_topalg_2,axiom,(
    k3_topalg_2 = k3_topmetr ),
    file(topalg_2,k3_topalg_2),
    []).

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

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

fof(t10_topalg_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( v2_topalg_2(k1_rcomp_2(A,B))
            & m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) ) ),
    file(topalg_2,t10_topalg_2),
    []).

fof(t111_borsuk_5,axiom,(
    ! [A] : 
      ( ( v2_connsp_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) ),
    file(borsuk_5,t111_borsuk_5),
    []).

fof(t11_topalg_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( v2_topalg_2(k2_rcomp_2(A,B))
            & m1_subset_1(k2_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) ) ),
    file(topalg_2,t11_topalg_2),
    []).

fof(t15_rcomp_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ~ ( ~ r1_xreal_0(B,A)
                & k2_rcomp_1(A,B) = k1_xboole_0 )
            & ( r1_xreal_0(A,B)
             => ( r2_hidden(A,k1_rcomp_1(A,B))
                & r2_hidden(B,k1_rcomp_1(A,B)) ) )
            & r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(A,B)) ) ) ) ),
    file(rcomp_1,t15_rcomp_1),
    []).

fof(t1_real,axiom,(
    ! [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),
    []).

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

fof(t2_real,axiom,(
    ! [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),
    []).

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

fof(t3_rcomp_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r2_hidden(A,k1_rcomp_2(B,C))
              <=> ( r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,A) ) ) ) ) ) ),
    file(rcomp_2,t3_rcomp_2),
    []).

fof(t3_real,axiom,(
    ! [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),
    []).

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

fof(t41_rcomp_3,axiom,(
    ! [A] : 
      ( ( v1_jct_misc(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ~ ( ~ v1_xboole_0(A)
          & A != k1_numbers
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k2_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k12_prob_1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k3_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => A != k4_limfunc1(B) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( r1_xreal_0(B,C)
                      & A = k1_rcomp_1(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k1_rcomp_2(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k2_rcomp_2(B,C) ) ) )
          & ! [B] : 
              ( v1_xreal_0(B)
             => ! [C] : 
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,B)
                      & A = k2_rcomp_1(B,C) ) ) ) ) ) ),
    file(rcomp_3,t41_rcomp_3),
    []).

fof(t4_rcomp_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r2_hidden(A,k2_rcomp_2(B,C))
              <=> ( ~ r1_xreal_0(A,B)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    file(rcomp_2,t4_rcomp_2),
    []).

fof(t4_real,axiom,(
    ! [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),
    []).

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

fof(t5_real,axiom,(
    ! [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),
    []).

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

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

fof(t6_real,axiom,(
    ! [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),
    []).

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

fof(t7_real,axiom,(
    ! [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),
    []).

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

fof(t8_real,axiom,(
    ! [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),
    []).

fof(t8_topalg_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( v2_topalg_2(k1_rcomp_1(A,B))
            & m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) ) ),
    file(topalg_2,t8_topalg_2),
    []).

fof(t9_topalg_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( v2_topalg_2(k2_rcomp_1(A,B))
            & m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) ) ) ),
    file(topalg_2,t9_topalg_2),
    []).