% Mizar problem: t10_toprealb,toprealb,581,54 
fof(t10_toprealb,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => m1_pre_topc(k7_toprealb(2,k16_euclid(2),A),k1_topreala(k4_xcmplx_0(A),A,k4_xcmplx_0(A),A)) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_tex_2,cc10_topreal6,cc11_tex_2,cc11_topreal6,cc12_tex_2,cc13_tex_2,cc14_tex_2,cc15_tex_2,cc16_tex_2,cc17_tex_2,cc18_tex_2,cc19_tex_2,cc1_borsuk_3,cc1_finseq_1,cc1_funct_1,cc1_monoid_0,cc1_nat_1,cc1_pre_topc,cc1_real_1,cc1_tex_2,cc1_topalg_3,cc1_topreal2,cc1_topreal6,cc1_topreala,cc1_tops_1,cc1_xcmplx_0,cc1_xreal_0,cc20_tex_2,cc21_tex_2,cc22_tex_2,cc23_tex_2,cc24_tex_2,cc25_tex_2,cc26_tex_2,cc27_tex_2,cc28_tex_2,cc29_tex_2,cc2_funct_1,cc2_int_1,cc2_monoid_0,cc2_nat_1,cc2_pscomp_1,cc2_tex_2,cc2_topalg_3,cc2_topreal6,cc2_topreala,cc2_tops_1,cc2_xcmplx_0,cc2_xreal_0,cc30_tex_2,cc31_tex_2,cc32_tex_2,cc33_tex_2,cc34_tex_2,cc35_tex_2,cc36_tex_2,cc37_tex_2,cc38_tex_2,cc39_tex_2,cc3_int_1,cc3_nat_1,cc3_tex_2,cc3_tops_1,cc3_xreal_0,cc40_tex_2,cc41_tex_2,cc42_tex_2,cc43_tex_2,cc44_tex_2,cc45_tex_2,cc46_tex_2,cc47_tex_2,cc48_tex_2,cc49_tex_2,cc4_int_1,cc4_monoid_0,cc4_tex_2,cc4_topgrp_1,cc4_topreal6,cc4_tops_1,cc4_xreal_0,cc50_tex_2,cc5_tex_2,cc5_topreal6,cc5_tops_1,cc5_xreal_0,cc6_tex_2,cc6_topreal6,cc6_tops_1,cc6_xreal_0,cc7_tex_2,cc7_topreal6,cc7_xreal_0,cc8_tex_2,cc8_topreal6,cc8_xreal_0,cc9_tex_2,cc9_topreal6,connectedness_r1_xreal_0,d1_struct_0,d2_jgraph_6,d3_tarski,d6_toprealb,dt_g1_pre_topc,dt_k15_euclid,dt_k16_complex1,dt_k16_euclid,dt_k18_complex1,dt_k1_numbers,dt_k1_topreala,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_euclid,dt_k22_euclid,dt_k2_jgraph_6,dt_k3_pre_topc,dt_k3_topreal9,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_toprns_1,dt_k7_toprealb,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_m2_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,existence_m2_subset_1,fc10_pscomp_1,fc13_xreal_0,fc14_topreal9,fc14_xreal_0,fc15_topreal9,fc17_topreala,fc19_toprealb,fc1_borsuk_6,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc1_topalg_3,fc1_topreal6,fc1_xreal_0,fc20_toprealb,fc21_toprealb,fc2_euclid,fc2_finseq_1,fc2_pscomp_1,fc2_topreal1,fc3_int_1,fc3_pre_topc,fc4_borsuk_3,fc4_pre_topc,fc5_int_1,fc6_xcmplx_0,fc7_borsuk_3,fc7_topreal9,fraenkel_a_1_0_toprealb,fraenkel_a_4_3_jgraph_6,free_g1_pre_topc,involutiveness_k4_xcmplx_0,projectivity_k16_complex1,projectivity_k18_complex1,rc10_pscomp_1,rc10_tex_2,rc11_tex_2,rc12_tex_2,rc13_tex_2,rc14_tex_2,rc15_tex_2,rc16_tex_2,rc17_tex_2,rc18_tex_2,rc19_tex_2,rc1_borsuk_3,rc1_finseq_1,rc1_funct_1,rc1_int_1,rc1_jordan16,rc1_monoid_0,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_tex_2,rc1_topreal2,rc1_topreal6,rc1_topreala,rc1_tops_1,rc1_xcmplx_0,rc1_xreal_0,rc20_tex_2,rc2_borsuk_3,rc2_funct_1,rc2_int_1,rc2_monoid_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_tex_2,rc2_tops_1,rc2_xcmplx_0,rc2_xreal_0,rc3_borsuk_1,rc3_borsuk_6,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_pre_topc,rc3_pscomp_1,rc3_struct_0,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_borsuk_1,rc4_funct_1,rc4_pre_topc,rc4_pscomp_1,rc4_tex_2,rc4_tops_1,rc4_xreal_0,rc5_pre_topc,rc5_struct_0,rc5_tex_2,rc5_tops_1,rc6_finseq_1,rc6_pre_topc,rc6_tex_2,rc6_topgrp_1,rc7_finseq_1,rc7_pre_topc,rc7_tex_2,rc8_finseq_1,rc8_tex_2,rc9_pscomp_1,rc9_tex_2,redefinition_k18_complex1,redefinition_k5_numbers,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc2_boole,spc2_numerals,t12_absvalue,t12_topreal9,t1_real,t1_subset,t2_real,t2_subset,t2_tarski,t2_topmetr,t3_real,t3_subset,t4_real,t4_subset,t4_tsep_1,t50_jgraph_1,t53_topreala,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,t9_toprealb]),
    [file(toprealb,t10_toprealb)]).

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_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    file(tex_2,cc10_tex_2),
    []).

fof(cc10_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( v1_topreal2(A)
       => v2_connsp_1(A,k15_euclid(2)) ) ) ),
    file(topreal6,cc10_topreal6),
    []).

fof(cc11_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc11_tex_2),
    []).

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(cc12_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc12_tex_2),
    []).

fof(cc13_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc13_tex_2),
    []).

fof(cc14_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc14_tex_2),
    []).

fof(cc15_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc15_tex_2),
    []).

fof(cc16_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v1_tdlat_3(B)
           => v2_pre_topc(B) ) ) ) ),
    file(tex_2,cc16_tex_2),
    []).

fof(cc17_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v2_tdlat_3(B)
           => v2_pre_topc(B) ) ) ) ),
    file(tex_2,cc17_tex_2),
    []).

fof(cc18_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v2_pre_topc(B)
           => ~ v1_tdlat_3(B) ) ) ) ),
    file(tex_2,cc18_tex_2),
    []).

fof(cc19_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v2_pre_topc(B)
           => ~ v2_tdlat_3(B) ) ) ) ),
    file(tex_2,cc19_tex_2),
    []).

fof(cc1_borsuk_3,axiom,(
    ! [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),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_monoid_0,axiom,(
    ! [A] : 
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(monoid_0,cc1_monoid_0),
    []).

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

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_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(real_1,cc1_real_1),
    []).

fof(cc1_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    []).

fof(cc1_topalg_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_struct_0(A)
       => v1_connsp_1(A) ) ) ),
    file(topalg_3,cc1_topalg_3),
    []).

fof(cc1_topreal2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( v1_topreal2(A)
       => ( ~ v1_xboole_0(A)
          & v6_compts_1(A,k15_euclid(2)) ) ) ) ),
    file(topreal2,cc1_topreal2),
    []).

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_topreala,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & v2_monoid_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v2_pre_topc(B)
            & v1_monoid_0(B)
            & v2_monoid_0(B) ) ) ) ),
    file(topreala,cc1_topreala),
    []).

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_xcmplx_0,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    []).

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

fof(cc20_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v1_tdlat_3(B)
           => v3_tdlat_3(B) ) ) ) ),
    file(tex_2,cc20_tex_2),
    []).

fof(cc21_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v3_tdlat_3(B)
           => ~ v1_tdlat_3(B) ) ) ) ),
    file(tex_2,cc21_tex_2),
    []).

fof(cc22_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v2_tdlat_3(B)
           => v3_tdlat_3(B) ) ) ) ),
    file(tex_2,cc22_tex_2),
    []).

fof(cc23_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v3_tdlat_3(B)
           => ~ v2_tdlat_3(B) ) ) ) ),
    file(tex_2,cc23_tex_2),
    []).

fof(cc24_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc24_tex_2),
    []).

fof(cc25_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & ~ v1_tdlat_3(B) ) ) ) ) ),
    file(tex_2,cc25_tex_2),
    []).

fof(cc26_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & ~ v2_tdlat_3(B) ) ) ) ) ),
    file(tex_2,cc26_tex_2),
    []).

fof(cc27_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc27_tex_2),
    []).

fof(cc28_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A) ) ) ) ) ),
    file(tex_2,cc28_tex_2),
    []).

fof(cc29_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v1_tsep_1(B,A)
           => ( v2_pre_topc(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc29_tex_2),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    []).

fof(cc2_monoid_0,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v2_monoid_0(A)
       => v1_monoid_0(A) ) ) ),
    file(monoid_0,cc2_monoid_0),
    []).

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

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_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    []).

fof(cc2_topalg_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_borsuk_2(A)
          & v1_connsp_1(A) ) ) ) ),
    file(topalg_3,cc2_topalg_3),
    []).

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_topreala,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v3_struct_0(A)
          & v2_pre_topc(A) )
       => ( v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A) ) ) ) ),
    file(topreala,cc2_topreala),
    []).

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_xcmplx_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_0),
    []).

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

fof(cc30_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v1_borsuk_1(B,A)
           => ( v2_pre_topc(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc30_tex_2),
    []).

fof(cc31_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc31_tex_2),
    []).

fof(cc32_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & ~ v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc32_tex_2),
    []).

fof(cc33_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc33_tex_2),
    []).

fof(cc34_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc34_tex_2),
    []).

fof(cc35_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tsep_1(B,A)
              & ~ v1_borsuk_1(B,A)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc35_tex_2),
    []).

fof(cc36_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc36_tex_2),
    []).

fof(cc37_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B) ) ) ) ) ),
    file(tex_2,cc37_tex_2),
    []).

fof(cc38_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v1_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc38_tex_2),
    []).

fof(cc39_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v5_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & ~ v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc39_tex_2),
    []).

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

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_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_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(cc40_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc40_tex_2),
    []).

fof(cc41_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v2_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc41_tex_2),
    []).

fof(cc42_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ~ v5_tex_2(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A)
              & v1_borsuk_1(B,A)
              & v1_tdlat_3(B)
              & v3_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc42_tex_2),
    []).

fof(cc43_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc43_tex_2),
    []).

fof(cc44_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc44_tex_2),
    []).

fof(cc45_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v3_realset2(B)
              & v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc45_tex_2),
    []).

fof(cc46_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tdlat_3(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc46_tex_2),
    []).

fof(cc47_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & v2_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc47_tex_2),
    []).

fof(cc48_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc48_tex_2),
    []).

fof(cc49_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_tex_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v3_realset2(B) ) ) ) ) ),
    file(tex_2,cc49_tex_2),
    []).

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_monoid_0,axiom,(
    ! [A] : 
      ( ( v2_monoid_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finset_1(B)
            & v1_finseq_1(B) ) ) ) ),
    file(monoid_0,cc4_monoid_0),
    []).

fof(cc4_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    []).

fof(cc4_topgrp_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v1_topgrp_1(A) ) ) ) ),
    file(topgrp_1,cc4_topgrp_1),
    []).

fof(cc4_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( ~ v1_sppol_1(A)
       => ~ v1_xboole_0(A) ) ) ),
    file(topreal6,cc4_topreal6),
    []).

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(cc50_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v2_tdlat_3(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v3_realset2(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B)
              & ~ v5_tex_2(B,A) ) ) ) ) ),
    file(tex_2,cc50_tex_2),
    []).

fof(cc5_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    []).

fof(cc5_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( ~ v2_sppol_1(A)
       => ~ v1_xboole_0(A) ) ) ),
    file(topreal6,cc5_topreal6),
    []).

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(cc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    []).

fof(cc6_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( v2_topreal4(A,k15_euclid(2))
       => ( v3_pre_topc(A,k15_euclid(2))
          & v2_connsp_1(A,k15_euclid(2)) ) ) ) ),
    file(topreal6,cc6_topreal6),
    []).

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(cc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    []).

fof(cc7_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( ( v3_pre_topc(A,k15_euclid(2))
          & v2_connsp_1(A,k15_euclid(2)) )
       => v2_topreal4(A,k15_euclid(2)) ) ) ),
    file(topreal6,cc7_topreal6),
    []).

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(cc8_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    file(tex_2,cc8_tex_2),
    []).

fof(cc8_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( v1_xboole_0(A)
       => v1_sppol_1(A) ) ) ),
    file(topreal6,cc8_topreal6),
    []).

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(cc9_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc9_tex_2),
    []).

fof(cc9_topreal6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( v1_xboole_0(A)
       => v2_sppol_1(A) ) ) ),
    file(topreal6,cc9_topreal6),
    []).

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

fof(d2_jgraph_6,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => k2_jgraph_6(A,B,C,D) = a_4_3_jgraph_6(A,B,C,D) ) ) ) ) ),
    file(jgraph_6,d2_jgraph_6),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d6_toprealb,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] : 
              ( v1_xreal_0(C)
             => k7_toprealb(A,B,C) = k3_pre_topc(k15_euclid(A),k3_topreal9(A,B,C)) ) ) ) ),
    file(toprealb,d6_toprealb),
    []).

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_k15_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & l1_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,k15_euclid),
    []).

fof(dt_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k16_complex1(A)) ) ),
    file(complex1,k16_complex1),
    []).

fof(dt_k16_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k16_euclid(A),u1_struct_0(k15_euclid(A))) ) ),
    file(euclid,k16_euclid),
    []).

fof(dt_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => m1_subset_1(k18_complex1(A),k1_numbers) ) ),
    file(complex1,k18_complex1),
    []).

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

fof(dt_k1_topreala,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_pre_topc(k1_topreala(A,B,C,D),k15_euclid(2)) ) ),
    file(topreala,k1_topreala),
    []).

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_k21_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => m1_subset_1(k21_euclid(A),k1_numbers) ) ),
    file(euclid,k21_euclid),
    []).

fof(dt_k22_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => m1_subset_1(k22_euclid(A),k1_numbers) ) ),
    file(euclid,k22_euclid),
    []).

fof(dt_k2_jgraph_6,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k2_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ),
    file(jgraph_6,k2_jgraph_6),
    []).

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_topreal9,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_subset_1(k3_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ),
    file(topreal9,k3_topreal9),
    []).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

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

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

fof(dt_k5_toprns_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k5_toprns_1(A,B),k1_numbers) ) ),
    file(toprns_1,k5_toprns_1),
    []).

fof(dt_k7_toprealb,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_pre_topc(k7_toprealb(A,B,C),k15_euclid(A)) ) ),
    file(toprealb,k7_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_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),
    []).

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(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),
    []).

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(fc13_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc13_xreal_0),
    []).

fof(fc14_topreal9,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & v3_xreal_0(C) )
     => ( v1_xboole_0(k3_topreal9(A,B,C))
        & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ),
    file(topreal9,fc14_topreal9),
    []).

fof(fc14_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    []).

fof(fc15_topreal9,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ( ~ v1_xboole_0(k3_topreal9(A,B,C))
        & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ),
    file(topreal9,fc15_topreal9),
    []).

fof(fc17_topreala,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B)
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C)
        & v1_xreal_0(D)
        & ~ v3_xreal_0(D) )
     => ( ~ v3_struct_0(k1_topreala(A,C,B,D))
        & v2_pre_topc(k1_topreala(A,C,B,D))
        & v1_monoid_0(k1_topreala(A,C,B,D))
        & v2_monoid_0(k1_topreala(A,C,B,D)) ) ) ),
    file(topreala,fc17_topreala),
    []).

fof(fc19_toprealb,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & m1_subset_1(B,u1_struct_0(k15_euclid(2))) )
     => ( ~ v1_xboole_0(k3_topreal9(2,B,A))
        & v4_pre_topc(k3_topreal9(2,B,A),k15_euclid(2))
        & v1_jordan2c(k3_topreal9(2,B,A),2)
        & v2_connsp_1(k3_topreal9(2,B,A),k15_euclid(2))
        & v6_compts_1(k3_topreal9(2,B,A),k15_euclid(2))
        & v1_topreal2(k3_topreal9(2,B,A)) ) ) ),
    file(toprealb,fc19_toprealb),
    []).

fof(fc1_borsuk_6,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v1_monoid_0(k15_euclid(A))
        & v2_monoid_0(k15_euclid(A)) ) ) ),
    file(borsuk_6,fc1_borsuk_6),
    []).

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_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_topalg_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & v1_connsp_1(A)
        & l1_pre_topc(A) )
     => ( v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v1_connsp_1(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ),
    file(topalg_3,fc1_topalg_3),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    []).

fof(fc20_toprealb,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ( ~ v3_struct_0(k7_toprealb(A,B,C))
        & v1_pre_topc(k7_toprealb(A,B,C))
        & v2_pre_topc(k7_toprealb(A,B,C))
        & v1_monoid_0(k7_toprealb(A,B,C))
        & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ),
    file(toprealb,fc20_toprealb),
    []).

fof(fc21_toprealb,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xboole_0(C)
        & v1_xreal_0(C) )
     => ( v2_pre_topc(k7_toprealb(A,B,C))
        & v3_realset2(k7_toprealb(A,B,C))
        & v1_monoid_0(k7_toprealb(A,B,C))
        & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ),
    file(toprealb,fc21_toprealb),
    []).

fof(fc2_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,fc2_euclid),
    []).

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_pscomp_1,axiom,
    ( ~ v1_xboole_0(k5_ordinal2)
    & v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2)
    & ~ v1_setfam_1(k5_ordinal2) ),
    file(pscomp_1,fc2_pscomp_1),
    []).

fof(fc2_topreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v3_compts_1(k15_euclid(A)) ) ) ),
    file(topreal1,fc2_topreal1),
    []).

fof(fc3_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc3_int_1),
    []).

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(fc4_borsuk_3,axiom,(
    ! [A,B] : 
      ( ( 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))
        & v2_t_0topsp(k3_pre_topc(A,B)) ) ) ),
    file(borsuk_3,fc4_borsuk_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(fc5_int_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc5_int_1),
    []).

fof(fc6_xcmplx_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A) )
     => ( ~ v1_xboole_0(k4_xcmplx_0(A))
        & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) ),
    file(xcmplx_0,fc6_xcmplx_0),
    []).

fof(fc7_borsuk_3,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v6_compts_1(B,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))
        & v2_compts_1(k3_pre_topc(A,B)) ) ) ),
    file(borsuk_3,fc7_borsuk_3),
    []).

fof(fc7_topreal9,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ),
    file(topreal9,fc7_topreal9),
    []).

fof(fraenkel_a_1_0_toprealb,axiom,(
    ! [A,B] : 
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_0_toprealb(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
            & A = C
            & r1_xreal_0(k4_xcmplx_0(B),k21_euclid(C))
            & r1_xreal_0(k21_euclid(C),B)
            & r1_xreal_0(k4_xcmplx_0(B),k22_euclid(C))
            & r1_xreal_0(k22_euclid(C),B) ) ) ) ),
    file(toprealb,a_1_0_toprealb),
    []).

fof(fraenkel_a_4_3_jgraph_6,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_3_jgraph_6(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,u1_struct_0(k15_euclid(2)))
            & A = F
            & r1_xreal_0(B,k21_euclid(F))
            & r1_xreal_0(k21_euclid(F),C)
            & r1_xreal_0(D,k22_euclid(F))
            & r1_xreal_0(k22_euclid(F),E) ) ) ) ),
    file(jgraph_6,a_4_3_jgraph_6),
    []).

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(involutiveness_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

fof(projectivity_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ),
    file(complex1,k16_complex1),
    []).

fof(projectivity_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ),
    file(complex1,k18_complex1),
    []).

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(rc10_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc10_tex_2),
    []).

fof(rc11_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & ~ v2_tex_2(B,A) ) ) ),
    file(tex_2,rc11_tex_2),
    []).

fof(rc12_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v3_realset2(B) ) ) ),
    file(tex_2,rc12_tex_2),
    []).

fof(rc13_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v3_realset2(B)
          & v2_tex_2(B,A) ) ) ),
    file(tex_2,rc13_tex_2),
    []).

fof(rc14_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v3_realset2(B) ) ) ),
    file(tex_2,rc14_tex_2),
    []).

fof(rc15_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v3_realset2(B) ) ) ),
    file(tex_2,rc15_tex_2),
    []).

fof(rc16_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tsep_1(B,A)
          & v1_borsuk_1(B,A) ) ) ),
    file(tex_2,rc16_tex_2),
    []).

fof(rc17_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tsep_1(B,A)
          & v1_borsuk_1(B,A)
          & v1_tdlat_3(B)
          & v3_tdlat_3(B)
          & v2_tex_2(B,A) ) ) ),
    file(tex_2,rc17_tex_2),
    []).

fof(rc18_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & ~ v1_tsep_1(B,A)
          & ~ v1_borsuk_1(B,A)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v2_tex_2(B,A) ) ) ),
    file(tex_2,rc18_tex_2),
    []).

fof(rc19_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v2_tex_2(B,A) ) ) ),
    file(tex_2,rc19_tex_2),
    []).

fof(rc1_borsuk_3,axiom,(
    ? [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),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_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_jordan16,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
          & v1_realset1(B) ) ) ),
    file(jordan16,rc1_jordan16),
    []).

fof(rc1_monoid_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v1_monoid_0(A) ) ),
    file(monoid_0,rc1_monoid_0),
    []).

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_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_tex_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    []).

fof(rc1_topreal2,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
      & v1_topreal2(A) ) ),
    file(topreal2,rc1_topreal2),
    []).

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_topreala,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_monoid_0(A)
      & v2_monoid_0(A) ) ),
    file(topreala,rc1_topreala),
    []).

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_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

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

fof(rc20_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B)
          & v5_tex_2(B,A) ) ) ),
    file(tex_2,rc20_tex_2),
    []).

fof(rc2_borsuk_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v6_compts_1(B,A) ) ) ),
    file(borsuk_3,rc2_borsuk_3),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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

fof(rc2_monoid_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v2_monoid_0(A) ) ),
    file(monoid_0,rc2_monoid_0),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_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_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_tex_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    []).

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_xcmplx_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    []).

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_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_borsuk_1(B,A) ) ) ),
    file(borsuk_1,rc3_borsuk_1),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_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_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_borsuk_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_borsuk_1(B,A) ) ) ),
    file(borsuk_1,rc4_borsuk_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

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_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_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_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_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    []).

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(rc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    []).

fof(rc6_topgrp_1,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_topgrp_1(A) ) ),
    file(topgrp_1,rc6_topgrp_1),
    []).

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(rc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    []).

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(rc8_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc8_tex_2),
    []).

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(rc9_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc9_tex_2),
    []).

fof(redefinition_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(A) = k16_complex1(A) ) ),
    file(complex1,k18_complex1),
    []).

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

fof(redefinition_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,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(t12_absvalue,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k4_xcmplx_0(A),B)
              & r1_xreal_0(B,A) )
          <=> r1_xreal_0(k18_complex1(B),A) ) ) ) ),
    file(absvalue,t12_absvalue),
    []).

fof(t12_topreal9,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( r2_hidden(C,k3_topreal9(A,k16_euclid(A),B))
               => k5_toprns_1(A,C) = B ) ) ) ) ),
    file(topreal9,t12_topreal9),
    []).

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

fof(t2_topmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    file(topmetr,t2_topmetr),
    []).

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(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(t4_tsep_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_pre_topc(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
              <=> m1_pre_topc(B,C) ) ) ) ) ),
    file(tsep_1,t4_tsep_1),
    []).

fof(t50_jgraph_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ( r1_xreal_0(k18_complex1(k21_euclid(A)),k5_toprns_1(2,A))
        & r1_xreal_0(k18_complex1(k22_euclid(A)),k5_toprns_1(2,A)) ) ) ),
    file(jgraph_1,t50_jgraph_1),
    []).

fof(t53_topreala,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => u1_struct_0(k1_topreala(A,B,C,D)) = k2_jgraph_6(A,B,C,D) ) ) ) ) ),
    file(topreala,t53_topreala),
    []).

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(t9_toprealb,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => u1_struct_0(k7_toprealb(A,C,B)) = k3_topreal9(A,C,B) ) ) ) ),
    file(toprealb,t9_toprealb),
    []).