% Mizar problem: t57_topreala,topreala,1411,14 
fof(t57_topreala,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( v1_funct_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))))
                      & v1_funct_2(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D)))
                      & m2_relset_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D))) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_yellow13,cc11_topreal6,cc11_yellow13,cc1_borsuk_6,cc1_finseq_1,cc1_monoid_0,cc1_nat_1,cc1_pre_topc,cc1_real_1,cc1_relset_1,cc1_topreal6,cc1_topreala,cc1_tops_1,cc1_xreal_0,cc2_borsuk_6,cc2_int_1,cc2_monoid_0,cc2_nat_1,cc2_pscomp_1,cc2_topreal6,cc2_topreala,cc2_tops_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc3_topalg_2,cc3_topreala,cc3_tops_1,cc3_xreal_0,cc4_int_1,cc4_monoid_0,cc4_topalg_2,cc4_topreal6,cc4_topreala,cc4_tops_1,cc4_xreal_0,cc4_yellow13,cc5_topalg_2,cc5_topreal6,cc5_tops_1,cc5_xreal_0,cc5_yellow13,cc6_topreal6,cc6_tops_1,cc6_xreal_0,cc6_yellow13,cc7_topreal6,cc7_xreal_0,cc7_yellow13,cc8_topreal6,cc8_xreal_0,cc8_yellow13,cc9_topreal6,cc9_yellow13,commutativity_k2_tarski,connectedness_r1_xreal_0,d14_euclid,d15_euclid,d1_funct_2,d1_rcomp_1,d1_topreala,d2_jgraph_6,d2_topreala,d3_tarski,d5_funct_1,d5_tarski,dt_g1_pre_topc,dt_k10_finseq_1,dt_k15_euclid,dt_k1_card_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_rcomp_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_topreala,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_euclid,dt_k22_euclid,dt_k2_jgraph_6,dt_k2_partfun1,dt_k2_relat_1,dt_k2_tarski,dt_k2_topreala,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_pre_topc,dt_k3_topalg_2,dt_k3_topmetr,dt_k4_relset_1,dt_k4_tarski,dt_k4_topmetr,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relset_1,dt_k6_borsuk_1,dt_k7_relat_1,dt_k8_borsuk_1,dt_k8_funct_2,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_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_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_pscomp_1,fc11_finseq_1,fc12_topreala,fc16_topreala,fc17_finseq_1,fc17_topreala,fc1_borsuk_6,fc1_pscomp_1,fc1_struct_0,fc1_topreal6,fc1_yellow13,fc2_borsuk_1,fc2_finseq_1,fc2_pscomp_1,fc3_pre_topc,fc4_pre_topc,fc5_finseq_1,fc5_yellow12,fc6_yellow12,fc7_borsuk_6,fc7_finseq_1,fc7_topreal6,fc8_topreal6,fraenkel_a_2_0_rcomp_1,fraenkel_a_4_0_topreala,fraenkel_a_4_3_jgraph_6,free_g1_pre_topc,l1_topreala,rc10_pscomp_1,rc1_borsuk_6,rc1_finseq_1,rc1_int_1,rc1_monoid_0,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_topreal6,rc1_topreala,rc1_tops_1,rc1_xreal_0,rc2_borsuk_6,rc2_finseq_1,rc2_int_1,rc2_monoid_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_tops_1,rc2_xreal_0,rc3_borsuk_6,rc3_finseq_1,rc3_nat_1,rc3_pre_topc,rc3_pscomp_1,rc3_struct_0,rc3_topalg_2,rc3_tops_1,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_k2_partfun1,redefinition_k3_finseq_1,redefinition_k3_topalg_2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k8_borsuk_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t106_zfmisc_1,t119_zfmisc_1,t1_real,t1_subset,t24_topmetr,t2_real,t2_subset,t2_tarski,t3_real,t3_subset,t48_rcomp_1,t48_topreala,t4_funct_2,t4_real,t4_subset,t53_topreala,t5_real,t5_subset,t61_finseq_1,t6_boole,t6_real,t70_funct_1,t7_boole,t7_real,t8_boole,t8_real,t91_relat_1,t9_domain_1]),
    [file(topreala,t57_topreala)]).

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_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_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(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_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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

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_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

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_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_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_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

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_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_topreala,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B) ) ) ) ) ),
    file(topreala,cc3_topreala),
    []).

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_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_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_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_topreala,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & l1_pre_topc(B) )
     => ! [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_xboole_0(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B) ) ) ) ) ),
    file(topreala,cc4_topreala),
    []).

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_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(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_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(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_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(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_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(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_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(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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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(d14_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( B = k21_euclid(A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ( A = C
                 => B = k1_funct_1(C,1) ) ) ) ) ) ),
    file(euclid,d14_euclid),
    []).

fof(d15_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( B = k22_euclid(A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ( A = C
                 => B = k1_funct_1(C,2) ) ) ) ) ) ),
    file(euclid,d15_euclid),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_rcomp_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k1_rcomp_1(A,B) = a_2_0_rcomp_1(A,B) ) ) ),
    file(rcomp_1,d1_rcomp_1),
    []).

fof(d1_topreala,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => k1_topreala(A,B,C,D) = k3_pre_topc(k15_euclid(2),k2_jgraph_6(A,B,C,D)) ) ) ) ) ),
    file(topreala,d1_topreala),
    []).

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(d2_topreala,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) )
     => ( A = k2_topreala
      <=> ! [B] : 
            ( v1_xreal_0(B)
           => ! [C] : 
                ( v1_xreal_0(C)
               => k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ) ),
    file(topreala,d2_topreala),
    []).

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

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

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_k10_finseq_1,axiom,(
    $true ),
    file(finseq_1,k10_finseq_1),
    []).

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_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_topreala,axiom,
    ( v1_funct_1(k2_topreala)
    & v1_funct_2(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2)))
    & m2_relset_1(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) ),
    file(topreala,k2_topreala),
    []).

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_topmetr,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( ~ v3_struct_0(k4_topmetr(A,B))
        & v1_pre_topc(k4_topmetr(A,B))
        & m1_pre_topc(k4_topmetr(A,B),k3_topmetr) ) ) ),
    file(topmetr,k4_topmetr),
    []).

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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

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

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k8_borsuk_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))) ) ),
    file(borsuk_1,k8_borsuk_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc12_topreala,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,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)) ) ) ),
    file(topreala,fc12_topreala),
    []).

fof(fc16_topreala,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,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)) ) ) ),
    file(topreala,fc16_topreala),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

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(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_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_borsuk_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B)) ) ) ),
    file(borsuk_1,fc2_borsuk_1),
    []).

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(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_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_finseq_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc5_finseq_1),
    []).

fof(fc5_yellow12,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ),
    file(yellow12,fc5_yellow12),
    []).

fof(fc6_yellow12,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(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))) ) ) ),
    file(yellow12,fc6_yellow12),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B))
      & v1_finset_1(k10_finseq_1(A,B))
      & v1_finseq_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc7_finseq_1),
    []).

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_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(fraenkel_a_2_0_rcomp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_0_rcomp_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_numbers)
            & A = D
            & r1_xreal_0(B,D)
            & r1_xreal_0(D,C) ) ) ) ),
    file(rcomp_1,a_2_0_rcomp_1),
    []).

fof(fraenkel_a_4_0_topreala,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_0_topreala(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(topreala,a_4_0_topreala),
    []).

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(l1_topreala,axiom,(
    u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)) = k2_zfmisc_1(u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) ),
    file(topreala,l1_topreala),
    []).

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_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_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_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_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_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_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_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_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_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_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_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_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

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

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k8_borsuk_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k8_borsuk_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(borsuk_1,k8_borsuk_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

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(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_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(t24_topmetr,axiom,(
    u1_struct_0(k3_topmetr) = k1_numbers ),
    file(topmetr,t24_topmetr),
    []).

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(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(t48_rcomp_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r2_hidden(C,k1_rcomp_1(A,B))
              <=> ( r1_xreal_0(A,C)
                  & r1_xreal_0(C,B) ) ) ) ) ) ),
    file(rcomp_1,t48_rcomp_1),
    []).

fof(t48_topreala,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))) = k2_zfmisc_1(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ),
    file(topreala,t48_topreala),
    []).

fof(t4_funct_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_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(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(t61_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    []).

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(t70_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    []).

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(t91_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    []).

fof(t9_domain_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
              & ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m1_subset_1(E,C)
                     => A != k4_tarski(D,E) ) ) ) ) ) ),
    file(domain_1,t9_domain_1),
    []).