% Mizar problem: t74_jgraph_5,jgraph_5,7519,49 
fof(t74_jgraph_5,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(2)))
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
                         => ( ( E = a_0_6_jgraph_5
                              & r1_jordan6(E,A,B)
                              & r1_jordan6(E,B,C)
                              & r1_jordan6(E,C,D) )
                           => ! [G] : 
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)))
                                  & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))) )
                               => ! [H] : 
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))) )
                                   => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(2))
                                        & v2_funct_1(G)
                                        & v5_pre_topc(H,k5_topmetr,k15_euclid(2))
                                        & v2_funct_1(H)
                                        & F = a_0_5_jgraph_5
                                        & k1_funct_1(G,0) = A
                                        & k1_funct_1(G,1) = C
                                        & k1_funct_1(H,0) = B
                                        & k1_funct_1(H,1) = D
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),G),F)
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),H),F)
                                        & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),H)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_2,cc1_borsuk_3,cc1_funct_1,cc1_membered,cc1_pre_topc,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_funct_1,cc2_membered,cc2_pscomp_1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_borsuk_2,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,connectedness_r1_xreal_0,d1_funct_2,d3_tarski,d5_funct_1,d5_tops_2,dt_g1_pre_topc,dt_k15_euclid,dt_k1_funct_1,dt_k1_numbers,dt_k1_pscomp_1,dt_k1_rcomp_1,dt_k1_real_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_euclid,dt_k22_borsuk_1,dt_k22_euclid,dt_k23_euclid,dt_k2_funct_1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tops_2,dt_k2_zfmisc_1,dt_k3_topmetr,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_topmetr,dt_k5_toprns_1,dt_k7_funct_2,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_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,fc13_xreal_0,fc14_xreal_0,fc1_borsuk_3,fc1_funct_1,fc1_pscomp_1,fc1_struct_0,fc1_xreal_0,fc2_borsuk_3,fc2_euclid,fc2_membered,fc2_pre_topc,fc2_pscomp_1,fc2_topmetr,fc2_topreal1,fc3_topmetr,fc5_borsuk_1,fc5_membered,fc5_pre_topc,fc6_membered,fc7_borsuk_2,fraenkel_a_0_1_jgraph_5,fraenkel_a_0_2_jgraph_2,fraenkel_a_0_2_jgraph_5,fraenkel_a_0_3_jgraph_5,fraenkel_a_0_4_jgraph_5,fraenkel_a_0_5_jgraph_5,fraenkel_a_0_6_jgraph_5,free_g1_pre_topc,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,l77_jgraph_5,l78_jgraph_5,l79_jgraph_5,l80_jgraph_5,rc10_pscomp_1,rc1_borsuk_3,rc1_funct_1,rc1_membered,rc1_pre_topc,rc1_pscomp_1,rc1_xreal_0,rc2_borsuk_3,rc2_funct_1,rc2_pre_topc,rc2_pscomp_1,rc2_xreal_0,rc3_funct_1,rc3_pre_topc,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pre_topc,rc4_pscomp_1,rc4_xreal_0,rc5_pre_topc,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,rc9_pscomp_1,redefinition_k1_pscomp_1,redefinition_k1_real_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_topmetr,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_jgraph_2__e15_77_1_2__jgraph_5,s1_jgraph_2__e17_77_1_2__jgraph_5,s1_jgraph_2__e19_77_1_2__jgraph_5,s1_jgraph_2__e21_77_1_2__jgraph_5,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r1_xboole_0,t18_jgraph_5,t1_numerals,t1_real,t1_subset,t22_funct_1,t2_real,t2_subset,t2_tarski,t3_real,t3_subset,t3_xboole_0,t48_rcomp_1,t4_real,t4_subset,t56_funct_1,t5_real,t5_subset,t6_boole,t6_real,t70_jgraph_5,t7_boole,t7_real,t83_borsuk_1,t8_boole,t8_jgraph_5,t8_real,t9_jgraph_5]),
    [file(jgraph_5,t74_jgraph_5)]).

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

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

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

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

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

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

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

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

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

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

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

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

fof(cc1_borsuk_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_2,cc1_borsuk_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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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

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

fof(cc1_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_xreal_0,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    []).

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

fof(cc2_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_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

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

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

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

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_borsuk_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_struct_0(A)
       => v2_t_0topsp(A) ) ) ),
    file(borsuk_2,cc4_borsuk_2),
    []).

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

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

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

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_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(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_tops_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_tops_2(C,A,B)
              <=> ( k1_relat_1(C) = k2_pre_topc(A)
                  & k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C)
                  & v5_pre_topc(C,A,B)
                  & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ),
    file(tops_2,d5_tops_2),
    []).

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_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k1_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(pscomp_1,k1_pscomp_1),
    []).

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_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k1_real_1(A),k1_numbers) ) ),
    file(real_1,k1_real_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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_borsuk_1,axiom,(
    l1_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,k22_borsuk_1),
    []).

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_k23_euclid,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k23_euclid(A,B),u1_struct_0(k15_euclid(2))) ) ),
    file(euclid,k23_euclid),
    []).

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

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

fof(dt_k2_tops_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k2_tops_2(A,B,C))
        & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(tops_2,k2_tops_2),
    []).

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

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

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_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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

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

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_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

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_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(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_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(fc1_borsuk_3,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(borsuk_3,fc1_borsuk_3),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

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_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(fc2_borsuk_3,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(A)
     => v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(borsuk_3,fc2_borsuk_3),
    []).

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

fof(fc2_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) ),
    file(pre_topc,fc2_pre_topc),
    []).

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_topmetr,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr) ),
    file(topmetr,fc2_topmetr),
    []).

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_topmetr,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & m1_relset_1(B,A,u1_struct_0(k3_topmetr)) )
     => ( v1_xcmplx_0(k1_funct_1(B,C))
        & v1_xreal_0(k1_funct_1(B,C)) ) ) ),
    file(topmetr,fc3_topmetr),
    []).

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

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

fof(fc5_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k2_pre_topc(A),A) ) ),
    file(pre_topc,fc5_pre_topc),
    []).

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

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

fof(fraenkel_a_0_1_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_1_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1
          & r1_xreal_0(k22_euclid(B),k21_euclid(B))
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ),
    file(jgraph_5,a_0_1_jgraph_5),
    []).

fof(fraenkel_a_0_2_jgraph_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_jgraph_2)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & p1_s1_jgraph_2(B) ) ) ),
    file(jgraph_2,a_0_2_jgraph_2),
    []).

fof(fraenkel_a_0_2_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1
          & r1_xreal_0(k21_euclid(B),k22_euclid(B))
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ),
    file(jgraph_5,a_0_2_jgraph_5),
    []).

fof(fraenkel_a_0_3_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_3_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1
          & r1_xreal_0(k21_euclid(B),k22_euclid(B))
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) ),
    file(jgraph_5,a_0_3_jgraph_5),
    []).

fof(fraenkel_a_0_4_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_4_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1
          & r1_xreal_0(k22_euclid(B),k21_euclid(B))
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) ),
    file(jgraph_5,a_0_4_jgraph_5),
    []).

fof(fraenkel_a_0_5_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_5_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & r1_xreal_0(1,k5_toprns_1(2,B)) ) ) ),
    file(jgraph_5,a_0_5_jgraph_5),
    []).

fof(fraenkel_a_0_6_jgraph_5,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_6_jgraph_5)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1 ) ) ),
    file(jgraph_5,a_0_6_jgraph_5),
    []).

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_k1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k1_real_1(k1_real_1(A)) = A ) ),
    file(real_1,k1_real_1),
    []).

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(l77_jgraph_5,axiom,
    ( k21_euclid(k23_euclid(k1_real_1(1),0)) = k1_real_1(1)
    & k22_euclid(k23_euclid(k1_real_1(1),0)) = 0
    & k21_euclid(k23_euclid(1,0)) = 1
    & k22_euclid(k23_euclid(1,0)) = 0
    & k21_euclid(k23_euclid(0,k1_real_1(1))) = 0
    & k22_euclid(k23_euclid(0,k1_real_1(1))) = k1_real_1(1)
    & k21_euclid(k23_euclid(0,1)) = 0
    & k22_euclid(k23_euclid(0,1)) = 1 ),
    file(jgraph_5,l77_jgraph_5),
    []).

fof(l78_jgraph_5,axiom,
    ( k5_toprns_1(2,k23_euclid(k1_real_1(1),0)) = 1
    & k5_toprns_1(2,k23_euclid(1,0)) = 1
    & k5_toprns_1(2,k23_euclid(0,k1_real_1(1))) = 1
    & k5_toprns_1(2,k23_euclid(0,1)) = 1 ),
    file(jgraph_5,l78_jgraph_5),
    []).

fof(l79_jgraph_5,axiom,(
    r2_hidden(0,k1_rcomp_1(0,1)) ),
    file(jgraph_5,l79_jgraph_5),
    []).

fof(l80_jgraph_5,axiom,(
    r2_hidden(1,k1_rcomp_1(0,1)) ),
    file(jgraph_5,l80_jgraph_5),
    []).

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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

fof(rc1_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_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

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_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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_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_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_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(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_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(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_k1_pscomp_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k1_pscomp_1(A,B,C) = k2_relat_1(C) ) ),
    file(pscomp_1,k1_pscomp_1),
    []).

fof(redefinition_k1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k1_real_1(A) = k4_xcmplx_0(A) ) ),
    file(real_1,k1_real_1),
    []).

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_topmetr,axiom,(
    k5_topmetr = k22_borsuk_1 ),
    file(topmetr,k5_topmetr),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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(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(s1_jgraph_2__e15_77_1_2__jgraph_5,axiom,(
    m1_subset_1(a_0_2_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ),
    file(jgraph_5,s1_jgraph_2__e15_77_1_2__jgraph_5),
    []).

fof(s1_jgraph_2__e17_77_1_2__jgraph_5,axiom,(
    m1_subset_1(a_0_2_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ),
    file(jgraph_5,s1_jgraph_2__e17_77_1_2__jgraph_5),
    []).

fof(s1_jgraph_2__e19_77_1_2__jgraph_5,axiom,(
    m1_subset_1(a_0_2_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ),
    file(jgraph_5,s1_jgraph_2__e19_77_1_2__jgraph_5),
    []).

fof(s1_jgraph_2__e21_77_1_2__jgraph_5,axiom,(
    m1_subset_1(a_0_2_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ),
    file(jgraph_5,s1_jgraph_2__e21_77_1_2__jgraph_5),
    []).

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

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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t18_jgraph_5,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k5_topmetr))
                                     => ~ ( H = 0
                                          & I = 1
                                          & v5_pre_topc(A,k5_topmetr,k15_euclid(2))
                                          & v2_funct_1(A)
                                          & v5_pre_topc(B,k5_topmetr,k15_euclid(2))
                                          & v2_funct_1(B)
                                          & C = a_0_5_jgraph_5
                                          & D = a_0_1_jgraph_5
                                          & E = a_0_2_jgraph_5
                                          & F = a_0_3_jgraph_5
                                          & G = a_0_4_jgraph_5
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),A,H),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),A,I),D)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),B,H),F)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),B,I),G)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),A),C)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),B),C)
                                          & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),B)) ) ) ) ) ) ) ) ) ) ) ),
    file(jgraph_5,t18_jgraph_5),
    []).

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

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(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    []).

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(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

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(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(t56_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k1_relat_1(B)) )
       => ( A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A))
          & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) ) ) ) ),
    file(funct_1,t56_funct_1),
    []).

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(t70_jgraph_5,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(2)))
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & A != B
                          & B != C
                          & C != D
                          & ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
                                & m2_relset_1(F,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) )
                             => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2))
                                  & ! [G] : 
                                      ( m1_subset_1(G,u1_struct_0(k15_euclid(2)))
                                     => k5_toprns_1(2,k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,G)) = k5_toprns_1(2,G) )
                                  & k23_euclid(k1_real_1(1),0) = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A)
                                  & k23_euclid(0,1) = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B)
                                  & k23_euclid(1,0) = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C)
                                  & k23_euclid(0,k1_real_1(1)) = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D) ) ) ) ) ) ) ) ) ),
    file(jgraph_5,t70_jgraph_5),
    []).

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(t83_borsuk_1,axiom,(
    u1_struct_0(k22_borsuk_1) = k1_rcomp_1(0,1) ),
    file(borsuk_1,t83_borsuk_1),
    []).

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

fof(t8_jgraph_5,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_pre_topc(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v3_tops_2(E,B,C)
                          & v5_pre_topc(D,A,B) )
                       => v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ),
    file(jgraph_5,t8_jgraph_5),
    []).

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_jgraph_5,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( l1_pre_topc(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v3_tops_2(E,B,C)
                          & v2_funct_1(D) )
                       => v2_funct_1(k5_relat_1(D,E)) ) ) ) ) ) ) ),
    file(jgraph_5,t9_jgraph_5),
    []).