% Mizar problem: t69_jgraph_5,jgraph_5,6816,60 
fof(t69_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)))) )
                     => ~ ( 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
                          & ~ r1_xreal_0(0,k21_euclid(A))
                          & ~ r1_xreal_0(0,k21_euclid(B))
                          & ~ r1_xreal_0(0,k21_euclid(C))
                          & ~ r1_xreal_0(0,k21_euclid(D))
                          & ~ r1_xreal_0(0,k22_euclid(A))
                          & ~ r1_xreal_0(0,k22_euclid(B))
                          & ~ r1_xreal_0(0,k22_euclid(C))
                          & ~ r1_xreal_0(0,k22_euclid(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) ) ) ) ) ) ) ) ) ),
    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_3,cc1_funct_1,cc1_membered,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,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,connectedness_r1_xreal_0,d1_funct_2,dt_g1_pre_topc,dt_k15_euclid,dt_k1_funct_1,dt_k1_numbers,dt_k1_real_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_euclid,dt_k22_euclid,dt_k23_euclid,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_jgraph_4,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_relset_1,dt_k4_xcmplx_0,dt_k5_jgraph_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_relat_1,dt_k5_square_1,dt_k5_toprns_1,dt_k6_real_1,dt_k6_xcmplx_0,dt_k7_funct_2,dt_k7_jgraph_4,dt_k7_square_1,dt_k7_xcmplx_0,dt_k8_funct_2,dt_k8_square_1,dt_k9_jgraph_4,dt_k9_square_1,dt_l1_pre_topc,dt_l1_struct_0,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_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_borsuk_3,fc1_funct_1,fc1_pscomp_1,fc1_square_1,fc1_struct_0,fc1_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_borsuk_3,fc2_euclid,fc2_membered,fc2_pscomp_1,fc2_square_1,fc2_topreal1,fc30_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,fraenkel_a_0_14_jgraph_3,fraenkel_a_0_6_jgraph_5,free_g1_pre_topc,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,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_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,rc9_pscomp_1,redefinition_k1_real_1,redefinition_k3_real_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k7_funct_2,redefinition_k7_square_1,redefinition_k8_funct_2,redefinition_k9_square_1,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t104_jgraph_4,t10_jgraph_3,t10_xreal_1,t112_jgraph_4,t114_jgraph_4,t117_jgraph_4,t118_jgraph_4,t120_jgraph_4,t135_jgraph_4,t143_jgraph_4,t149_jgraph_4,t1_arithm,t1_jgraph_3,t1_numerals,t1_real,t1_subset,t22_funct_1,t2_arithm,t2_real,t2_subset,t2_tarski,t2_xreal_1,t36_jgraph_3,t3_arithm,t3_real,t3_subset,t40_jgraph_4,t48_jgraph_4,t48_jgraph_5,t49_jgraph_4,t4_arithm,t4_jgraph_5,t4_real,t4_subset,t51_jgraph_4,t52_xreal_1,t54_jgraph_4,t56_jgraph_4,t57_euclid,t5_arithm,t5_jordan7,t5_real,t5_subset,t60_square_1,t60_xreal_1,t61_square_1,t6_arithm,t6_boole,t6_jgraph_2,t6_real,t71_tops_2,t73_jgraph_4,t78_square_1,t7_boole,t7_real,t81_jgraph_4,t82_jgraph_4,t86_jgraph_4,t87_jgraph_4,t89_jgraph_4,t8_boole,t8_real]),
    [file(jgraph_5,t69_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_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_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(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_1),
    []).

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

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(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_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_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_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_jgraph_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_funct_1(k3_jgraph_4(A))
        & v1_funct_2(k3_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(k3_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) ) ) ),
    file(jgraph_4,k3_jgraph_4),
    []).

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

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

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_jgraph_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_funct_1(k5_jgraph_4(A))
        & v1_funct_2(k5_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(k5_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) ) ) ),
    file(jgraph_4,k5_jgraph_4),
    []).

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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ),
    file(real_1,k5_real_1),
    []).

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_square_1,axiom,(
    $true ),
    file(square_1,k5_square_1),
    []).

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_k6_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ),
    file(real_1,k6_real_1),
    []).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

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_k7_jgraph_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_funct_1(k7_jgraph_4(A))
        & v1_funct_2(k7_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(k7_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) ) ) ),
    file(jgraph_4,k7_jgraph_4),
    []).

fof(dt_k7_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k7_square_1(A),k1_numbers) ) ),
    file(square_1,k7_square_1),
    []).

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

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_k8_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xreal_0(k8_square_1(A)) ) ),
    file(square_1,k8_square_1),
    []).

fof(dt_k9_jgraph_4,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_funct_1(k9_jgraph_4(A))
        & v1_funct_2(k9_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
        & m2_relset_1(k9_jgraph_4(A),u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) ) ) ),
    file(jgraph_4,k9_jgraph_4),
    []).

fof(dt_k9_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k9_square_1(A),k1_numbers) ) ),
    file(square_1,k9_square_1),
    []).

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_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_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(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

fof(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

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(fc15_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    []).

fof(fc16_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    []).

fof(fc17_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    []).

fof(fc18_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    []).

fof(fc19_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_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_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k5_square_1(A)) ) ),
    file(square_1,fc1_square_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(fc20_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    []).

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

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

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

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

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

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

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

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_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_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k5_square_1(A))
        & v1_xreal_0(k5_square_1(A)) ) ) ),
    file(square_1,fc2_square_1),
    []).

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

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

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

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

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_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

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

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

fof(fc7_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

fof(fraenkel_a_0_14_jgraph_3,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_14_jgraph_3)
    <=> ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
          & A = B
          & k5_toprns_1(2,B) = 1 ) ) ),
    file(jgraph_3,a_0_14_jgraph_3),
    []).

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(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_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_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_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(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_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_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_real_1),
    []).

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

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_k7_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k7_square_1(A) = k5_square_1(A) ) ),
    file(square_1,k7_square_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_k9_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k9_square_1(A) = k8_square_1(A) ) ),
    file(square_1,k9_square_1),
    []).

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(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(t104_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,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)),k7_jgraph_4(A),B)) = k5_toprns_1(2,B) ) ) ),
    file(jgraph_4,t104_jgraph_4),
    []).

fof(t10_jgraph_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ( k5_toprns_1(2,A) = k9_square_1(k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))))
        & k7_square_1(k5_toprns_1(2,A)) = k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))) ) ) ),
    file(jgraph_3,t10_jgraph_3),
    []).

fof(t10_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & r1_xreal_0(C,D)
                      & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ),
    file(xreal_1,t10_xreal_1),
    []).

fof(t112_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
          & ~ r1_xreal_0(1,A)
          & ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
                & m2_relset_1(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) )
             => ~ ( B = k7_jgraph_4(A)
                  & v3_tops_2(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) ),
    file(jgraph_4,t112_jgraph_4),
    []).

fof(t114_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
              & ~ r1_xreal_0(1,A)
              & ~ r1_xreal_0(k21_euclid(B),0)
              & ~ r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(2,B)))
              & ? [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                  & C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(A),B)
                  & ~ ( ~ r1_xreal_0(k21_euclid(C),0)
                      & ~ r1_xreal_0(0,k22_euclid(C)) ) ) ) ) ) ),
    file(jgraph_4,t114_jgraph_4),
    []).

fof(t117_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
             => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
                  & ~ r1_xreal_0(1,A)
                  & ~ r1_xreal_0(k21_euclid(B),0)
                  & ~ r1_xreal_0(k21_euclid(C),0)
                  & ~ r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(2,C)),k6_real_1(k22_euclid(B),k5_toprns_1(2,B)))
                  & ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(2)))
                      & ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(2)))
                          & D = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(A),B)
                          & E = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(A),C)
                          & r1_xreal_0(k6_real_1(k22_euclid(E),k5_toprns_1(2,E)),k6_real_1(k22_euclid(D),k5_toprns_1(2,D))) ) ) ) ) ) ) ),
    file(jgraph_4,t117_jgraph_4),
    []).

fof(t118_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( k6_real_1(k22_euclid(B),k5_toprns_1(2,B)) = A
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(k21_euclid(B),0)
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(k21_euclid(C),0)
                      & k22_euclid(C) = 0 ) ) ) ) ) ) ) ),
    file(jgraph_4,t118_jgraph_4),
    []).

fof(t120_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(2,A)))
             => ( r1_xreal_0(0,k22_euclid(A))
                | k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k9_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B))),k3_xcmplx_0(k5_toprns_1(2,A),k4_xcmplx_0(k8_square_1(k6_xcmplx_0(1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B)))))))) ) )
            & ( r1_xreal_0(0,k22_euclid(A))
             => k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k9_jgraph_4(B),A) = A ) ) ) ) ),
    file(jgraph_4,t120_jgraph_4),
    []).

fof(t135_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,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)),k9_jgraph_4(A),B)) = k5_toprns_1(2,B) ) ) ),
    file(jgraph_4,t135_jgraph_4),
    []).

fof(t143_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
          & ~ r1_xreal_0(1,A)
          & ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
                & m2_relset_1(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) )
             => ~ ( B = k9_jgraph_4(A)
                  & v3_tops_2(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) ),
    file(jgraph_4,t143_jgraph_4),
    []).

fof(t149_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( k6_real_1(k21_euclid(B),k5_toprns_1(2,B)) = A
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(0,k22_euclid(B))
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k9_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(0,k22_euclid(C))
                      & k21_euclid(C) = 0 ) ) ) ) ) ) ) ),
    file(jgraph_4,t149_jgraph_4),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_jgraph_3,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ~ ( k5_square_1(A) = k5_square_1(B)
              & A != B
              & A != k4_xcmplx_0(B) ) ) ) ),
    file(jgraph_3,t1_jgraph_3),
    []).

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_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    []).

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

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

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

fof(t2_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    []).

fof(t36_jgraph_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2))))
     => ( A = a_0_14_jgraph_3
       => v1_topreal2(A) ) ) ),
    file(jgraph_3,t36_jgraph_3),
    []).

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

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(t40_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,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)),k3_jgraph_4(A),B)) = k5_toprns_1(2,B) ) ) ),
    file(jgraph_4,t40_jgraph_4),
    []).

fof(t48_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
          & ~ r1_xreal_0(1,A)
          & ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
                & m2_relset_1(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) )
             => ~ ( B = k3_jgraph_4(A)
                  & v3_tops_2(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) ),
    file(jgraph_4,t48_jgraph_4),
    []).

fof(t48_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] : 
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(2))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B) )
               => ( A = B
                  | r1_xreal_0(0,k21_euclid(A))
                  | r1_xreal_0(0,k21_euclid(B))
                  | r1_xreal_0(0,k22_euclid(A))
                  | r1_xreal_0(0,k22_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
                    & ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) ) ) ) ) ) ) ),
    file(jgraph_5,t48_jgraph_5),
    []).

fof(t49_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(2,B)))
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(0,k21_euclid(B))
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k3_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(0,k21_euclid(C))
                      & r1_xreal_0(0,k22_euclid(C)) ) ) ) ) ) ) ) ),
    file(jgraph_4,t49_jgraph_4),
    []).

fof(t4_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    []).

fof(t4_jgraph_5,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ( r1_xreal_0(k5_toprns_1(2,A),1)
       => ( k21_euclid(A) = 0
          | k22_euclid(A) = 0
          | ( ~ r1_xreal_0(k21_euclid(A),k1_real_1(1))
            & ~ r1_xreal_0(1,k21_euclid(A))
            & ~ r1_xreal_0(k22_euclid(A),k1_real_1(1))
            & ~ r1_xreal_0(1,k22_euclid(A)) ) ) ) ) ),
    file(jgraph_5,t4_jgraph_5),
    []).

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(t51_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
             => ( ( r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(2,B)))
                  & r1_xreal_0(A,k6_real_1(k22_euclid(C),k5_toprns_1(2,C))) )
               => ( r1_xreal_0(A,k1_real_1(1))
                  | r1_xreal_0(1,A)
                  | r1_xreal_0(0,k21_euclid(B))
                  | r1_xreal_0(0,k21_euclid(C))
                  | r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(2,C)),k6_real_1(k22_euclid(B),k5_toprns_1(2,B)))
                  | ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(2)))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(2)))
                         => ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k3_jgraph_4(A),B)
                              & E = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k3_jgraph_4(A),C)
                              & r1_xreal_0(k6_real_1(k22_euclid(E),k5_toprns_1(2,E)),k6_real_1(k22_euclid(D),k5_toprns_1(2,D))) ) ) ) ) ) ) ) ) ),
    file(jgraph_4,t51_jgraph_4),
    []).

fof(t52_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & r1_xreal_0(k6_xcmplx_0(B,A),0) ) ) ) ),
    file(xreal_1,t52_xreal_1),
    []).

fof(t54_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( k6_real_1(k22_euclid(B),k5_toprns_1(2,B)) = A
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(0,k21_euclid(B))
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k3_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(0,k21_euclid(C))
                      & k22_euclid(C) = 0 ) ) ) ) ) ) ) ),
    file(jgraph_4,t54_jgraph_4),
    []).

fof(t56_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(B,k6_real_1(k21_euclid(A),k5_toprns_1(2,A)))
             => ( r1_xreal_0(k22_euclid(A),0)
                | k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B))),k3_xcmplx_0(k5_toprns_1(2,A),k8_square_1(k6_xcmplx_0(1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k21_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B))))))) ) )
            & ( r1_xreal_0(k22_euclid(A),0)
             => k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(B),A) = A ) ) ) ) ),
    file(jgraph_4,t56_jgraph_4),
    []).

fof(t57_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => A = k23_euclid(k21_euclid(A),k22_euclid(A)) ) ),
    file(euclid,t57_euclid),
    []).

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

fof(t5_jordan7,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(2))
        & m1_subset_1(A,k1_zfmisc_1(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)))
             => ( ( v1_topreal2(A)
                  & r1_jordan6(A,B,C) )
               => ( r2_hidden(B,A)
                  & r2_hidden(C,A) ) ) ) ) ) ),
    file(jordan7,t5_jordan7),
    []).

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(t60_square_1,axiom,(
    k7_square_1(0) = 0 ),
    file(square_1,t60_square_1),
    []).

fof(t60_xreal_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ ( ~ r1_xreal_0(0,A)
            & r1_xreal_0(k4_xcmplx_0(A),0) )
        & ~ ( ~ r1_xreal_0(k4_xcmplx_0(A),0)
            & r1_xreal_0(0,A) ) ) ) ),
    file(xreal_1,t60_xreal_1),
    []).

fof(t61_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)) ) ),
    file(square_1,t61_square_1),
    []).

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

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

fof(t6_jgraph_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(0,A)
           => ( r1_xreal_0(k5_square_1(A),k5_square_1(B))
              | ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
                & ~ r1_xreal_0(A,B) ) ) ) ) ) ),
    file(jgraph_2,t6_jgraph_2),
    []).

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(t71_tops_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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(D,A,B)
                          & v3_tops_2(E,B,C) )
                       => v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ),
    file(tops_2,t71_tops_2),
    []).

fof(t73_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,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)),k5_jgraph_4(A),B)) = k5_toprns_1(2,B) ) ) ),
    file(jgraph_4,t73_jgraph_4),
    []).

fof(t78_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & ~ r1_xreal_0(B,A)
              & r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) ),
    file(square_1,t78_square_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(t81_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
          & ~ r1_xreal_0(1,A)
          & ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)))
                & m2_relset_1(B,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) )
             => ~ ( B = k5_jgraph_4(A)
                  & v3_tops_2(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) ),
    file(jgraph_4,t81_jgraph_4),
    []).

fof(t82_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(2,B)))
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(k22_euclid(B),0)
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(k22_euclid(C),0)
                      & r1_xreal_0(0,k21_euclid(C)) ) ) ) ) ) ) ) ),
    file(jgraph_4,t82_jgraph_4),
    []).

fof(t86_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
             => ~ ( ~ r1_xreal_0(A,k1_real_1(1))
                  & ~ r1_xreal_0(1,A)
                  & ~ r1_xreal_0(k22_euclid(B),0)
                  & ~ r1_xreal_0(k22_euclid(C),0)
                  & ~ r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(2,C)),k6_real_1(k21_euclid(B),k5_toprns_1(2,B)))
                  & ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(2)))
                      & ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(2)))
                          & D = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(A),B)
                          & E = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(A),C)
                          & r1_xreal_0(k6_real_1(k21_euclid(E),k5_toprns_1(2,E)),k6_real_1(k21_euclid(D),k5_toprns_1(2,D))) ) ) ) ) ) ) ),
    file(jgraph_4,t86_jgraph_4),
    []).

fof(t87_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(2)))
         => ( k6_real_1(k21_euclid(B),k5_toprns_1(2,B)) = A
           => ( r1_xreal_0(A,k1_real_1(1))
              | r1_xreal_0(1,A)
              | r1_xreal_0(k22_euclid(B),0)
              | ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(A),B)
                   => ( ~ r1_xreal_0(k22_euclid(C),0)
                      & k21_euclid(C) = 0 ) ) ) ) ) ) ) ),
    file(jgraph_4,t87_jgraph_4),
    []).

fof(t89_jgraph_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(2)))
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(B,k6_real_1(k22_euclid(A),k5_toprns_1(2,A)))
             => ( r1_xreal_0(k21_euclid(A),0)
                | k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(B),A) = k23_euclid(k3_xcmplx_0(k5_toprns_1(2,A),k8_square_1(k6_xcmplx_0(1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B)))))),k3_xcmplx_0(k5_toprns_1(2,A),k7_xcmplx_0(k6_xcmplx_0(k6_real_1(k22_euclid(A),k5_toprns_1(2,A)),B),k6_xcmplx_0(1,B)))) ) )
            & ( r1_xreal_0(k21_euclid(A),0)
             => k8_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(B),A) = A ) ) ) ) ),
    file(jgraph_4,t89_jgraph_4),
    []).

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),
    []).