SET007 Axioms: SET007+766.ax


%------------------------------------------------------------------------------
% File     : SET007+766 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : General Fashoda Meet Theorem for Unit Circle and Square
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : jgraph_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  140 (   5 unit)
%            Number of atoms       : 1367 ( 242 equality)
%            Maximal formula depth :   37 (  12 average)
%            Number of connectives : 1380 ( 153 ~  ;  30  |; 637  &)
%                                         (  41 <=>; 519 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   1 propositional; 0-5 arity)
%            Number of functors    :  104 (  23 constant; 0-4 arity)
%            Number of variables   :  560 (   0 singleton; 528 !;  32 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => v6_compts_1(k5_jgraph_6(A,B,C),k15_euclid(np__2)) ) )).

fof(fc2_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ( ~ v1_xboole_0(k5_jgraph_6(A,B,C))
        & v6_compts_1(k5_jgraph_6(A,B,C),k15_euclid(np__2)) ) ) )).

fof(t1_jgraph_6,axiom,(
    $true )).

fof(t2_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(np__0,C)
                  & r1_xreal_0(C,np__1)
                  & r1_xreal_0(A,B) )
               => ( r1_xreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,C),A),k3_xcmplx_0(C,B)))
                  & r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,C),A),k3_xcmplx_0(C,B)),B) ) ) ) ) ) )).

fof(t3_jgraph_6,axiom,(
    $true )).

fof(t4_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k1_real_1(np__1),A)
              & r1_xreal_0(A,np__1)
              & r1_xreal_0(k1_real_1(np__1),B)
              & r1_xreal_0(B,np__1) )
           => r1_xreal_0(k3_xcmplx_0(k5_square_1(A),k5_square_1(B)),np__1) ) ) ) )).

fof(t5_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(np__0,A)
              & r1_xreal_0(np__0,B) )
           => k3_xcmplx_0(A,k8_square_1(B)) = k8_square_1(k3_xcmplx_0(k5_square_1(A),B)) ) ) ) )).

fof(t6_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k1_real_1(np__1),A)
              & r1_xreal_0(A,np__1)
              & r1_xreal_0(k1_real_1(np__1),B)
              & r1_xreal_0(B,np__1) )
           => ( r1_xreal_0(k3_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B))))
              & r1_xreal_0(k4_xcmplx_0(k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))),k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A))))) ) ) ) ) )).

fof(t7_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k1_real_1(np__1),A)
              & r1_xreal_0(A,np__1)
              & r1_xreal_0(k1_real_1(np__1),B)
              & r1_xreal_0(B,np__1) )
           => r1_xreal_0(k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))) ) ) ) )).

fof(t8_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(B,A)
           => r1_xreal_0(k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),k3_xcmplx_0(A,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B))))) ) ) ) )).

fof(t9_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(B,C)
                      & r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,B),k23_euclid(A,C))) )
                   => ( k21_euclid(D) = A
                      & r1_xreal_0(B,k22_euclid(D))
                      & r1_xreal_0(k22_euclid(D),C) ) ) ) ) ) ) )).

fof(t10_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( k21_euclid(D) = A
                      & r1_xreal_0(B,k22_euclid(D))
                      & r1_xreal_0(k22_euclid(D),C) )
                   => ( r1_xreal_0(C,B)
                      | r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,B),k23_euclid(A,C))) ) ) ) ) ) ) )).

fof(t11_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(A,B)
                      & r2_hidden(D,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) )
                   => ( k22_euclid(D) = C
                      & r1_xreal_0(A,k21_euclid(D))
                      & r1_xreal_0(k21_euclid(D),B) ) ) ) ) ) ) )).

fof(t12_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
             => ( C = k1_rcomp_1(A,B)
               => v4_pre_topc(C,k5_topmetr) ) ) ) ) )).

fof(t13_jgraph_6,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(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( k1_relat_1(D) = k1_relat_1(E)
                        & k1_relat_1(D) = u1_struct_0(A)
                        & k1_relat_1(D) = k2_pre_topc(A) ) ) ) ) ) ) )).

fof(t14_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A))
              & m2_relset_1(C,u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A))
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_pre_topc(A,B)))
                 => k8_funct_2(u1_struct_0(k3_pre_topc(A,B)),u1_struct_0(A),C,D) = D )
              & v5_pre_topc(C,k3_pre_topc(A,B),A) ) ) ) )).

fof(t15_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k6_xcmplx_0(F,C) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t16_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k6_xcmplx_0(C,F) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t17_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                 => ~ ( v5_pre_topc(D,A,k3_topmetr)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
                         => ~ ( ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),E,F) = k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,F),B,C) )
                              & v5_pre_topc(E,A,k15_euclid(B)) ) ) ) ) ) ) ) )).

fof(t18_jgraph_6,axiom,(
    k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,k23_euclid(k1_real_1(np__1),np__0)) = k23_euclid(k1_real_1(np__1),np__0) )).

fof(t20_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
                 => ~ ( v5_pre_topc(C,A,k15_euclid(B))
                      & v5_pre_topc(D,A,k15_euclid(B))
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
                         => ~ ( ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),E,F) = k17_euclid(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),C,F),k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),D,F)) )
                              & v5_pre_topc(E,A,k15_euclid(B)) ) ) ) ) ) ) ) )).

fof(t21_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k3_topmetr))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                         => ~ ( v5_pre_topc(E,A,k3_topmetr)
                              & v5_pre_topc(F,A,k3_topmetr)
                              & ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(A),u1_struct_0(k15_euclid(B)))
                                    & m2_relset_1(G,u1_struct_0(A),u1_struct_0(k15_euclid(B))) )
                                 => ~ ( ! [H] :
                                          ( m1_subset_1(H,u1_struct_0(A))
                                         => k8_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),G,H) = k17_euclid(B,k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),E,H),B,C),k18_euclid(k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),F,H),B,D)) )
                                      & v5_pre_topc(G,A,k15_euclid(B)) ) ) ) ) ) ) ) ) ) )).

fof(t22_jgraph_6,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_funct_1(A)
            & r1_tarski(B,k1_relat_1(A)) )
         => k9_relat_1(k2_funct_1(A),k9_relat_1(A,B)) = B ) ) )).

fof(t28_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_xreal_0(A,B)
                          & r1_xreal_0(C,D)
                          & r2_hidden(E,k1_sppol_2(A,B,C,D)) )
                       => ( r1_xreal_0(A,k21_euclid(E))
                          & r1_xreal_0(k21_euclid(E),B)
                          & r1_xreal_0(C,k22_euclid(E))
                          & r1_xreal_0(k22_euclid(E),D) ) ) ) ) ) ) ) )).

fof(t30_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( v1_topreal2(A)
           => ( ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                    & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
                 => ~ v3_tops_2(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) )
              | v1_topreal2(B) ) ) ) ) )).

fof(t31_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => v6_compts_1(A,k15_euclid(np__2)) ) ) )).

fof(t38_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                                 => ! [I] :
                                      ( ( ~ v1_xboole_0(I)
                                        & v6_compts_1(I,k15_euclid(np__2))
                                        & m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                                     => ! [J] :
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                                            & m2_relset_1(J,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                                         => ( ( I = k5_jgraph_6(np__0,np__0,np__1)
                                              & A = k6_jgraph_6(np__0,np__0,np__1)
                                              & B = k8_jgraph_6(np__0,np__0,np__1)
                                              & C = k7_jgraph_6(np__0,np__0,np__1)
                                              & D = k9_jgraph_6(np__0,np__0,np__1)
                                              & E = k1_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                              & F = k3_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                              & G = k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                              & H = k4_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                              & J = k1_jgraph_3 )
                                           => ( k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)) = I
                                              & k9_relat_1(k2_funct_1(J),I) = k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                              & k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,E) = A
                                              & k9_relat_1(k2_funct_1(J),A) = E
                                              & k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,F) = B
                                              & k9_relat_1(k2_funct_1(J),B) = F
                                              & k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,G) = C
                                              & k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),J,H) = D
                                              & k9_relat_1(k2_funct_1(J),C) = G
                                              & k9_relat_1(k2_funct_1(J),D) = H ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_jgraph_6,axiom,(
    $true )).

fof(t41_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) = k1_struct_0(k15_euclid(np__2),k23_euclid(A,C)) ) ) ) ) ) )).

fof(t42_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(B,C)) ) ) ) ) ) )).

fof(t43_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(B,D)) ) ) ) ) ) )).

fof(t44_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) = k1_struct_0(k15_euclid(np__2),k23_euclid(A,D)) ) ) ) ) ) )).

fof(t46_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k18_pscomp_1(k1_sppol_2(A,B,C,D)) = A ) ) ) ) ) )).

fof(t47_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k19_pscomp_1(k1_sppol_2(A,B,C,D)) = D ) ) ) ) ) )).

fof(t48_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k20_pscomp_1(k1_sppol_2(A,B,C,D)) = B ) ) ) ) ) )).

fof(t49_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k21_pscomp_1(k1_sppol_2(A,B,C,D)) = C ) ) ) ) ) )).

fof(t50_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k23_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,D) ) ) ) ) ) )).

fof(t51_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k24_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,D) ) ) ) ) ) )).

fof(t52_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k22_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,C) ) ) ) ) ) )).

fof(t53_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k25_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,C) ) ) ) ) ) )).

fof(t54_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k26_pscomp_1(k1_sppol_2(A,B,C,D)) = k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)) ) ) ) ) ) )).

fof(t55_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k28_pscomp_1(k1_sppol_2(A,B,C,D)) = k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)) ) ) ) ) ) )).

fof(t56_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( k30_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(A,C)
                      & k34_pscomp_1(k1_sppol_2(A,B,C,D)) = k23_euclid(B,D) ) ) ) ) ) ) )).

fof(t57_jgraph_6,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(D,C)
                      & ~ ( r1_topreal1(k15_euclid(np__2),k30_pscomp_1(k1_sppol_2(A,B,C,D)),k34_pscomp_1(k1_sppol_2(A,B,C,D)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))))
                          & r1_topreal1(k15_euclid(np__2),k34_pscomp_1(k1_sppol_2(A,B,C,D)),k30_pscomp_1(k1_sppol_2(A,B,C,D)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)))) ) ) ) ) ) ) )).

fof(t58_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k15_euclid(np__2)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
                                         => ( ( G = k23_euclid(A,C)
                                              & H = k23_euclid(B,D)
                                              & I = k23_euclid(A,D)
                                              & J = k23_euclid(B,C)
                                              & E = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),G,I,H)
                                              & F = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),G,J,H) )
                                           => ( r1_xreal_0(B,A)
                                              | r1_xreal_0(D,C)
                                              | ( v4_topreal1(E)
                                                & k5_topreal1(np__2,E) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,G,I),k3_topreal1(np__2,I,H))
                                                & v4_topreal1(F)
                                                & k5_topreal1(np__2,F) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,G,J),k3_topreal1(np__2,J,H))
                                                & k1_sppol_2(A,B,C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,E),k5_topreal1(np__2,F))
                                                & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,E),k5_topreal1(np__2,F)) = k2_struct_0(k15_euclid(np__2),G,H)
                                                & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1) = G
                                                & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E)) = H
                                                & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,np__1) = G
                                                & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,k3_finseq_1(F)) = H ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t59_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ! [F] :
                          ( v1_xreal_0(F)
                         => ! [G] :
                              ( m2_finseq_1(G,u1_struct_0(k15_euclid(np__2)))
                             => ! [H] :
                                  ( m2_finseq_1(H,u1_struct_0(k15_euclid(np__2)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k15_euclid(np__2)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k15_euclid(np__2)))
                                         => ( ( I = k23_euclid(C,E)
                                              & J = k23_euclid(D,F)
                                              & G = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),k23_euclid(C,E),k23_euclid(C,F),k23_euclid(D,F))
                                              & H = k3_finseq_4(u1_struct_0(k15_euclid(np__2)),k23_euclid(C,E),k23_euclid(D,E),k23_euclid(D,F))
                                              & A = k5_topreal1(np__2,G)
                                              & B = k5_topreal1(np__2,H) )
                                           => ( r1_xreal_0(D,C)
                                              | r1_xreal_0(F,E)
                                              | ( r1_topreal1(k15_euclid(np__2),I,J,A)
                                                & r1_topreal1(k15_euclid(np__2),I,J,B)
                                                & ~ v1_xboole_0(A)
                                                & ~ v1_xboole_0(B)
                                                & k1_sppol_2(C,D,E,F) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)
                                                & k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B) = k2_struct_0(k15_euclid(np__2),I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t60_jgraph_6,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(D,C)
                      & ~ v1_topreal2(k1_sppol_2(A,B,C,D)) ) ) ) ) ) )).

fof(t61_jgraph_6,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(D,C)
                      & k8_jordan6(k1_sppol_2(A,B,C,D)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) ) ) ) ) ) )).

fof(t62_jgraph_6,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(D,C)
                      & k9_jordan6(k1_sppol_2(A,B,C,D)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) ) ) ) ) ) )).

fof(t63_jgraph_6,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(D,C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D)))))
                            & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D))))) )
                         => ~ ( v3_tops_2(E,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D))))
                              & k1_funct_1(E,np__0) = k30_pscomp_1(k1_sppol_2(A,B,C,D))
                              & k1_funct_1(E,np__1) = k34_pscomp_1(k1_sppol_2(A,B,C,D))
                              & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(k1_sppol_2(A,B,C,D)))),E) = k8_jordan6(k1_sppol_2(A,B,C,D))
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)))
                                   => k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k4_real_1(np__2,F)),np__2,k23_euclid(A,C)),k18_euclid(k4_real_1(np__2,F),np__2,k23_euclid(A,D))) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(k6_real_1(np__1,np__2),np__1))
                                   => k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k5_real_1(k4_real_1(np__2,F),np__1)),np__2,k23_euclid(A,D)),k18_euclid(k5_real_1(k4_real_1(np__2,F),np__1),np__2,k23_euclid(B,D))) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
                                   => ( r1_xreal_0(np__0,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2))
                                      & r1_xreal_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2),np__1)
                                      & k1_funct_1(E,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),C),k6_xcmplx_0(D,C)),np__2)) = F ) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
                                   => ( r1_xreal_0(np__0,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2)))
                                      & r1_xreal_0(k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2)),np__1)
                                      & k1_funct_1(E,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),A),k6_xcmplx_0(B,A)),np__2),k6_real_1(np__1,np__2))) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t64_jgraph_6,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(D,C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D)))))
                            & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D))))) )
                         => ~ ( v3_tops_2(E,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D))))
                              & k1_funct_1(E,np__0) = k34_pscomp_1(k1_sppol_2(A,B,C,D))
                              & k1_funct_1(E,np__1) = k30_pscomp_1(k1_sppol_2(A,B,C,D))
                              & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(k1_sppol_2(A,B,C,D)))),E) = k9_jordan6(k1_sppol_2(A,B,C,D))
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)))
                                   => k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k4_real_1(np__2,F)),np__2,k23_euclid(B,D)),k18_euclid(k4_real_1(np__2,F),np__2,k23_euclid(B,C))) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(k6_real_1(np__1,np__2),np__1))
                                   => k1_funct_1(E,F) = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,k5_real_1(k4_real_1(np__2,F),np__1)),np__2,k23_euclid(B,C)),k18_euclid(k5_real_1(k4_real_1(np__2,F),np__1),np__2,k23_euclid(A,C))) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
                                   => ( r1_xreal_0(np__0,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2))
                                      & r1_xreal_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2),np__1)
                                      & k1_funct_1(E,k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k22_euclid(F),D),k6_xcmplx_0(C,D)),np__2)) = F ) ) )
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                                   => ( r1_xreal_0(np__0,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2)))
                                      & r1_xreal_0(k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2)),np__1)
                                      & k1_funct_1(E,k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k21_euclid(F),B),k6_xcmplx_0(A,B)),np__2),k6_real_1(np__1,np__2))) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t65_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
                              & r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D))) )
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> r1_xreal_0(k22_euclid(E),k22_euclid(F)) ) ) ) ) ) ) ) ) ) )).

fof(t66_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
                              & r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))) )
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> r1_xreal_0(k21_euclid(E),k21_euclid(F)) ) ) ) ) ) ) ) ) ) )).

fof(t67_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)))
                              & r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D))) )
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> r1_xreal_0(k22_euclid(F),k22_euclid(E)) ) ) ) ) ) ) ) ) ) )).

fof(t68_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)))
                              & r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C))) )
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                                 => ( E = k30_pscomp_1(k1_sppol_2(A,B,C,D))
                                    | ( r1_xreal_0(k21_euclid(F),k21_euclid(E))
                                      & F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) )
                                & ( r1_xreal_0(k21_euclid(F),k21_euclid(E))
                                 => ( F = k30_pscomp_1(k1_sppol_2(A,B,C,D))
                                    | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                                      & E != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t69_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> ~ ( ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)))
                                        & r1_xreal_0(k22_euclid(E),k22_euclid(F)) )
                                    & ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
                                    & ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
                                    & ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                                        & F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t70_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> ~ ( ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)))
                                        & r1_xreal_0(k21_euclid(E),k21_euclid(F)) )
                                    & ~ r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
                                    & ~ ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                                        & F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t71_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> ( ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)))
                                    & r1_xreal_0(k22_euclid(F),k22_euclid(E)) )
                                  | ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                                    & F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t72_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ( r2_hidden(E,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                           => ( r1_xreal_0(B,A)
                              | r1_xreal_0(D,C)
                              | E = k30_pscomp_1(k1_sppol_2(A,B,C,D))
                              | ( r1_jordan6(k1_sppol_2(A,B,C,D),E,F)
                              <=> ( r2_hidden(F,k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))
                                  & r1_xreal_0(k21_euclid(F),k21_euclid(E))
                                  & F != k30_pscomp_1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) )).

fof(t73_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( v1_xreal_0(C)
         => ! [D] :
              ( v1_xreal_0(D)
             => ! [E] :
                  ( v1_xreal_0(E)
                 => ~ ( r2_hidden(A,k1_sppol_2(B,C,D,E))
                      & ~ r1_xreal_0(C,B)
                      & ~ r1_xreal_0(E,D)
                      & ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,E)))
                      & ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(B,E),k23_euclid(C,E)))
                      & ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(C,E),k23_euclid(C,D)))
                      & ~ r2_hidden(A,k3_topreal1(np__2,k23_euclid(C,D),k23_euclid(B,D))) ) ) ) ) ) )).

fof(t74_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
              & r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
              & ~ ( r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                  & r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
              & ~ r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),np__1),k23_euclid(np__1,np__1)))
              & ~ r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,np__1),k23_euclid(np__1,k1_real_1(np__1))))
              & ~ ( r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),k1_real_1(np__1))))
                  & B != k23_euclid(k1_real_1(np__1),k1_real_1(np__1)) ) ) ) ) )).

fof(t75_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(np__2))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                    & m2_relset_1(D,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                 => ( ( C = k5_jgraph_6(np__0,np__0,np__1)
                      & D = k1_jgraph_3
                      & r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                      & r1_xreal_0(np__0,k22_euclid(A))
                      & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B) )
                   => r1_jordan6(C,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),D,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),D,B)) ) ) ) ) ) )).

fof(t76_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v6_compts_1(D,k15_euclid(np__2))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                        & m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                     => ( ( D = k5_jgraph_6(np__0,np__0,np__1)
                          & E = k1_jgraph_3
                          & r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                          & r1_xreal_0(np__0,k22_euclid(A))
                          & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
                          & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),B,C) )
                       => r1_jordan6(D,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,C)) ) ) ) ) ) ) )).

fof(t77_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
            & m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
         => ( ( B = k1_jgraph_3
              & k21_euclid(A) = k1_real_1(np__1) )
           => ( r1_xreal_0(np__0,k22_euclid(A))
              | ( ~ r1_xreal_0(np__0,k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,A)))
                & ~ r1_xreal_0(np__0,k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),B,A))) ) ) ) ) ) )).

fof(t78_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                & m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
             => ( ( B = k5_jgraph_6(np__0,np__0,np__1)
                  & C = k1_jgraph_3 )
               => ( r1_xreal_0(np__0,k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)))
                <=> r1_xreal_0(np__0,k21_euclid(A)) ) ) ) ) ) )).

fof(t79_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                & m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
             => ( ( B = k5_jgraph_6(np__0,np__0,np__1)
                  & C = k1_jgraph_3 )
               => ( r1_xreal_0(np__0,k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)))
                <=> r1_xreal_0(np__0,k22_euclid(A)) ) ) ) ) ) )).

fof(t80_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                & m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
             => ( ( C = k1_jgraph_3
                  & r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                  & r2_hidden(B,k3_topreal1(np__2,k23_euclid(np__1,k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),k1_real_1(np__1)))) )
               => r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A)),k21_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,B))) ) ) ) ) )).

fof(t81_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                & m2_relset_1(C,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
             => ( ( C = k1_jgraph_3
                  & r2_hidden(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                  & r2_hidden(B,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__1)),k23_euclid(k1_real_1(np__1),np__1)))
                  & r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
               => ( r1_xreal_0(np__0,k22_euclid(A))
                  | r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,B)),k22_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),C,A))) ) ) ) ) ) )).

fof(t82_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                            & m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                         => ( ( E = k5_jgraph_6(np__0,np__0,np__1)
                              & F = k1_jgraph_3
                              & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B)
                              & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),B,C)
                              & r1_jordan6(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),C,D) )
                           => r1_jordan17(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) ) ) ) ) ) ) ) )).

fof(t83_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(np__2))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( v1_topreal2(C)
                  & r2_hidden(A,C)
                  & r2_hidden(B,C) )
               => ( r1_jordan6(C,A,B)
                  | r1_jordan6(C,B,A) ) ) ) ) ) )).

fof(t84_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v6_compts_1(D,k15_euclid(np__2))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ~ ( v1_topreal2(D)
                      & r2_hidden(A,D)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D)
                      & ~ ( r1_jordan6(D,A,B)
                          & r1_jordan6(D,B,C) )
                      & ~ ( r1_jordan6(D,A,C)
                          & r1_jordan6(D,C,B) )
                      & ~ ( r1_jordan6(D,B,A)
                          & r1_jordan6(D,A,C) )
                      & ~ ( r1_jordan6(D,B,C)
                          & r1_jordan6(D,C,A) )
                      & ~ ( r1_jordan6(D,C,A)
                          & r1_jordan6(D,A,B) )
                      & ~ ( r1_jordan6(D,C,B)
                          & r1_jordan6(D,B,A) ) ) ) ) ) ) )).

fof(t85_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v6_compts_1(D,k15_euclid(np__2))
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                 => ~ ( v1_topreal2(D)
                      & r2_hidden(A,D)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D)
                      & r1_jordan6(D,B,C)
                      & ~ r1_jordan6(D,A,B)
                      & ~ ( r1_jordan6(D,B,A)
                          & r1_jordan6(D,A,C) )
                      & ~ r1_jordan6(D,C,A) ) ) ) ) ) )).

fof(t86_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ~ ( v1_topreal2(E)
                          & r2_hidden(A,E)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & r2_hidden(D,E)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ~ r1_jordan6(E,A,B)
                          & ~ ( r1_jordan6(E,B,A)
                              & r1_jordan6(E,A,C) )
                          & ~ ( r1_jordan6(E,C,A)
                              & r1_jordan6(E,A,D) )
                          & ~ r1_jordan6(E,D,A) ) ) ) ) ) ) )).

fof(t87_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                            & m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                         => ( ( E = k5_jgraph_6(np__0,np__0,np__1)
                              & F = k1_jgraph_3
                              & r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B))
                              & r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C))
                              & r1_jordan6(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) )
                           => r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D) ) ) ) ) ) ) ) )).

fof(t88_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                            & m2_relset_1(F,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                         => ( ( E = k5_jgraph_6(np__0,np__0,np__1)
                              & F = k1_jgraph_3 )
                           => ( r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D)
                            <=> r1_jordan17(E,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C),k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)) ) ) ) ) ) ) ) ) )).

fof(t89_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ( r1_jordan17(k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1),A,B,C,D)
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                              & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                                  & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                               => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(np__2))
                                    & v2_funct_1(F)
                                    & v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
                                    & v2_funct_1(G)
                                    & E = k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__1),np__1)
                                    & k1_funct_1(F,np__0) = A
                                    & k1_funct_1(F,np__1) = C
                                    & k1_funct_1(G,np__0) = B
                                    & k1_funct_1(G,np__1) = D
                                    & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),E)
                                    & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),E)
                                    & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G)) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k1_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k2_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k2_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k3_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k3_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k4_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k4_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k5_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => m1_subset_1(k5_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k6_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => m1_subset_1(k6_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k7_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => m1_subset_1(k7_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k8_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => m1_subset_1(k8_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k9_jgraph_6,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => m1_subset_1(k9_jgraph_6(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(t19_jgraph_6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( A = a_0_0_jgraph_6
       => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,k23_euclid(k1_real_1(np__1),np__0)) = k30_pscomp_1(A) ) ) )).

fof(t23_jgraph_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k5_topmetr))
                                     => ~ ( H = np__0
                                          & I = np__1
                                          & v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
                                          & v2_funct_1(A)
                                          & v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
                                          & v2_funct_1(B)
                                          & C = a_0_1_jgraph_6
                                          & D = a_0_2_jgraph_6
                                          & E = a_0_3_jgraph_6
                                          & F = a_0_4_jgraph_6
                                          & G = a_0_5_jgraph_6
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),D)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),F)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),G)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
                                          & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_jgraph_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k5_topmetr))
                                     => ~ ( H = np__0
                                          & I = np__1
                                          & v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
                                          & v2_funct_1(A)
                                          & v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
                                          & v2_funct_1(B)
                                          & C = a_0_1_jgraph_6
                                          & D = a_0_2_jgraph_6
                                          & E = a_0_3_jgraph_6
                                          & F = a_0_4_jgraph_6
                                          & G = a_0_5_jgraph_6
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),D)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H),G)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I),F)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
                                          & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B),C)
                                          & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ( ( E = a_0_0_jgraph_6
                              & 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(np__2)))
                                  & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                                   => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(G)
                                        & v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(H)
                                        & F = a_0_1_jgraph_6
                                        & k1_funct_1(G,np__0) = C
                                        & k1_funct_1(G,np__1) = A
                                        & k1_funct_1(H,np__0) = B
                                        & k1_funct_1(H,np__1) = D
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
                                        & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ( ( E = a_0_0_jgraph_6
                              & 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(np__2)))
                                  & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                                   => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(G)
                                        & v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(H)
                                        & F = a_0_1_jgraph_6
                                        & k1_funct_1(G,np__0) = C
                                        & k1_funct_1(G,np__1) = A
                                        & k1_funct_1(H,np__0) = D
                                        & k1_funct_1(H,np__1) = B
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
                                        & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v6_compts_1(E,k15_euclid(np__2))
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ( ( E = a_0_0_jgraph_6
                              & r1_jordan17(E,A,B,C,D) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                                  & m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)))
                                      & m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2))) )
                                   => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(G)
                                        & v5_pre_topc(H,k5_topmetr,k15_euclid(np__2))
                                        & v2_funct_1(H)
                                        & F = a_0_1_jgraph_6
                                        & k1_funct_1(G,np__0) = A
                                        & k1_funct_1(G,np__1) = C
                                        & k1_funct_1(H,np__0) = B
                                        & k1_funct_1(H,np__1) = D
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),F)
                                        & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H),F)
                                        & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k1_jgraph_6(A,B,C,D) = a_4_0_jgraph_6(A,B,C,D) ) ) ) ) )).

fof(d2_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k2_jgraph_6(A,B,C,D) = a_4_1_jgraph_6(A,B,C,D) ) ) ) ) )).

fof(d3_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k3_jgraph_6(A,B,C,D) = a_4_2_jgraph_6(A,B,C,D) ) ) ) ) )).

fof(d4_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k4_jgraph_6(A,B,C,D) = a_4_3_jgraph_6(A,B,C,D) ) ) ) ) )).

fof(t29_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                     => ( ( r1_xreal_0(np__0,C)
                          & D = a_0_0_jgraph_6
                          & E = a_3_0_jgraph_6(A,B,C) )
                       => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(C,A,C,B),D) = E ) ) ) ) ) ) )).

fof(t32_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                 => ( D = a_3_0_jgraph_6(A,B,C)
                   => ( r1_xreal_0(C,np__0)
                      | v1_topreal2(D) ) ) ) ) ) ) )).

fof(d5_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k5_jgraph_6(A,B,C) = a_3_0_jgraph_6(A,B,C) ) ) ) )).

fof(d6_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k6_jgraph_6(A,B,C) = a_3_1_jgraph_6(A,B,C) ) ) ) )).

fof(d7_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k7_jgraph_6(A,B,C) = a_3_2_jgraph_6(A,B,C) ) ) ) )).

fof(d8_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k8_jgraph_6(A,B,C) = a_3_3_jgraph_6(A,B,C) ) ) ) )).

fof(d9_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => k9_jgraph_6(A,B,C) = a_3_4_jgraph_6(A,B,C) ) ) ) )).

fof(t33_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( k6_jgraph_6(np__0,np__0,A) = a_1_0_jgraph_6(A)
        & ( ~ r1_xreal_0(A,np__0)
         => k5_jgraph_6(np__0,np__0,A) = a_1_1_jgraph_6(A) )
        & k8_jgraph_6(np__0,np__0,A) = a_1_2_jgraph_6(A)
        & k7_jgraph_6(np__0,np__0,A) = a_1_3_jgraph_6(A)
        & k9_jgraph_6(np__0,np__0,A) = a_1_4_jgraph_6(A) ) ) )).

fof(t34_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_6_jgraph_6
              & B = a_0_7_jgraph_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) )).

fof(t35_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_8_jgraph_6
              & B = a_0_9_jgraph_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) )).

fof(t36_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_10_jgraph_6
              & B = a_0_1_jgraph_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) )).

fof(t37_jgraph_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_11_jgraph_6
              & B = a_0_12_jgraph_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) )).

fof(t39_jgraph_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)) = a_3_5_jgraph_6(A,C,D)
                      & k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D)) = a_3_6_jgraph_6(A,B,D)
                      & k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(B,C)) = a_3_6_jgraph_6(A,B,C)
                      & k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(B,D)) = a_3_5_jgraph_6(B,C,D) ) ) ) ) ) ) )).

fof(t45_jgraph_6,axiom,(
    a_0_13_jgraph_6 = a_0_14_jgraph_6 )).

fof(fraenkel_a_0_0_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1 ) ) )).

fof(fraenkel_a_0_1_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k5_toprns_1(np__2,B),np__1) ) ) )).

fof(fraenkel_a_0_2_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1
          & r1_xreal_0(k22_euclid(B),k21_euclid(B))
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_3_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1
          & r1_xreal_0(k21_euclid(B),k22_euclid(B))
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) )).

fof(fraenkel_a_0_4_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1
          & r1_xreal_0(k21_euclid(B),k22_euclid(B))
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_5_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1
          & r1_xreal_0(k22_euclid(B),k21_euclid(B))
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) )).

fof(fraenkel_a_4_0_jgraph_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_0_jgraph_6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & ~ r1_xreal_0(k21_euclid(F),B)
            & ~ r1_xreal_0(C,k21_euclid(F))
            & ~ r1_xreal_0(k22_euclid(F),D)
            & ~ r1_xreal_0(E,k22_euclid(F)) ) ) ) )).

fof(fraenkel_a_4_1_jgraph_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_1_jgraph_6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & r1_xreal_0(B,k21_euclid(F))
            & r1_xreal_0(k21_euclid(F),C)
            & r1_xreal_0(D,k22_euclid(F))
            & r1_xreal_0(k22_euclid(F),E) ) ) ) )).

fof(fraenkel_a_4_2_jgraph_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_2_jgraph_6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & ~ ( r1_xreal_0(B,k21_euclid(F))
                & r1_xreal_0(k21_euclid(F),C)
                & r1_xreal_0(D,k22_euclid(F))
                & r1_xreal_0(k22_euclid(F),E) ) ) ) ) )).

fof(fraenkel_a_4_3_jgraph_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_3_jgraph_6(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & ~ ( ~ r1_xreal_0(k21_euclid(F),B)
                & ~ r1_xreal_0(C,k21_euclid(F))
                & ~ r1_xreal_0(k22_euclid(F),D)
                & ~ r1_xreal_0(E,k22_euclid(F)) ) ) ) ) )).

fof(fraenkel_a_3_0_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_0_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))) = D ) ) ) )).

fof(fraenkel_a_3_1_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_1_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & ~ r1_xreal_0(D,k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C)))) ) ) ) )).

fof(fraenkel_a_3_2_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_2_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))),D) ) ) ) )).

fof(fraenkel_a_3_3_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_3_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & ~ r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C))),D) ) ) ) )).

fof(fraenkel_a_3_4_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_4_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & r1_xreal_0(D,k5_toprns_1(np__2,k20_euclid(np__2,E,k23_euclid(B,C)))) ) ) ) )).

fof(fraenkel_a_1_0_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_0_jgraph_6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ r1_xreal_0(B,k5_toprns_1(np__2,C)) ) ) ) )).

fof(fraenkel_a_1_1_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_1_jgraph_6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & k5_toprns_1(np__2,C) = B ) ) ) )).

fof(fraenkel_a_1_2_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_2_jgraph_6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ r1_xreal_0(k5_toprns_1(np__2,C),B) ) ) ) )).

fof(fraenkel_a_1_3_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_3_jgraph_6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(k5_toprns_1(np__2,C),B) ) ) ) )).

fof(fraenkel_a_1_4_jgraph_6,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_4_jgraph_6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r1_xreal_0(B,k5_toprns_1(np__2,C)) ) ) ) )).

fof(fraenkel_a_0_6_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
          & ~ r1_xreal_0(np__1,k21_euclid(B))
          & ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
          & ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_7_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_7_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ r1_xreal_0(np__1,k5_toprns_1(np__2,B)) ) ) )).

fof(fraenkel_a_0_8_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_8_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ ( r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
              & r1_xreal_0(k21_euclid(B),np__1)
              & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
              & r1_xreal_0(k22_euclid(B),np__1) ) ) ) )).

fof(fraenkel_a_0_9_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_9_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ r1_xreal_0(k5_toprns_1(np__2,B),np__1) ) ) )).

fof(fraenkel_a_0_10_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_10_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
          & r1_xreal_0(k21_euclid(B),np__1)
          & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
          & r1_xreal_0(k22_euclid(B),np__1) ) ) )).

fof(fraenkel_a_0_11_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_11_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ ( ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,k21_euclid(B))
              & ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) ) )).

fof(fraenkel_a_0_12_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_12_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(np__1,k5_toprns_1(np__2,B)) ) ) )).

fof(fraenkel_a_3_5_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_5_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & k21_euclid(E) = B
            & r1_xreal_0(k22_euclid(E),D)
            & r1_xreal_0(C,k22_euclid(E)) ) ) ) )).

fof(fraenkel_a_3_6_jgraph_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_6_jgraph_6(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
            & A = E
            & r1_xreal_0(k21_euclid(E),C)
            & r1_xreal_0(B,k21_euclid(E))
            & k22_euclid(E) = D ) ) ) )).

fof(fraenkel_a_0_13_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_13_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ ( ~ ( k1_real_1(np__1) = k21_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k21_euclid(B) = np__1
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k1_real_1(np__1) = k22_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) )
              & ~ ( np__1 = k22_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) )).

fof(fraenkel_a_0_14_jgraph_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_14_jgraph_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ ( ~ ( k21_euclid(B) = k1_real_1(np__1)
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k22_euclid(B) = np__1
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) )
              & ~ ( k21_euclid(B) = np__1
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k22_euclid(B) = k1_real_1(np__1)
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) )).
%------------------------------------------------------------------------------