SET007 Axioms: SET007+725.ax


%------------------------------------------------------------------------------
% File     : SET007+725 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : General Fashoda Meet Theorem for Unit Circle
% 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   83 (   1 unit)
%            Number of atoms       : 1316 ( 255 equality)
%            Maximal formula depth :   51 (  18 average)
%            Number of connectives : 1462 ( 229 ~  ;  61  |; 758  &)
%                                         (   9 <=>; 405 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   55 (  16 constant; 0-5 arity)
%            Number of variables   :  377 (   0 singleton; 362 !;  15 ?)
%            Maximal term depth    :    5 (   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(t1_jgraph_5,axiom,(
    $true )).

fof(t2_jgraph_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,np__0)
              & ~ r1_xreal_0(A,B)
              & r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) )).

fof(t3_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(k5_toprns_1(np__2,A),np__1)
       => ( r1_xreal_0(k1_real_1(np__1),k21_euclid(A))
          & r1_xreal_0(k21_euclid(A),np__1)
          & r1_xreal_0(k1_real_1(np__1),k22_euclid(A))
          & r1_xreal_0(k22_euclid(A),np__1) ) ) ) )).

fof(t4_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(k5_toprns_1(np__2,A),np__1)
       => ( k21_euclid(A) = np__0
          | k22_euclid(A) = np__0
          | ( ~ r1_xreal_0(k21_euclid(A),k1_real_1(np__1))
            & ~ r1_xreal_0(np__1,k21_euclid(A))
            & ~ r1_xreal_0(k22_euclid(A),k1_real_1(np__1))
            & ~ r1_xreal_0(np__1,k22_euclid(A)) ) ) ) ) )).

fof(t5_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & l1_metric_1(F) )
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & l1_metric_1(G) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(F))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(G))
                                     => ( ( r1_xreal_0(C,A)
                                          & r1_xreal_0(A,B)
                                          & r1_xreal_0(B,D)
                                          & F = k2_topmetr(A,B)
                                          & G = k2_topmetr(C,D)
                                          & H = I
                                          & r2_hidden(H,u1_struct_0(F))
                                          & r2_hidden(I,u1_struct_0(G)) )
                                       => r1_tarski(k9_metric_1(F,H,E),k9_metric_1(G,I,E)) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_jgraph_5,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,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D))))
                     => ( ( r1_xreal_0(C,A)
                          & r1_xreal_0(A,B)
                          & r1_xreal_0(B,D)
                          & E = k1_rcomp_1(A,B) )
                       => k4_topmetr(A,B) = k3_pre_topc(k4_topmetr(C,D),E) ) ) ) ) ) ) )).

fof(t7_jgraph_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
             => ( ( r1_xreal_0(np__0,A)
                  & r1_xreal_0(A,B)
                  & r1_xreal_0(B,np__1)
                  & C = k1_rcomp_1(A,B) )
               => k4_topmetr(A,B) = k3_pre_topc(k5_topmetr,C) ) ) ) ) )).

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

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

fof(t10_jgraph_5,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(A),u1_struct_0(C))
                                & m2_relset_1(G,u1_struct_0(A),u1_struct_0(C)) )
                             => ( ( G = k5_relat_1(E,F)
                                  & v5_pre_topc(E,A,k3_pre_topc(B,D))
                                  & v5_pre_topc(F,B,C) )
                               => v5_pre_topc(G,A,C) ) ) ) ) ) ) ) ) )).

fof(t11_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                                        & m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                                     => ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
                                          & k1_funct_1(I,E) = G
                                          & k1_funct_1(I,F) = H
                                          & k1_funct_1(I,A) = C
                                          & k1_funct_1(I,B) = D
                                          & r1_xreal_0(C,D)
                                          & r1_xreal_0(G,H)
                                          & r2_hidden(E,k1_rcomp_1(A,B))
                                          & r2_hidden(F,k1_rcomp_1(A,B)) )
                                       => r1_xreal_0(E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                                        & m2_relset_1(I,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) )
                                     => ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D))
                                          & k1_funct_1(I,E) = G
                                          & k1_funct_1(I,F) = H
                                          & k1_funct_1(I,A) = D
                                          & k1_funct_1(I,B) = C
                                          & r1_xreal_0(C,D)
                                          & r1_xreal_0(H,G)
                                          & r2_hidden(E,k1_rcomp_1(A,B))
                                          & r2_hidden(F,k1_rcomp_1(A,B)) )
                                       => r1_xreal_0(E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_jgraph_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k19_euclid(A,k16_euclid(A)) = k16_euclid(A) ) )).

fof(t14_jgraph_5,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_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k5_topmetr))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                 => ~ ( G = np__0
                                      & H = 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 != D
                                      & E != F
                                      & k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)) = C
                                      & r1_xreal_0(E,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)))
                                      & r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)),F)
                                      & k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)) = D
                                      & r1_xreal_0(E,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)))
                                      & r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H)),F)
                                      & k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)) = E
                                      & r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)))
                                      & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)),D)
                                      & k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)) = F
                                      & r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)))
                                      & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,H)),D)
                                      & ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(k5_topmetr))
                                         => ( ~ ( ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)),C)
                                                & ~ r1_xreal_0(D,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)))
                                                & ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)),E)
                                                & ~ r1_xreal_0(F,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I))) )
                                            & ~ ( ~ r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)),C)
                                                & ~ r1_xreal_0(D,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)))
                                                & ~ r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)),E)
                                                & ~ r1_xreal_0(F,k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I))) ) ) )
                                      & 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(t15_jgraph_5,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))) )
     => ~ ( v5_pre_topc(A,k5_topmetr,k15_euclid(np__2))
          & v2_funct_1(A)
          & ! [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))) )
             => ~ ( k1_funct_1(B,np__0) = k1_funct_1(A,np__1)
                  & k1_funct_1(B,np__1) = k1_funct_1(A,np__0)
                  & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B) = k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A)
                  & v5_pre_topc(B,k5_topmetr,k15_euclid(np__2))
                  & v2_funct_1(B) ) ) ) ) )).

fof(t21_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,A)
              & ~ r1_xreal_0(k22_euclid(B),np__0)
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                  & C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
                  & r1_xreal_0(k22_euclid(C),np__0) ) ) ) ) )).

fof(t22_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_xreal_0(np__0,k22_euclid(B))
           => ( r1_xreal_0(A,k1_real_1(np__1))
              | r1_xreal_0(np__1,A)
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
                   => r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) )).

fof(t23_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_xreal_0(np__0,k22_euclid(B))
           => ( r1_xreal_0(A,k1_real_1(np__1))
              | r1_xreal_0(np__1,A)
              | r1_xreal_0(A,k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
              | k5_toprns_1(np__2,B) = np__0
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
                   => ( r1_xreal_0(np__0,k22_euclid(C))
                      & ~ r1_xreal_0(np__0,k21_euclid(C)) ) ) ) ) ) ) ) )).

fof(t24_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_xreal_0(np__0,k22_euclid(B))
                  & r1_xreal_0(np__0,k22_euclid(C)) )
               => ( r1_xreal_0(A,k1_real_1(np__1))
                  | r1_xreal_0(np__1,A)
                  | k5_toprns_1(np__2,B) = np__0
                  | k5_toprns_1(np__2,C) = np__0
                  | r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
                  | ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),B)
                              & E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k5_jgraph_4(A),C)
                              & r1_xreal_0(k6_real_1(k21_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) )).

fof(t25_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,A)
              & ~ r1_xreal_0(k21_euclid(B),np__0)
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                  & C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
                  & r1_xreal_0(k21_euclid(C),np__0) ) ) ) ) )).

fof(t26_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_xreal_0(np__0,k21_euclid(B))
           => ( r1_xreal_0(A,k1_real_1(np__1))
              | r1_xreal_0(np__1,A)
              | r1_xreal_0(A,k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
              | k5_toprns_1(np__2,B) = np__0
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
                   => ( r1_xreal_0(np__0,k21_euclid(C))
                      & ~ r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) ) ) ) )).

fof(t27_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_xreal_0(np__0,k21_euclid(B))
                  & r1_xreal_0(np__0,k21_euclid(C)) )
               => ( r1_xreal_0(A,k1_real_1(np__1))
                  | r1_xreal_0(np__1,A)
                  | k5_toprns_1(np__2,B) = np__0
                  | k5_toprns_1(np__2,C) = np__0
                  | r1_xreal_0(k6_real_1(k22_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k22_euclid(B),k5_toprns_1(np__2,B)))
                  | ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),B)
                              & E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k7_jgraph_4(A),C)
                              & r1_xreal_0(k6_real_1(k22_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k22_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) )).

fof(t28_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,A)
              & ~ r1_xreal_0(np__0,k22_euclid(B))
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                  & C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
                  & r1_xreal_0(np__0,k22_euclid(C)) ) ) ) ) )).

fof(t29_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
              & ~ r1_xreal_0(np__1,A)
              & ~ r1_xreal_0(np__0,k22_euclid(B))
              & ~ r1_xreal_0(k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)),A)
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                  & C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
                  & ~ ( ~ r1_xreal_0(np__0,k22_euclid(C))
                      & ~ r1_xreal_0(k21_euclid(C),np__0) ) ) ) ) ) )).

fof(t30_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_xreal_0(k22_euclid(B),np__0)
                  & r1_xreal_0(k22_euclid(C),np__0) )
               => ( r1_xreal_0(A,k1_real_1(np__1))
                  | r1_xreal_0(np__1,A)
                  | k5_toprns_1(np__2,B) = np__0
                  | k5_toprns_1(np__2,C) = np__0
                  | r1_xreal_0(k6_real_1(k21_euclid(C),k5_toprns_1(np__2,C)),k6_real_1(k21_euclid(B),k5_toprns_1(np__2,B)))
                  | ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
                              & E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C)
                              & r1_xreal_0(k6_real_1(k21_euclid(E),k5_toprns_1(np__2,E)),k6_real_1(k21_euclid(D),k5_toprns_1(np__2,D))) ) ) ) ) ) ) ) ) )).

fof(t34_jgraph_5,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr))
        & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr)) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr),A,B) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B) )
       => v5_pre_topc(A,k15_euclid(np__2),k3_topmetr) ) ) )).

fof(t35_jgraph_5,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr))
        & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr)) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr),A,B) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,B) )
       => v5_pre_topc(A,k15_euclid(np__2),k3_topmetr) ) ) )).

fof(t39_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( r1_xreal_0(A,B)
                      & ~ r1_xreal_0(D,np__0)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C))))
                            & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C)))) )
                         => ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k3_real_1(k4_real_1(D,A),C),k3_real_1(k4_real_1(D,B),C)))
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(A,B))
                                   => k1_funct_1(E,F) = k3_real_1(k4_real_1(D,F),C) ) ) ) ) ) ) ) ) ) )).

fof(t40_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( r1_xreal_0(A,B)
                      & ~ r1_xreal_0(np__0,D)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C))))
                            & m2_relset_1(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C)))) )
                         => ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k3_real_1(k4_real_1(D,B),C),k3_real_1(k4_real_1(D,A),C)))
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( r2_hidden(F,k1_rcomp_1(A,B))
                                   => k1_funct_1(E,F) = k3_real_1(k4_real_1(D,F),C) ) ) ) ) ) ) ) ) ) )).

fof(t41_jgraph_5,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
      & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
      & v3_tops_2(A,k5_topmetr,k4_topmetr(k1_real_1(np__1),np__1))
      & ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( r2_hidden(B,k1_rcomp_1(np__0,np__1))
           => k1_funct_1(A,B) = k3_real_1(k4_real_1(k1_real_1(np__2),B),np__1) ) )
      & k1_funct_1(A,np__0) = np__1
      & k1_funct_1(A,np__1) = k1_real_1(np__1) ) )).

fof(t42_jgraph_5,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
      & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)))
      & v3_tops_2(A,k5_topmetr,k4_topmetr(k1_real_1(np__1),np__1))
      & ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( r2_hidden(B,k1_rcomp_1(np__0,np__1))
           => k1_funct_1(A,B) = k5_real_1(k4_real_1(np__2,B),np__1) ) )
      & k1_funct_1(A,np__0) = k1_real_1(np__1)
      & k1_funct_1(A,np__1) = np__1 ) )).

fof(t60_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_xreal_0(k22_euclid(B),np__0)
           => ( r1_xreal_0(A,k1_real_1(np__1))
              | r1_xreal_0(np__1,A)
              | ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( C = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
                   => r1_xreal_0(k22_euclid(C),np__0) ) ) ) ) ) ) )).

fof(t16_jgraph_5,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_0_jgraph_5
                                          & D = a_0_1_jgraph_5
                                          & E = a_0_2_jgraph_5
                                          & F = a_0_3_jgraph_5
                                          & G = a_0_4_jgraph_5
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
                                          & 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(t17_jgraph_5,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_5_jgraph_5
                                          & D = a_0_1_jgraph_5
                                          & E = a_0_2_jgraph_5
                                          & F = a_0_3_jgraph_5
                                          & G = a_0_4_jgraph_5
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
                                          & 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(t18_jgraph_5,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_5_jgraph_5
                                          & D = a_0_1_jgraph_5
                                          & E = a_0_2_jgraph_5
                                          & F = a_0_3_jgraph_5
                                          & G = a_0_4_jgraph_5
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,H),E)
                                          & r2_hidden(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I),D)
                                          & 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(t19_jgraph_5,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))))
             => ~ ( C = a_0_5_jgraph_5
                  & 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)
                  & k1_funct_1(A,np__0) = k23_euclid(k1_real_1(np__1),np__0)
                  & k1_funct_1(A,np__1) = k23_euclid(np__1,np__0)
                  & k1_funct_1(B,np__1) = k23_euclid(np__0,np__1)
                  & k1_funct_1(B,np__0) = k23_euclid(np__0,k1_real_1(np__1))
                  & 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(t20_jgraph_5,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))))
                     => ( ( E = a_0_5_jgraph_5
                          & k5_toprns_1(np__2,A) = np__1
                          & k5_toprns_1(np__2,B) = np__1
                          & k5_toprns_1(np__2,C) = np__1
                          & k5_toprns_1(np__2,D) = np__1 )
                       => ( ! [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))) )
                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                  & r1_tarski(k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),F,E),E)
                                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A) = k23_euclid(k1_real_1(np__1),np__0)
                                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B) = k23_euclid(np__0,np__1)
                                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C) = k23_euclid(np__1,np__0)
                                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) = k23_euclid(np__0,k1_real_1(np__1)) ) )
                          | ! [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)
                                      & k1_funct_1(F,np__0) = A
                                      & k1_funct_1(F,np__1) = C
                                      & k1_funct_1(G,np__0) = D
                                      & k1_funct_1(G,np__1) = B
                                      & 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(t31_jgraph_5,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_6_jgraph_5
       => ( k18_pscomp_1(A) = k1_real_1(np__1)
          & k20_pscomp_1(A) = np__1
          & k21_pscomp_1(A) = k1_real_1(np__1)
          & k19_pscomp_1(A) = np__1 ) ) ) )).

fof(t32_jgraph_5,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_6_jgraph_5
       => k30_pscomp_1(A) = k23_euclid(k1_real_1(np__1),np__0) ) ) )).

fof(t33_jgraph_5,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_6_jgraph_5
       => k34_pscomp_1(A) = k23_euclid(np__1,np__0) ) ) )).

fof(t36_jgraph_5,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_6_jgraph_5
       => ( r1_tarski(k8_jordan6(A),A)
          & r1_tarski(k9_jordan6(A),A) ) ) ) )).

fof(t37_jgraph_5,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_6_jgraph_5
       => k8_jordan6(A) = a_1_0_jgraph_5(A) ) ) )).

fof(t38_jgraph_5,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_6_jgraph_5
       => k9_jordan6(A) = a_1_1_jgraph_5(A) ) ) )).

fof(t43_jgraph_5,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_6_jgraph_5
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A))))
                & m2_relset_1(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))) )
             => ~ ( v3_tops_2(B,k4_topmetr(k1_real_1(np__1),np__1),k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))
                  & ! [C] :
                      ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                     => ( r2_hidden(C,k9_jordan6(A))
                       => k1_funct_1(B,k21_euclid(C)) = C ) )
                  & k1_funct_1(B,k1_real_1(np__1)) = k30_pscomp_1(A)
                  & k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) )).

fof(t44_jgraph_5,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_6_jgraph_5
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A))))
                & m2_relset_1(B,u1_struct_0(k4_topmetr(k1_real_1(np__1),np__1)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))) )
             => ~ ( v3_tops_2(B,k4_topmetr(k1_real_1(np__1),np__1),k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))
                  & ! [C] :
                      ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                     => ( r2_hidden(C,k8_jordan6(A))
                       => k1_funct_1(B,k21_euclid(C)) = C ) )
                  & k1_funct_1(B,k1_real_1(np__1)) = k30_pscomp_1(A)
                  & k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) )).

fof(t45_jgraph_5,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_6_jgraph_5
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A))))
                & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))) )
             => ~ ( v3_tops_2(B,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k9_jordan6(A)))
                  & ! [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_numbers)
                             => ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( ( k1_funct_1(B,E) = C
                                      & k1_funct_1(B,F) = D
                                      & r2_hidden(E,k1_rcomp_1(np__0,np__1))
                                      & r2_hidden(F,k1_rcomp_1(np__0,np__1)) )
                                   => ( ~ ( ~ r1_xreal_0(F,E)
                                          & r1_xreal_0(k21_euclid(C),k21_euclid(D)) )
                                      & ~ ( ~ r1_xreal_0(k21_euclid(C),k21_euclid(D))
                                          & r1_xreal_0(F,E) ) ) ) ) ) ) )
                  & k1_funct_1(B,np__0) = k34_pscomp_1(A)
                  & k1_funct_1(B,np__1) = k30_pscomp_1(A) ) ) ) ) )).

fof(t46_jgraph_5,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_6_jgraph_5
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A))))
                & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))) )
             => ~ ( v3_tops_2(B,k5_topmetr,k3_pre_topc(k15_euclid(np__2),k8_jordan6(A)))
                  & ! [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_numbers)
                             => ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ( ( k1_funct_1(B,E) = C
                                      & k1_funct_1(B,F) = D
                                      & r2_hidden(E,k1_rcomp_1(np__0,np__1))
                                      & r2_hidden(F,k1_rcomp_1(np__0,np__1)) )
                                   => ( ~ ( ~ r1_xreal_0(F,E)
                                          & r1_xreal_0(k21_euclid(D),k21_euclid(C)) )
                                      & ~ ( ~ r1_xreal_0(k21_euclid(D),k21_euclid(C))
                                          & r1_xreal_0(F,E) ) ) ) ) ) ) )
                  & k1_funct_1(B,np__0) = k30_pscomp_1(A)
                  & k1_funct_1(B,np__1) = k34_pscomp_1(A) ) ) ) ) )).

fof(t47_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(B,k8_jordan6(C))
                  & r1_jordan6(C,A,B) )
               => r2_hidden(A,k8_jordan6(C)) ) ) ) ) )).

fof(t48_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B) )
               => ( A = B
                  | r1_xreal_0(np__0,k21_euclid(A))
                  | r1_xreal_0(np__0,k21_euclid(B))
                  | r1_xreal_0(np__0,k22_euclid(A))
                  | r1_xreal_0(np__0,k22_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
                    & ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) ) ) ) ) ) ) )).

fof(t49_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B)
                  & r1_xreal_0(np__0,k22_euclid(A))
                  & r1_xreal_0(np__0,k22_euclid(B)) )
               => ( A = B
                  | r1_xreal_0(np__0,k21_euclid(A))
                  | r1_xreal_0(np__0,k21_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
                    & ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) ) ) ) ) ) ) )).

fof(t50_jgraph_5,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)))) )
             => ~ ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B)
                  & A != B
                  & r1_xreal_0(np__0,k22_euclid(A))
                  & r1_xreal_0(np__0,k22_euclid(B))
                  & r1_xreal_0(k21_euclid(B),k21_euclid(A)) ) ) ) ) )).

fof(t51_jgraph_5,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)))) )
             => ~ ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B)
                  & A != B
                  & r1_xreal_0(k22_euclid(A),np__0)
                  & r1_xreal_0(k22_euclid(B),np__0)
                  & A != k30_pscomp_1(C)
                  & r1_xreal_0(k21_euclid(A),k21_euclid(B)) ) ) ) ) )).

fof(t52_jgraph_5,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)))) )
             => ~ ( C = a_0_6_jgraph_5
                  & ( r1_xreal_0(np__0,k22_euclid(B))
                    | r1_xreal_0(np__0,k21_euclid(B)) )
                  & r1_jordan6(C,A,B)
                  & ~ r1_xreal_0(np__0,k22_euclid(A))
                  & ~ r1_xreal_0(np__0,k21_euclid(A)) ) ) ) ) )).

fof(t53_jgraph_5,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)))) )
             => ~ ( C = a_0_6_jgraph_5
                  & r1_jordan6(C,A,B)
                  & A != B
                  & r1_xreal_0(np__0,k21_euclid(A))
                  & r1_xreal_0(np__0,k21_euclid(B))
                  & r1_xreal_0(k22_euclid(A),k22_euclid(B)) ) ) ) ) )).

fof(t54_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C) )
               => ( r1_xreal_0(np__0,k21_euclid(A))
                  | r1_xreal_0(np__0,k21_euclid(B))
                  | r1_xreal_0(np__0,k22_euclid(A))
                  | r1_xreal_0(np__0,k22_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
                    & ~ r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
                  | r1_jordan6(C,A,B) ) ) ) ) ) )).

fof(t55_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C) )
               => ( r1_xreal_0(k21_euclid(A),np__0)
                  | r1_xreal_0(k21_euclid(B),np__0)
                  | r1_xreal_0(np__0,k22_euclid(A))
                  | r1_xreal_0(np__0,k22_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(A))
                    & ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
                  | r1_jordan6(C,A,B) ) ) ) ) ) )).

fof(t56_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C)
                  & r1_xreal_0(np__0,k22_euclid(A))
                  & r1_xreal_0(np__0,k22_euclid(B)) )
               => ( r1_xreal_0(np__0,k21_euclid(A))
                  | r1_xreal_0(np__0,k21_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
                    & ~ r1_xreal_0(k22_euclid(A),k22_euclid(B)) )
                  | r1_jordan6(C,A,B) ) ) ) ) ) )).

fof(t57_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C)
                  & r1_xreal_0(np__0,k22_euclid(A))
                  & r1_xreal_0(np__0,k22_euclid(B))
                  & r1_xreal_0(k21_euclid(A),k21_euclid(B)) )
               => r1_jordan6(C,A,B) ) ) ) ) )).

fof(t58_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C)
                  & r1_xreal_0(np__0,k21_euclid(A))
                  & r1_xreal_0(np__0,k21_euclid(B))
                  & r1_xreal_0(k22_euclid(B),k22_euclid(A)) )
               => r1_jordan6(C,A,B) ) ) ) ) )).

fof(t59_jgraph_5,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)))) )
             => ( ( C = a_0_6_jgraph_5
                  & r2_hidden(A,C)
                  & r2_hidden(B,C)
                  & r1_xreal_0(k22_euclid(A),np__0)
                  & r1_xreal_0(k22_euclid(B),np__0)
                  & r1_xreal_0(k21_euclid(B),k21_euclid(A)) )
               => ( B = k30_pscomp_1(C)
                  | r1_jordan6(C,A,B) ) ) ) ) ) )).

fof(t61_jgraph_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [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,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( ( ~ v1_xboole_0(F)
                            & v6_compts_1(F,k15_euclid(np__2))
                            & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( F = a_0_6_jgraph_5
                              & r1_jordan6(F,B,C)
                              & D = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),B)
                              & E = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k9_jgraph_4(A),C) )
                           => ( r1_xreal_0(A,k1_real_1(np__1))
                              | r1_xreal_0(np__1,A)
                              | r1_jordan6(F,D,E) ) ) ) ) ) ) ) ) )).

fof(t62_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ~ r1_xreal_0(np__0,k21_euclid(A))
                          & r1_xreal_0(np__0,k22_euclid(A))
                          & ~ r1_xreal_0(np__0,k21_euclid(B))
                          & r1_xreal_0(np__0,k22_euclid(B))
                          & ~ r1_xreal_0(np__0,k21_euclid(C))
                          & r1_xreal_0(np__0,k22_euclid(C))
                          & ~ r1_xreal_0(np__0,k21_euclid(D))
                          & r1_xreal_0(np__0,k22_euclid(D))
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t63_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & r1_xreal_0(np__0,k22_euclid(A))
                          & r1_xreal_0(np__0,k22_euclid(B))
                          & r1_xreal_0(np__0,k22_euclid(C))
                          & ~ r1_xreal_0(k22_euclid(D),np__0)
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t64_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & r1_xreal_0(np__0,k22_euclid(A))
                          & r1_xreal_0(np__0,k22_euclid(B))
                          & r1_xreal_0(np__0,k22_euclid(C))
                          & ~ r1_xreal_0(k22_euclid(D),np__0)
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t65_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ( r1_xreal_0(np__0,k22_euclid(A))
                            | r1_xreal_0(np__0,k21_euclid(A)) )
                          & ( r1_xreal_0(np__0,k22_euclid(B))
                            | r1_xreal_0(np__0,k21_euclid(B)) )
                          & ( r1_xreal_0(np__0,k22_euclid(C))
                            | r1_xreal_0(np__0,k21_euclid(C)) )
                          & ~ ( r1_xreal_0(k22_euclid(D),np__0)
                              & r1_xreal_0(k21_euclid(D),np__0) )
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & r1_xreal_0(np__0,k22_euclid(G))
                                                  & r1_xreal_0(np__0,k22_euclid(H))
                                                  & r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(k22_euclid(J),np__0)
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t66_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ( r1_xreal_0(np__0,k22_euclid(A))
                            | r1_xreal_0(np__0,k21_euclid(A)) )
                          & ( r1_xreal_0(np__0,k22_euclid(B))
                            | r1_xreal_0(np__0,k21_euclid(B)) )
                          & ( r1_xreal_0(np__0,k22_euclid(C))
                            | r1_xreal_0(np__0,k21_euclid(C)) )
                          & ~ ( r1_xreal_0(k22_euclid(D),np__0)
                              & r1_xreal_0(k21_euclid(D),np__0) )
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t67_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & D = k30_pscomp_1(E)
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t68_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & ! [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))) )
                             => ! [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)))
                                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                                  & ! [K] :
                                                      ( m1_subset_1(K,u1_struct_0(k15_euclid(np__2)))
                                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,K)) = k5_toprns_1(np__2,K) )
                                                  & G = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                                  & H = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                                  & I = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                                  & J = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D)
                                                  & ~ r1_xreal_0(np__0,k21_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(G))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(H))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(I))
                                                  & ~ r1_xreal_0(np__0,k21_euclid(J))
                                                  & ~ r1_xreal_0(np__0,k22_euclid(J))
                                                  & r1_jordan6(E,G,H)
                                                  & r1_jordan6(E,H,I)
                                                  & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t69_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & A != B
                          & B != C
                          & C != D
                          & ~ r1_xreal_0(np__0,k21_euclid(A))
                          & ~ r1_xreal_0(np__0,k21_euclid(B))
                          & ~ r1_xreal_0(np__0,k21_euclid(C))
                          & ~ r1_xreal_0(np__0,k21_euclid(D))
                          & ~ r1_xreal_0(np__0,k22_euclid(A))
                          & ~ r1_xreal_0(np__0,k22_euclid(B))
                          & ~ r1_xreal_0(np__0,k22_euclid(C))
                          & ~ r1_xreal_0(np__0,k22_euclid(D))
                          & ! [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))) )
                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                  & ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,G)) = k5_toprns_1(np__2,G) )
                                  & k23_euclid(k1_real_1(np__1),np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                  & k23_euclid(np__0,np__1) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                  & k23_euclid(np__1,np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                  & k23_euclid(np__0,k1_real_1(np__1)) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) ) ) ) ) ) ) ) ) )).

fof(t70_jgraph_5,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)))) )
                     => ~ ( E = a_0_6_jgraph_5
                          & r1_jordan6(E,A,B)
                          & r1_jordan6(E,B,C)
                          & r1_jordan6(E,C,D)
                          & A != B
                          & B != C
                          & C != D
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(k15_euclid(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))) )
                             => ~ ( v3_tops_2(F,k15_euclid(np__2),k15_euclid(np__2))
                                  & ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                     => k5_toprns_1(np__2,k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,G)) = k5_toprns_1(np__2,G) )
                                  & k23_euclid(k1_real_1(np__1),np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,A)
                                  & k23_euclid(np__0,np__1) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,B)
                                  & k23_euclid(np__1,np__0) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,C)
                                  & k23_euclid(np__0,k1_real_1(np__1)) = k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),F,D) ) ) ) ) ) ) ) ) )).

fof(t71_jgraph_5,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_6_jgraph_5
                              & r1_jordan6(E,A,B)
                              & r1_jordan6(E,B,C)
                              & r1_jordan6(E,C,D) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(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_0_jgraph_5
                                        & 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(t72_jgraph_5,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_6_jgraph_5
                              & r1_jordan6(E,A,B)
                              & r1_jordan6(E,B,C)
                              & r1_jordan6(E,C,D) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(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_0_jgraph_5
                                        & k1_funct_1(G,np__0) = A
                                        & k1_funct_1(G,np__1) = C
                                        & 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(t73_jgraph_5,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_6_jgraph_5
                              & r1_jordan6(E,A,B)
                              & r1_jordan6(E,B,C)
                              & r1_jordan6(E,C,D) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(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_5_jgraph_5
                                        & k1_funct_1(G,np__0) = A
                                        & k1_funct_1(G,np__1) = C
                                        & 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(t74_jgraph_5,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_6_jgraph_5
                              & r1_jordan6(E,A,B)
                              & r1_jordan6(E,B,C)
                              & r1_jordan6(E,C,D) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(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_5_jgraph_5
                                        & 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(fraenkel_a_0_0_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_jgraph_5)
    <=> ? [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_1_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_jgraph_5)
    <=> ? [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_2_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_jgraph_5)
    <=> ? [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_3_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_jgraph_5)
    <=> ? [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_4_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_jgraph_5)
    <=> ? [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_0_5_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_jgraph_5)
    <=> ? [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_6_jgraph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_jgraph_5)
    <=> ? [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_1_0_jgraph_5,axiom,(
    ! [A,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)))) )
     => ( r2_hidden(A,a_1_0_jgraph_5(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r2_hidden(C,B)
            & r1_xreal_0(np__0,k22_euclid(C)) ) ) ) )).

fof(fraenkel_a_1_1_jgraph_5,axiom,(
    ! [A,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)))) )
     => ( r2_hidden(A,a_1_1_jgraph_5(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & r2_hidden(C,B)
            & r1_xreal_0(k22_euclid(C),np__0) ) ) ) )).
%------------------------------------------------------------------------------