SET007 Axioms: SET007+704.ax


%------------------------------------------------------------------------------
% File     : SET007+704 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Simple Closed Curve Property of the Circle
% Version  : [Urb08] axioms.
% English  : Simple Closed Curve Property of the Circle and the Fashoda Meet
%            Theorem for It

% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   73 (   5 unit)
%            Number of atoms       :  691 ( 154 equality)
%            Maximal formula depth :   37 (  10 average)
%            Number of connectives :  730 ( 112 ~  ;   6  |; 370  &)
%                                         (  15 <=>; 227 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-3 arity)
%            Number of functors    :   58 (  21 constant; 0-4 arity)
%            Number of variables   :  207 (   0 singleton; 191 !;  16 ?)
%            Maximal term depth    :    8 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jgraph_3,axiom,
    ( v1_relat_1(k1_jgraph_3)
    & v1_funct_1(k1_jgraph_3)
    & v2_funct_1(k1_jgraph_3)
    & v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )).

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

fof(t2_jgraph_3,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ~ ( k5_square_1(A) = np__1
          & A != np__1
          & A != k1_real_1(np__1) ) ) )).

fof(t3_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(np__0,A)
          & r1_xreal_0(A,np__1) )
       => r1_xreal_0(k5_square_1(A),A) ) ) )).

fof(t4_jgraph_3,axiom,(
    $true )).

fof(t5_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(k6_xcmplx_0(k5_square_1(A),np__1),np__0)
       => ( r1_xreal_0(k1_real_1(np__1),A)
          & r1_xreal_0(A,np__1) ) ) ) )).

fof(t6_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,A) )
              <=> ~ r1_xreal_0(k1_square_1(B,C),A) ) ) ) ) )).

fof(t7_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(A,np__0)
       => ( ~ r1_xreal_0(A,k7_xcmplx_0(A,np__3))
          & ~ r1_xreal_0(A,k7_xcmplx_0(A,np__4)) ) ) ) )).

fof(t8_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(np__1,A)
         => r1_xreal_0(np__1,k8_square_1(A)) )
        & ~ ( ~ r1_xreal_0(A,np__1)
            & r1_xreal_0(k8_square_1(A),np__1) ) ) ) )).

fof(t9_jgraph_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_1(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) )).

fof(t10_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( k5_toprns_1(np__2,A) = k9_square_1(k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))))
        & k7_square_1(k5_toprns_1(np__2,A)) = k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))) ) ) )).

fof(t11_jgraph_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k9_relat_1(k7_relat_1(A,B),C) = k9_relat_1(A,k3_xboole_0(C,B)) ) )).

fof(t12_jgraph_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D))
                    & v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B))
                    & m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B)) ) ) ) ) ) )).

fof(t13_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
                         => ( ( k3_subset_1(u1_struct_0(A),D) = k1_struct_0(A,C)
                              & k3_subset_1(u1_struct_0(B),E) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C))
                              & v3_compts_1(A)
                              & v3_compts_1(B)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k3_pre_topc(A,D)))
                                 => k1_funct_1(F,G) != k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C) )
                              & v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D))
                              & v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(k3_pre_topc(B,E)))
                              & v5_pre_topc(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),k3_pre_topc(A,D),k3_pre_topc(B,E))
                              & m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(B),F,D),u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(k3_pre_topc(B,E)))
                              & ! [G] :
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
                                 => ~ ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C),G)
                                      & v3_pre_topc(G,B)
                                      & ! [H] :
                                          ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                         => ~ ( r2_hidden(C,H)
                                              & v3_pre_topc(H,A)
                                              & r1_tarski(k4_pre_topc(A,B,F,H),G) ) ) ) ) )
                           => v5_pre_topc(F,A,B) ) ) ) ) ) ) ) )).

fof(d1_jgraph_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
     => ( A = k1_jgraph_3
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( ( B = k16_euclid(np__2)
               => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) = B )
              & ~ ( ( ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
                      & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
                    | ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
                      & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) )
                  & B != k16_euclid(np__2)
                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) != k23_euclid(k6_real_1(k21_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(B),k21_euclid(B)))))),k6_real_1(k22_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(B),k21_euclid(B))))))) )
              & ~ ( ~ ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
                      & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
                  & ~ ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
                      & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) )
                  & B != k16_euclid(np__2)
                  & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),A,B) != k23_euclid(k6_real_1(k21_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(B),k22_euclid(B)))))),k6_real_1(k22_euclid(B),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(B),k22_euclid(B))))))) ) ) ) ) ) )).

fof(t14_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( A != k16_euclid(np__2)
       => ( ( ( ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                & r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
              | ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                & r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) ) )
           => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A) = k23_euclid(k6_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k6_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) )
          & ~ ( ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                  & r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
              & ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                  & r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) )
              & k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A) != k23_euclid(k6_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k6_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) ) ) ) ) )).

fof(t15_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ~ ( v5_pre_topc(B,A,k3_topmetr)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ? [D] :
                      ( v1_xreal_0(D)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) = D
                      & r1_xreal_0(np__0,D) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                 => ~ ( ! [D] :
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ! [E] :
                              ( v1_xreal_0(E)
                             => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,D) = E
                               => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) = k8_square_1(E) ) ) )
                      & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).

fof(t16_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k5_square_1(k7_xcmplx_0(F,G)) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t17_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t18_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G)))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t19_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k7_xcmplx_0(F,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t20_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k7_xcmplx_0(G,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t21_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k6_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k21_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t22_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k6_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k21_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t23_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k6_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k22_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t24_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k6_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k22_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t29_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ~ ( B = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
                  & v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) )).

fof(t30_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
       => k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) ) ) )).

fof(t31_jgraph_3,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
      & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
      & A = k1_jgraph_3
      & v5_pre_topc(A,k15_euclid(np__2),k15_euclid(np__2)) ) )).

fof(t32_jgraph_3,axiom,(
    v2_funct_1(k1_jgraph_3) )).

fof(t38_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( A = k16_euclid(np__2)
         => k1_funct_1(k2_funct_1(k1_jgraph_3),A) = k16_euclid(np__2) )
        & ~ ( ( ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                & r1_xreal_0(k1_real_1(k21_euclid(A)),k22_euclid(A)) )
              | ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                & r1_xreal_0(k22_euclid(A),k1_real_1(k21_euclid(A))) ) )
            & A != k16_euclid(np__2)
            & k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) )
        & ~ ( ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                & r1_xreal_0(k1_real_1(k21_euclid(A)),k22_euclid(A)) )
            & ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                & r1_xreal_0(k22_euclid(A),k1_real_1(k21_euclid(A))) )
            & A != k16_euclid(np__2)
            & k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) ) ) ) )).

fof(t39_jgraph_3,axiom,
    ( v1_funct_1(k2_funct_1(k1_jgraph_3))
    & v1_funct_2(k2_funct_1(k1_jgraph_3),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
    & m2_relset_1(k2_funct_1(k1_jgraph_3),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )).

fof(t40_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( A != k16_euclid(np__2)
       => ( ( ( ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                & r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
              | ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                & r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) ) )
           => k1_funct_1(k2_funct_1(k1_jgraph_3),A) = k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(A),k22_euclid(A))))))) )
          & ~ ( ~ ( r1_xreal_0(k21_euclid(A),k22_euclid(A))
                  & r1_xreal_0(k1_real_1(k22_euclid(A)),k21_euclid(A)) )
              & ~ ( r1_xreal_0(k22_euclid(A),k21_euclid(A))
                  & r1_xreal_0(k21_euclid(A),k1_real_1(k22_euclid(A))) )
              & k1_funct_1(k2_funct_1(k1_jgraph_3),A) != k23_euclid(k4_real_1(k21_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A)))))),k4_real_1(k22_euclid(A),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(A),k21_euclid(A))))))) ) ) ) ) )).

fof(t41_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(F,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t42_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & v5_pre_topc(C,A,k3_topmetr)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != np__0 )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                          & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,E) = G )
                                       => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(G,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(k7_xcmplx_0(F,G))))) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t43_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k4_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k21_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t44_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k4_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k22_euclid(C),k21_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k21_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t45_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k4_real_1(k22_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k22_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t46_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                   => k1_funct_1(B,C) = k4_real_1(k21_euclid(C),k9_square_1(k3_real_1(np__1,k7_square_1(k6_real_1(k21_euclid(C),k22_euclid(C)))))) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                      & k22_euclid(C) = np__0 ) ) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t51_jgraph_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ~ ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ~ ( B = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
                  & v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) )).

fof(t52_jgraph_3,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
      & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
      & A = k2_funct_1(k1_jgraph_3)
      & v5_pre_topc(A,k15_euclid(np__2),k15_euclid(np__2)) ) )).

fof(t53_jgraph_3,axiom,(
    $true )).

fof(t54_jgraph_3,axiom,
    ( v1_funct_1(k1_jgraph_3)
    & v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
    & m2_relset_1(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
    & k1_pscomp_1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3) = u1_struct_0(k15_euclid(np__2))
    & ! [A] :
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
          & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
       => ( A = k1_jgraph_3
         => v3_tops_2(A,k15_euclid(np__2),k15_euclid(np__2)) ) ) )).

fof(dt_k1_jgraph_3,axiom,
    ( v1_funct_1(k1_jgraph_3)
    & v1_funct_2(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
    & m2_relset_1(k1_jgraph_3,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )).

fof(t25_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
             => ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
                  & B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & A = a_0_0_jgraph_3 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t26_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
             => ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,A)
                  & B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & A = a_0_1_jgraph_3 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t27_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,B)
                  & A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & B = a_0_0_jgraph_3 )
               => ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
                  & v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) )).

fof(t28_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ( ( C = k2_partfun1(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),k1_jgraph_3,B)
                  & A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & B = a_0_1_jgraph_3 )
               => ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
                  & v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) )).

fof(t33_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_2_jgraph_3
              & B = a_0_3_jgraph_3 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,A) = B ) ) ) )).

fof(t34_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ( ( B = a_0_2_jgraph_3
                  & v3_tops_2(C,k3_pre_topc(k15_euclid(np__2),B),k3_pre_topc(k15_euclid(np__2),A)) )
               => v1_topreal2(A) ) ) ) ) )).

fof(t35_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( A = a_0_2_jgraph_3
       => ( v1_topreal2(A)
          & v6_compts_1(A,k15_euclid(np__2)) ) ) ) )).

fof(t36_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( A = a_0_3_jgraph_3
       => v1_topreal2(A) ) ) )).

fof(t37_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( A = a_0_4_jgraph_3
              & B = a_0_5_jgraph_3 )
           => r1_tarski(k5_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k1_jgraph_3,B),A) ) ) ) )).

fof(t47_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
             => ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
                  & B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & A = a_0_0_jgraph_3 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t48_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))) )
             => ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),A)
                  & B = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & A = a_0_1_jgraph_3 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t49_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),B)
                  & A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & B = a_0_0_jgraph_3 )
               => ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
                  & v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) )).

fof(t50_jgraph_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
                & m2_relset_1(C,u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B)),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
             => ( ( C = k7_relat_1(k2_funct_1(k1_jgraph_3),B)
                  & A = k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))
                  & B = a_0_1_jgraph_3 )
               => ( v5_pre_topc(C,k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B),k3_pre_topc(k15_euclid(np__2),A))
                  & v4_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) ) )).

fof(t55_jgraph_3,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_3
                                          & D = a_0_6_jgraph_3
                                          & E = a_0_7_jgraph_3
                                          & F = a_0_8_jgraph_3
                                          & G = a_0_9_jgraph_3
                                          & 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(s1_jgraph_3,axiom,(
    r1_tarski(a_0_10_jgraph_3,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) )).

fof(s2_jgraph_3,axiom,(
    a_0_11_jgraph_3 = k3_xboole_0(a_0_12_jgraph_3,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) )).

fof(fraenkel_a_0_0_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ( ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
              & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) )
            | ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
              & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) )
          & B != k16_euclid(np__2) ) ) )).

fof(fraenkel_a_0_1_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ( ( r1_xreal_0(k21_euclid(B),k22_euclid(B))
              & r1_xreal_0(k1_real_1(k22_euclid(B)),k21_euclid(B)) )
            | ( r1_xreal_0(k22_euclid(B),k21_euclid(B))
              & r1_xreal_0(k21_euclid(B),k1_real_1(k22_euclid(B))) ) )
          & B != k16_euclid(np__2) ) ) )).

fof(fraenkel_a_0_2_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ ( ~ ( k1_real_1(np__1) = k21_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k21_euclid(B) = np__1
                  & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(B),np__1) )
              & ~ ( k1_real_1(np__1) = k22_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) )
              & ~ ( np__1 = k22_euclid(B)
                  & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(B),np__1) ) ) ) ) )).

fof(fraenkel_a_0_3_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & k5_toprns_1(np__2,B) = np__1 ) ) )).

fof(fraenkel_a_0_4_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k1_real_1(np__1),k21_euclid(B))
          & r1_xreal_0(k21_euclid(B),np__1)
          & r1_xreal_0(k1_real_1(np__1),k22_euclid(B))
          & r1_xreal_0(k22_euclid(B),np__1) ) ) )).

fof(fraenkel_a_0_5_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_jgraph_3)
    <=> ? [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_6_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_jgraph_3)
    <=> ? [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_7_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_7_jgraph_3)
    <=> ? [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_8_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_8_jgraph_3)
    <=> ? [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_9_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_9_jgraph_3)
    <=> ? [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_10_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_10_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & p1_s1_jgraph_3(B)
          & B != k16_euclid(np__2) ) ) )).

fof(fraenkel_a_0_11_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_11_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & p1_s2_jgraph_3(B)
          & B != k16_euclid(np__2) ) ) )).

fof(fraenkel_a_0_12_jgraph_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_12_jgraph_3)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & p1_s2_jgraph_3(B) ) ) )).
%------------------------------------------------------------------------------