SET007 Axioms: SET007+692.ax


%------------------------------------------------------------------------------
% File     : SET007+692 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Outside Fashoda Meet Theorem
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   5 unit)
%            Number of atoms       :  777 ( 140 equality)
%            Maximal formula depth :   47 (  11 average)
%            Number of connectives :  827 ( 132 ~  ;   7  |; 416  &)
%                                         (  19 <=>; 253 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   1 propositional; 0-3 arity)
%            Number of functors    :   71 (  26 constant; 0-6 arity)
%            Number of variables   :  252 (   0 singleton; 235 !;  17 ?)
%            Maximal term depth    :    6 (   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_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( v1_relat_1(k2_jgraph_2(A,B,C,D))
        & v1_funct_1(k2_jgraph_2(A,B,C,D))
        & v1_funct_2(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
        & v5_pre_topc(k2_jgraph_2(A,B,C,D),k15_euclid(np__2),k15_euclid(np__2)) ) ) )).

fof(t1_jgraph_2,axiom,(
    $true )).

fof(t2_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(A,k5_square_1(A)) ) ) )).

fof(t3_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(A,k1_real_1(np__1))
       => r1_xreal_0(k4_xcmplx_0(A),k5_square_1(A)) ) ) )).

fof(t4_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(k1_real_1(np__1),A)
          & r1_xreal_0(k5_square_1(A),k4_xcmplx_0(A)) ) ) )).

fof(t5_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k5_square_1(B),k5_square_1(A))
              & r1_xreal_0(np__0,A) )
           => ( r1_xreal_0(k4_xcmplx_0(A),B)
              & r1_xreal_0(B,A) ) ) ) ) )).

fof(t6_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(np__0,A)
           => ( r1_xreal_0(k5_square_1(A),k5_square_1(B))
              | ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
                & ~ r1_xreal_0(A,B) ) ) ) ) ) )).

fof(t7_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k4_xcmplx_0(A),B)
              & r1_xreal_0(B,A) )
           => r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) )).

fof(t8_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
              & ~ r1_xreal_0(A,B)
              & r1_xreal_0(k5_square_1(A),k5_square_1(B)) ) ) ) )).

fof(t9_jgraph_2,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] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(B))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
                         => ! [G] :
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D)))
                             => ! [H] :
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D)))
                                 => ~ ( m1_pre_topc(A,D)
                                      & m1_pre_topc(C,D)
                                      & G = k2_pre_topc(A)
                                      & H = k2_pre_topc(C)
                                      & k2_xboole_0(k2_pre_topc(A),k2_pre_topc(C)) = k2_pre_topc(D)
                                      & v4_pre_topc(G,D)
                                      & v4_pre_topc(H,D)
                                      & v5_pre_topc(E,A,B)
                                      & v5_pre_topc(F,C,B)
                                      & ! [I] :
                                          ( r2_hidden(I,k3_xboole_0(k2_pre_topc(A),k2_pre_topc(C)))
                                         => k1_funct_1(E,I) = k1_funct_1(F,I) )
                                      & ! [I] :
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,u1_struct_0(D),u1_struct_0(B))
                                            & m2_relset_1(I,u1_struct_0(D),u1_struct_0(B)) )
                                         => ~ ( I = k1_funct_4(E,F)
                                              & v5_pre_topc(I,D,B) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t11_jgraph_2,axiom,
    ( k21_euclid(k16_euclid(np__2)) = np__0
    & k22_euclid(k16_euclid(np__2)) = np__0 )).

fof(t12_jgraph_2,axiom,(
    k5_jordan2c(np__2) = k10_finseq_1(np__1,np__1) )).

fof(t13_jgraph_2,axiom,
    ( k21_euclid(k5_jordan2c(np__2)) = np__1
    & k22_euclid(k5_jordan2c(np__2)) = np__1 )).

fof(t14_jgraph_2,axiom,
    ( k1_wellfnd1(k15_euclid(np__2),k1_numbers,k16_pscomp_1) = u1_struct_0(k15_euclid(np__2))
    & k1_wellfnd1(k15_euclid(np__2),k1_numbers,k16_pscomp_1) = k1_euclid(np__2) )).

fof(t15_jgraph_2,axiom,
    ( k1_wellfnd1(k15_euclid(np__2),k1_numbers,k17_pscomp_1) = u1_struct_0(k15_euclid(np__2))
    & k1_wellfnd1(k15_euclid(np__2),k1_numbers,k17_pscomp_1) = k1_euclid(np__2) )).

fof(t16_jgraph_2,axiom,(
    $true )).

fof(t17_jgraph_2,axiom,(
    $true )).

fof(t18_jgraph_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => A = k23_euclid(k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) )).

fof(t19_jgraph_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( A = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
       => ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0
          & k4_xboole_0(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0 ) ) ) )).

fof(t20_jgraph_2,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] :
              ( ( 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)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                       => ~ ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),E)
                            & v3_pre_topc(E,B)
                            & ! [F] :
                                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                               => ~ ( r2_hidden(D,F)
                                    & v3_pre_topc(F,A)
                                    & r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ) ) )).

fof(t22_jgraph_2,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] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
                     => ! [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)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E)))
                                & m2_relset_1(G,u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E))) )
                             => ~ ( v5_pre_topc(F,A,B)
                                  & v5_pre_topc(G,k3_pre_topc(B,D),k3_pre_topc(C,E))
                                  & r1_tarski(k1_pscomp_1(u1_struct_0(A),u1_struct_0(B),F),D)
                                  & D != k1_xboole_0
                                  & E != k1_xboole_0
                                  & ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(A),u1_struct_0(C))
                                        & m2_relset_1(H,u1_struct_0(A),u1_struct_0(C)) )
                                     => ~ ( v5_pre_topc(H,A,C)
                                          & H = k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(k3_pre_topc(B,D)),u1_struct_0(k3_pre_topc(C,E)),F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_jgraph_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))))
        & m2_relset_1(A,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) )
     => ( A = k1_jgraph_2
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ( B != k16_euclid(np__2)
             => ( ( ( ( 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))) ) )
                 => k1_funct_1(A,B) = k23_euclid(k6_real_1(np__1,k21_euclid(B)),k6_real_1(k6_real_1(k22_euclid(B),k21_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))) )
                    & k1_funct_1(A,B) != k23_euclid(k6_real_1(k6_real_1(k21_euclid(B),k22_euclid(B)),k22_euclid(B)),k6_real_1(np__1,k22_euclid(B))) ) ) ) ) ) ) )).

fof(t23_jgraph_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_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))) )
          & ~ ( 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))) ) ) ) )).

fof(t24_jgraph_2,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(k1_jgraph_2,A) = k23_euclid(k6_real_1(k6_real_1(k21_euclid(A),k22_euclid(A)),k22_euclid(A)),k6_real_1(np__1,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(k1_jgraph_2,A) != k23_euclid(k6_real_1(np__1,k21_euclid(A)),k6_real_1(k6_real_1(k22_euclid(A),k21_euclid(A)),k21_euclid(A))) ) ) ) ) )).

fof(t29_jgraph_2,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] :
                      ( ( 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(F,G) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t30_jgraph_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ? [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))
                 => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) = B )
              & v5_pre_topc(C,A,k3_topmetr) ) ) ) )).

fof(t31_jgraph_2,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] :
                      ( ( 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) = k6_xcmplx_0(F,G) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t32_jgraph_2,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] :
                  ( ( 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) = k3_xcmplx_0(E,E) ) ) )
                      & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).

fof(t33_jgraph_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k3_xcmplx_0(C,F) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t34_jgraph_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( v5_pre_topc(B,A,k3_topmetr)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ~ ( ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,E) = F
                                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,E) = k2_xcmplx_0(F,C) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t35_jgraph_2,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] :
                      ( ( 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,G) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t36_jgraph_2,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))
                 => k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) != np__0 )
              & ! [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) = k7_xcmplx_0(np__1,E) ) ) )
                      & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).

fof(t37_jgraph_2,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,G) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t38_jgraph_2,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(k7_xcmplx_0(F,G),G) ) ) ) )
                          & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).

fof(t39_jgraph_2,axiom,(
    ! [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(k3_pre_topc(k15_euclid(np__2),A)))
               => k1_funct_1(B,C) = k1_funct_1(k16_pscomp_1,C) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t40_jgraph_2,axiom,(
    ! [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(k3_pre_topc(k15_euclid(np__2),A)))
               => k1_funct_1(B,C) = k1_funct_1(k17_pscomp_1,C) )
           => v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr) ) ) ) )).

fof(t41_jgraph_2,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(np__1,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(t42_jgraph_2,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(np__1,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(t43_jgraph_2,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(k6_real_1(k22_euclid(C),k21_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_2,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(k6_real_1(k21_euclid(C),k22_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(t45_jgraph_2,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))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
                    & m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr))
                        & m2_relset_1(E,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k3_topmetr)) )
                     => ( ( v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr)
                          & v5_pre_topc(E,k3_pre_topc(k15_euclid(np__2),A),k3_topmetr)
                          & ! [F] :
                              ( v1_xreal_0(F)
                             => ! [G] :
                                  ( v1_xreal_0(G)
                                 => ! [H] :
                                      ( v1_xreal_0(H)
                                     => ! [I] :
                                          ( v1_xreal_0(I)
                                         => ( ( r2_hidden(k23_euclid(F,G),A)
                                              & H = k1_funct_1(D,k23_euclid(F,G))
                                              & I = k1_funct_1(E,k23_euclid(F,G)) )
                                           => k1_funct_1(C,k23_euclid(F,G)) = k23_euclid(H,I) ) ) ) ) ) )
                       => ( A = k1_xboole_0
                          | B = k1_xboole_0
                          | v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) ) ) ) )).

fof(t50_jgraph_2,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 = k1_jgraph_2
                  & v5_pre_topc(B,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),A)) ) ) ) ) )).

fof(t53_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                        & m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                           => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F) = k23_euclid(k2_xcmplx_0(k3_xcmplx_0(A,k21_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k22_euclid(F)),D)) )
                       => v5_pre_topc(E,k15_euclid(np__2),k15_euclid(np__2)) ) ) ) ) ) ) )).

fof(d2_jgraph_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
                        & m2_relset_1(E,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) )
                     => ( E = k2_jgraph_2(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                           => k8_funct_2(u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)),E,F) = k23_euclid(k2_xcmplx_0(k3_xcmplx_0(A,k21_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k22_euclid(F)),D)) ) ) ) ) ) ) ) )).

fof(t54_jgraph_2,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,np__0)
                      & ~ r1_xreal_0(C,np__0)
                      & ~ v2_funct_1(k2_jgraph_2(A,B,C,D)) ) ) ) ) ) )).

fof(t55_jgraph_2,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] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ! [F] :
                          ( v1_xreal_0(F)
                         => ! [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)
                                      & k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)) = C
                                      & 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,G)))
                                      & r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,G)),F)
                                      & 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
                                      & 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,G)))
                                      & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,G)),D)
                                      & 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)
                                      & ~ r1_xreal_0(D,C)
                                      & ~ r1_xreal_0(F,E)
                                      & ! [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))) ) )
                                      & ! [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)),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(dt_k1_jgraph_2,axiom,
    ( v1_funct_1(k1_jgraph_2)
    & v1_funct_2(k1_jgraph_2,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))))
    & m2_relset_1(k1_jgraph_2,k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)))) )).

fof(dt_k2_jgraph_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( v1_funct_1(k2_jgraph_2(A,B,C,D))
        & v1_funct_2(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(np__2)),u1_struct_0(k15_euclid(np__2))) ) ) )).

fof(t10_jgraph_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( C = B
                   => k9_metric_1(k14_euclid(A),B,D) = a_3_0_jgraph_2(A,C,D) ) ) ) ) ) )).

fof(t21_jgraph_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ~ ( v3_pre_topc(B,k15_euclid(np__2))
              & r2_hidden(A,B)
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & r1_tarski(a_2_0_jgraph_2(A,C),B) ) ) ) ) ) )).

fof(t25_jgraph_2,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))))
         => ( B = a_0_0_jgraph_2
           => r1_tarski(k2_relat_1(k2_partfun1(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,B)),u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B))) ) ) ) )).

fof(t26_jgraph_2,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))))
         => ( B = a_0_1_jgraph_2
           => r1_tarski(k2_relat_1(k2_partfun1(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,B)),u1_struct_0(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),A),B))) ) ) ) )).

fof(t27_jgraph_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ( A = a_0_0_jgraph_2
          & k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) )
       => ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))))
          & ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) )).

fof(t28_jgraph_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ( A = a_0_1_jgraph_2
          & k3_subset_1(u1_struct_0(k15_euclid(np__2)),B) = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2)) )
       => ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),B))))
          & ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) )).

fof(t46_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t47_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
               => v5_pre_topc(C,k3_pre_topc(k15_euclid(np__2),A),k3_pre_topc(k15_euclid(np__2),B)) ) ) ) ) )).

fof(t48_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
               => ( 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(t49_jgraph_2,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(k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k4_xboole_0(u1_struct_0(k15_euclid(np__2)),k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))),k1_jgraph_2,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_2 )
               => ( 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(t51_jgraph_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ~ ( A = k1_struct_0(k15_euclid(np__2),k16_euclid(np__2))
                  & B = a_0_2_jgraph_2
                  & C = a_0_3_jgraph_2
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))))
                        & m2_relset_1(D,u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A))),u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))) )
                     => ~ ( v5_pre_topc(D,k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))
                          & v2_funct_1(D)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                             => ~ ( r2_hidden(E,B)
                                  & E != k16_euclid(np__2)
                                  & r2_hidden(k1_funct_1(D,E),k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)) ) )
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                             => ( ~ r2_hidden(E,k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C))
                               => r2_hidden(k1_funct_1(D,E),B) ) )
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                             => ( r2_hidden(E,C)
                               => k1_funct_1(D,E) = E ) ) ) ) ) ) ) ) )).

fof(t52_jgraph_2,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,u1_struct_0(k5_topmetr))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                     => ~ ( D = np__0
                          & E = 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_2_jgraph_2
                          & k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)) = k1_real_1(np__1)
                          & k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)) = np__1
                          & r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)))
                          & r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,D)),np__1)
                          & r1_xreal_0(k1_real_1(np__1),k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)))
                          & r1_xreal_0(k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,E)),np__1)
                          & k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)) = k1_real_1(np__1)
                          & k22_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)) = np__1
                          & r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)))
                          & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,D)),np__1)
                          & r1_xreal_0(k1_real_1(np__1),k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)))
                          & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,E)),np__1)
                          & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A),C)
                          & r1_xboole_0(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(t56_jgraph_2,axiom,
    ( v4_pre_topc(a_0_4_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_4_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
    & v4_pre_topc(a_0_5_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_5_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t57_jgraph_2,axiom,
    ( v4_pre_topc(a_0_6_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_6_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
    & v4_pre_topc(a_0_7_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_7_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t58_jgraph_2,axiom,
    ( v4_pre_topc(a_0_8_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_8_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
    & v4_pre_topc(a_0_9_jgraph_2,k15_euclid(np__2))
    & m1_subset_1(a_0_9_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(s1_jgraph_2,axiom,(
    m1_subset_1(a_0_10_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(s2_jgraph_2,axiom,
    ( f1_s2_jgraph_2 = a_0_11_jgraph_2
   => k3_subset_1(u1_struct_0(k15_euclid(np__2)),f1_s2_jgraph_2) = a_0_12_jgraph_2 )).

fof(s3_jgraph_2,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)))
             => ( f1_s3_jgraph_2(k20_euclid(np__2,A,B)) = k6_xcmplx_0(f1_s3_jgraph_2(A),f1_s3_jgraph_2(B))
                & f2_s3_jgraph_2(k20_euclid(np__2,A,B)) = k6_xcmplx_0(f2_s3_jgraph_2(A),f2_s3_jgraph_2(B)) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
             => k7_square_1(k5_toprns_1(np__2,k20_euclid(np__2,A,B))) = k2_xcmplx_0(k5_square_1(f1_s3_jgraph_2(k20_euclid(np__2,A,B))),k5_square_1(f2_s3_jgraph_2(k20_euclid(np__2,A,B)))) ) ) )
   => ( v4_pre_topc(a_0_13_jgraph_2,k15_euclid(np__2))
      & m1_subset_1(a_0_13_jgraph_2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(fraenkel_a_3_0_jgraph_2,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_subset_1(C,u1_struct_0(k15_euclid(B)))
        & v1_xreal_0(D) )
     => ( r2_hidden(A,a_3_0_jgraph_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
            & A = E
            & ~ r1_xreal_0(D,k5_toprns_1(B,k20_euclid(B,C,E))) ) ) ) )).

fof(fraenkel_a_2_0_jgraph_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_0_jgraph_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
            & A = D
            & ~ r1_xreal_0(k21_euclid(D),k6_xcmplx_0(k21_euclid(B),C))
            & ~ r1_xreal_0(k2_xcmplx_0(k21_euclid(B),C),k21_euclid(D))
            & ~ r1_xreal_0(k22_euclid(D),k6_xcmplx_0(k22_euclid(B),C))
            & ~ r1_xreal_0(k2_xcmplx_0(k22_euclid(B),C),k22_euclid(D)) ) ) ) )).

fof(fraenkel_a_0_0_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_jgraph_2)
    <=> ? [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_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_jgraph_2)
    <=> ? [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_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ r1_xreal_0(k21_euclid(B),k1_real_1(np__1))
          & ~ r1_xreal_0(np__1,k21_euclid(B))
          & ~ r1_xreal_0(k22_euclid(B),k1_real_1(np__1))
          & ~ r1_xreal_0(np__1,k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_3_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_jgraph_2)
    <=> ? [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_4_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k21_euclid(B)) ) ) )).

fof(fraenkel_a_0_5_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k21_euclid(B),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_6_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_7_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_7_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) )).

fof(fraenkel_a_0_8_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_8_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k1_real_1(k22_euclid(B)),k21_euclid(B)) ) ) )).

fof(fraenkel_a_0_9_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_9_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k21_euclid(B),k1_real_1(k22_euclid(B))) ) ) )).

fof(fraenkel_a_0_10_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_10_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & p1_s1_jgraph_2(B) ) ) )).

fof(fraenkel_a_0_11_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_11_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & p1_s2_jgraph_2(B) ) ) )).

fof(fraenkel_a_0_12_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_12_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & ~ p1_s2_jgraph_2(B) ) ) )).

fof(fraenkel_a_0_13_jgraph_2,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_13_jgraph_2)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(f1_s3_jgraph_2(B),f2_s3_jgraph_2(B)) ) ) )).
%------------------------------------------------------------------------------