SET007 Axioms: SET007+563.ax


%------------------------------------------------------------------------------
% File     : SET007+563 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Graph Theoretical Properties of Arcs in the Plane
% Version  : [Urb08] axioms.
% English  : Graph Theoretical Properties of Arcs in the Plane and
%            Fashoda Meet Theorem

% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (  18 unit)
%            Number of atoms       :  500 (  75 equality)
%            Maximal formula depth :   38 (   8 average)
%            Number of connectives :  495 (  72 ~  ;  13  |; 207  &)
%                                         (   5 <=>; 198 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   49 (   1 propositional; 0-4 arity)
%            Number of functors    :   58 (   7 constant; 0-4 arity)
%            Number of variables   :  177 (   0 singleton; 172 !;   5 ?)
%            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_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => v2_graph_1(k1_jgraph_1(A)) ) )).

fof(t1_jgraph_1,axiom,(
    $true )).

fof(t2_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => r1_xreal_0(k9_square_1(k3_real_1(k7_square_1(A),k7_square_1(B))),k3_real_1(k18_complex1(A),k18_complex1(B))) ) ) )).

fof(t3_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( r1_xreal_0(k18_complex1(A),k9_square_1(k3_real_1(k7_square_1(A),k7_square_1(B))))
            & r1_xreal_0(k18_complex1(B),k9_square_1(k3_real_1(k7_square_1(A),k7_square_1(B)))) ) ) ) )).

fof(t4_jgraph_1,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ( ( v1_graph_4(B,A)
                  & r3_graph_4(A,C,B) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(np__1,D)
                            & r1_xreal_0(E,k3_finseq_1(C))
                            & k1_funct_1(C,D) = k1_funct_1(C,E) )
                         => ( r1_xreal_0(E,D)
                            | ( D = np__1
                              & E = k3_finseq_1(C) ) ) ) ) ) ) ) ) ) )).

fof(d1_jgraph_1,axiom,(
    ! [A] : k1_jgraph_1(A) = g1_graph_1(A,k2_zfmisc_1(A,A),k9_funct_3(A,A),k10_funct_3(A,A)) )).

fof(t5_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v2_graph_1(k1_jgraph_1(A))
        & l1_graph_1(k1_jgraph_1(A)) ) ) )).

fof(t6_jgraph_1,axiom,(
    ! [A] : u1_graph_1(k1_jgraph_1(A)) = A )).

fof(d2_jgraph_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( B = k2_jgraph_1(A)
          <=> ( k3_finseq_1(B) = k5_binarith(k3_finseq_1(A),np__1)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,C)
                   => ( r1_xreal_0(k3_finseq_1(A),C)
                      | k1_funct_1(B,C) = k4_tarski(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,np__1))) ) ) ) ) ) ) ) )).

fof(t7_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => m2_finseq_1(B,u1_graph_1(k1_jgraph_1(A))) ) ) )).

fof(t8_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => m2_finseq_1(k2_jgraph_1(B),u2_graph_1(k1_jgraph_1(A))) ) ) )).

fof(t9_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,k3_finseq_1(k3_jgraph_1(A,C))) )
               => r2_hidden(k1_funct_1(k3_jgraph_1(A,C),B),u2_graph_1(k1_jgraph_1(A))) ) ) ) ) )).

fof(t10_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v8_graph_1(k3_jgraph_1(A,B),k1_jgraph_1(A))
            & m2_graph_1(k3_jgraph_1(A,B),k1_jgraph_1(A)) ) ) ) )).

fof(t11_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(k1_jgraph_1(A)))
             => ( ( r1_xreal_0(np__1,k3_finseq_1(B))
                  & B = C )
               => r3_graph_4(k1_jgraph_1(A),C,k4_jgraph_1(A,B)) ) ) ) ) )).

fof(d3_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( r1_jgraph_1(A,B,C)
              <=> ( k1_funct_1(B,np__1) = k1_funct_1(C,np__1)
                  & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(C,k3_finseq_1(C))
                  & ? [D] :
                      ( m1_graph_2(D,u2_graph_1(k1_jgraph_1(A)),k4_jgraph_1(A,B))
                      & ? [E] :
                          ( m1_graph_2(E,A,B)
                          & ? [F] :
                              ( v8_graph_1(F,k1_jgraph_1(A))
                              & v3_graph_2(F,k1_jgraph_1(A))
                              & m2_graph_1(F,k1_jgraph_1(A))
                              & ? [G] :
                                  ( m2_finseq_1(G,u1_graph_1(k1_jgraph_1(A)))
                                  & k15_finseq_1(D) = F
                                  & k15_finseq_1(E) = C
                                  & G = C
                                  & r3_graph_4(k1_jgraph_1(A),G,F) ) ) ) ) ) ) ) ) ) )).

fof(t12_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( r1_jgraph_1(A,B,C)
               => ( r1_xreal_0(np__1,k3_finseq_1(C))
                  & r1_xreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) ) )).

fof(t13_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ~ ( r1_xreal_0(np__1,k3_finseq_1(B))
              & ! [C] :
                  ( m2_finseq_1(C,A)
                 => ~ r1_jgraph_1(A,B,C) ) ) ) ) )).

fof(t14_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( r1_jgraph_1(A,B,C)
               => r1_tarski(k2_relat_1(k4_jgraph_1(A,C)),k2_relat_1(k4_jgraph_1(A,B))) ) ) ) ) )).

fof(t15_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ( r1_jgraph_1(A,B,C)
               => ( k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B))
                  | ( v2_funct_1(C)
                    & r1_tarski(k2_relat_1(k4_jgraph_1(A,C)),k2_relat_1(k4_jgraph_1(A,B)))
                    & k1_funct_1(C,np__1) = k1_funct_1(B,np__1)
                    & k1_funct_1(C,k3_finseq_1(C)) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) ) ) ) )).

fof(d4_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(A)))
         => ( v1_jgraph_1(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( ~ r1_xboole_0(k4_topreal1(A,B,C),k4_topreal1(A,B,D))
                        & ~ ( k5_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal1(A,B,C),k4_topreal1(A,B,D)) = k1_tarski(k1_funct_1(B,C))
                            & ( k1_funct_1(B,C) = k1_funct_1(B,D)
                              | k1_funct_1(B,C) = k1_funct_1(B,k1_nat_1(D,np__1)) ) )
                        & ~ ( k5_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal1(A,B,C),k4_topreal1(A,B,D)) = k1_tarski(k1_funct_1(B,k1_nat_1(C,np__1)))
                            & ( k1_funct_1(B,k1_nat_1(C,np__1)) = k1_funct_1(B,D)
                              | k1_funct_1(B,k1_nat_1(C,np__1)) = k1_funct_1(B,k1_nat_1(D,np__1)) ) )
                        & k4_topreal1(A,B,C) != k4_topreal1(A,B,D) ) ) ) ) ) ) )).

fof(t16_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v3_topreal1(A)
       => v1_goboard5(A) ) ) )).

fof(t17_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v1_goboard5(A)
          & r1_xboole_0(k4_topreal1(np__2,A,np__1),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1))) )
       => v3_topreal1(A) ) ) )).

fof(t18_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v1_jgraph_1(A,np__2)
          & v1_graph_4(k4_jgraph_1(u1_struct_0(k15_euclid(np__2)),A),k1_jgraph_1(u1_struct_0(k15_euclid(np__2)))) )
       => v1_goboard5(A) ) ) )).

fof(t19_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v1_jgraph_1(A,np__2)
          & v1_graph_4(k4_jgraph_1(u1_struct_0(k15_euclid(np__2)),A),k1_jgraph_1(u1_struct_0(k15_euclid(np__2)))) )
       => ( k1_funct_1(A,np__1) = k1_funct_1(A,k3_finseq_1(A))
          | v3_topreal1(A) ) ) ) )).

fof(t20_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ~ ( ? [E] :
                          ( E != C
                          & r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,B,C),k3_topreal1(A,C,D))) )
                      & ~ r2_hidden(B,k3_topreal1(A,C,D))
                      & ~ r2_hidden(D,k3_topreal1(A,B,C)) ) ) ) ) ) )).

fof(t21_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v3_topreal1(A)
          & r1_tarski(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,np__1),k4_topreal1(np__2,A,k1_nat_1(np__1,np__1))),k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(np__1,np__1))))
          & r1_tarski(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__2)),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1))),k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1)))) )
       => v2_topreal1(A) ) ) )).

fof(t22_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v1_graph_4(k4_jgraph_1(A,B),k1_jgraph_1(A))
           => ( k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B))
              | ( v2_funct_1(B)
                & k3_finseq_1(B) != np__1 ) ) ) ) ) )).

fof(t23_jgraph_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v2_funct_1(B)
           => ( r1_xreal_0(k3_finseq_1(B),np__1)
              | ( v1_graph_4(k4_jgraph_1(A,B),k1_jgraph_1(A))
                & k1_funct_1(B,np__1) != k1_funct_1(B,k3_finseq_1(B)) ) ) ) ) ) )).

fof(t24_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v1_jgraph_1(A,np__2)
          & v1_graph_4(k4_jgraph_1(u1_struct_0(k15_euclid(np__2)),A),k1_jgraph_1(u1_struct_0(k15_euclid(np__2)))) )
       => ( k1_funct_1(A,np__1) = k1_funct_1(A,k3_finseq_1(A))
          | v2_topreal1(A) ) ) ) )).

fof(t25_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_jgraph_1(u1_struct_0(k15_euclid(np__2)),A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1))
                          & k1_funct_1(A,D) = k1_funct_1(B,C)
                          & k1_funct_1(A,k1_nat_1(D,np__1)) = k1_funct_1(B,k1_nat_1(C,np__1)) ) ) ) ) ) ) )).

fof(t26_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_jgraph_1(u1_struct_0(k15_euclid(np__2)),A,B)
           => r1_tarski(k2_relat_1(B),k2_relat_1(A)) ) ) ) )).

fof(t27_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_jgraph_1(u1_struct_0(k15_euclid(np__2)),A,B)
           => r1_tarski(k5_topreal1(np__2,B),k5_topreal1(np__2,A)) ) ) ) )).

fof(t28_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v1_topreal1(A)
              & r1_jgraph_1(u1_struct_0(k15_euclid(np__2)),A,B) )
           => v1_topreal1(B) ) ) ) )).

fof(t29_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ ( v1_topreal1(A)
          & r1_xreal_0(np__2,k3_finseq_1(A))
          & k1_funct_1(A,np__1) != k1_funct_1(A,k3_finseq_1(A))
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_xreal_0(np__2,k3_finseq_1(B))
                  & v1_topreal1(B)
                  & v2_funct_1(B)
                  & r1_tarski(k5_topreal1(np__2,B),k5_topreal1(np__2,A))
                  & k1_funct_1(A,np__1) = k1_funct_1(B,np__1)
                  & k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,k3_finseq_1(B))
                  & r1_tarski(k2_relat_1(B),k2_relat_1(A)) ) ) ) ) )).

fof(t30_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( v1_topreal1(A)
              & v1_topreal1(B)
              & r1_xreal_0(np__2,k3_finseq_1(A))
              & r1_xreal_0(np__2,k3_finseq_1(B))
              & k1_funct_1(A,np__1) != k1_funct_1(A,k3_finseq_1(A))
              & k1_funct_1(B,np__1) != k1_funct_1(B,k3_finseq_1(B))
              & r1_goboard4(k2_goboard1(A),k1_goboard1(k2_goboard1(A),np__1),k1_goboard1(k2_goboard1(A),k3_finseq_1(A)))
              & r1_goboard4(k2_goboard1(B),k1_goboard1(k2_goboard1(A),np__1),k1_goboard1(k2_goboard1(A),k3_finseq_1(A)))
              & r1_goboard4(k3_goboard1(A),k1_goboard1(k3_goboard1(B),np__1),k1_goboard1(k3_goboard1(B),k3_finseq_1(B)))
              & r1_goboard4(k3_goboard1(B),k1_goboard1(k3_goboard1(B),np__1),k1_goboard1(k3_goboard1(B),k3_finseq_1(B)))
              & r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,B)) ) ) ) )).

fof(t31_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( r1_xreal_0(A,C)
                      & r1_xreal_0(C,B)
                      & r1_xreal_0(A,D)
                      & r1_xreal_0(D,B) )
                   => r1_xreal_0(k18_complex1(k5_real_1(C,D)),k5_real_1(B,A)) ) ) ) ) ) )).

fof(d5_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( C = k5_toprns_1(A,B)
              <=> ! [D] :
                    ( m2_finseq_2(D,k1_numbers,k1_euclid(A))
                   => ( B = D
                     => C = k12_euclid(D) ) ) ) ) ) ) )).

fof(t32_jgraph_1,axiom,(
    $true )).

fof(t33_jgraph_1,axiom,(
    $true )).

fof(t34_jgraph_1,axiom,(
    $true )).

fof(t35_jgraph_1,axiom,(
    $true )).

fof(t36_jgraph_1,axiom,(
    $true )).

fof(t37_jgraph_1,axiom,(
    $true )).

fof(t38_jgraph_1,axiom,(
    $true )).

fof(t39_jgraph_1,axiom,(
    $true )).

fof(t40_jgraph_1,axiom,(
    $true )).

fof(t41_jgraph_1,axiom,(
    $true )).

fof(t42_jgraph_1,axiom,(
    $true )).

fof(t43_jgraph_1,axiom,(
    $true )).

fof(t44_jgraph_1,axiom,(
    $true )).

fof(t45_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                     => ( ( D = B
                          & E = C )
                       => k5_toprns_1(A,k20_euclid(A,B,C)) = k4_metric_1(k14_euclid(A),D,E) ) ) ) ) ) ) )).

fof(t46_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => 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(t47_jgraph_1,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)))) ) )).

fof(t48_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => r1_xreal_0(k5_toprns_1(np__2,A),k3_real_1(k18_complex1(k21_euclid(A)),k18_complex1(k22_euclid(A)))) ) )).

fof(t49_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,A,B)),k3_real_1(k18_complex1(k5_real_1(k21_euclid(A),k21_euclid(B))),k18_complex1(k5_real_1(k22_euclid(A),k22_euclid(B))))) ) ) )).

fof(t50_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(k18_complex1(k21_euclid(A)),k5_toprns_1(np__2,A))
        & r1_xreal_0(k18_complex1(k22_euclid(A)),k5_toprns_1(np__2,A)) ) ) )).

fof(t51_jgraph_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_xreal_0(k18_complex1(k5_real_1(k21_euclid(A),k21_euclid(B))),k5_toprns_1(np__2,k20_euclid(np__2,A,B)))
            & r1_xreal_0(k18_complex1(k5_real_1(k22_euclid(A),k22_euclid(B))),k5_toprns_1(np__2,k20_euclid(np__2,A,B))) ) ) ) )).

fof(t52_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ~ ( r2_hidden(B,k3_topreal1(A,C,D))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( r1_xreal_0(np__0,E)
                              & r1_xreal_0(E,np__1)
                              & B = k17_euclid(A,k18_euclid(k5_real_1(np__1,E),A,C),k18_euclid(E,A,D)) ) ) ) ) ) ) ) )).

fof(t53_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(B,k3_topreal1(A,C,D))
                   => ( r1_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C)),k5_toprns_1(A,k20_euclid(A,C,D)))
                      & r1_xreal_0(k5_toprns_1(A,k20_euclid(A,B,D)),k5_toprns_1(A,k20_euclid(A,C,D))) ) ) ) ) ) ) )).

fof(t54_jgraph_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
             => ( ( v6_compts_1(B,k5_pcomps_1(A))
                  & v6_compts_1(C,k5_pcomps_1(A)) )
               => ( B = k1_xboole_0
                  | C = k1_xboole_0
                  | r1_xreal_0(np__0,k9_weierstr(A,B,C)) ) ) ) ) ) )).

fof(t55_jgraph_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
             => ( ( v6_compts_1(B,k5_pcomps_1(A))
                  & v6_compts_1(C,k5_pcomps_1(A)) )
               => ( B = k1_xboole_0
                  | C = k1_xboole_0
                  | ( r1_xboole_0(B,C)
                  <=> ~ r1_xreal_0(k9_weierstr(A,B,C),np__0) ) ) ) ) ) ) )).

fof(t56_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( r1_xreal_0(np__1,k3_finseq_1(A))
                      & r1_goboard4(k2_goboard1(A),k1_goboard1(k2_goboard1(A),np__1),k1_goboard1(k2_goboard1(A),k3_finseq_1(A)))
                      & r1_goboard4(k3_goboard1(A),C,D)
                      & ~ r1_xreal_0(B,np__0)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                              & r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1))))) ) )
                      & ! [E] :
                          ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( v1_topreal1(E)
                              & k1_funct_1(E,np__1) = k1_funct_1(A,np__1)
                              & k1_funct_1(E,k3_finseq_1(E)) = k1_funct_1(A,k3_finseq_1(A))
                              & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(E))
                              & r1_goboard4(k2_goboard1(E),k1_goboard1(k2_goboard1(A),np__1),k1_goboard1(k2_goboard1(A),k3_finseq_1(A)))
                              & r1_goboard4(k3_goboard1(E),C,D)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(F,k4_finseq_1(E))
                                      & ! [G] :
                                          ( m2_subset_1(G,k1_numbers,k5_numbers)
                                         => ~ ( r2_hidden(G,k4_finseq_1(A))
                                              & ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,F),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,G)))) ) ) ) )
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(np__1,F)
                                      & r1_xreal_0(k1_nat_1(F,np__1),k3_finseq_1(E))
                                      & r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,F),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(F,np__1))))) ) ) ) ) ) ) ) ) ) )).

fof(t57_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( r1_xreal_0(np__1,k3_finseq_1(A))
                      & r1_goboard4(k3_goboard1(A),k1_goboard1(k3_goboard1(A),np__1),k1_goboard1(k3_goboard1(A),k3_finseq_1(A)))
                      & r1_goboard4(k2_goboard1(A),C,D)
                      & ~ r1_xreal_0(B,np__0)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                              & r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1))))) ) )
                      & ! [E] :
                          ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( v1_topreal1(E)
                              & k1_funct_1(E,np__1) = k1_funct_1(A,np__1)
                              & k1_funct_1(E,k3_finseq_1(E)) = k1_funct_1(A,k3_finseq_1(A))
                              & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(E))
                              & r1_goboard4(k3_goboard1(E),k1_goboard1(k3_goboard1(A),np__1),k1_goboard1(k3_goboard1(A),k3_finseq_1(A)))
                              & r1_goboard4(k2_goboard1(E),C,D)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(F,k4_finseq_1(E))
                                      & ! [G] :
                                          ( m2_subset_1(G,k1_numbers,k5_numbers)
                                         => ~ ( r2_hidden(G,k4_finseq_1(A))
                                              & ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,F),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,G)))) ) ) ) )
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r1_xreal_0(np__1,F)
                                      & r1_xreal_0(k1_nat_1(F,np__1),k3_finseq_1(E))
                                      & r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,F),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(F,np__1))))) ) ) ) ) ) ) ) ) ) )).

fof(t58_jgraph_1,axiom,(
    $true )).

fof(t59_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__1,k3_finseq_1(A))
       => ( k3_finseq_1(k2_goboard1(A)) = k3_finseq_1(A)
          & k1_goboard1(k2_goboard1(A),np__1) = k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1))
          & k1_goboard1(k2_goboard1(A),k3_finseq_1(A)) = k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) ) ) ) )).

fof(t60_jgraph_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__1,k3_finseq_1(A))
       => ( k3_finseq_1(k3_goboard1(A)) = k3_finseq_1(A)
          & k1_goboard1(k3_goboard1(A),np__1) = k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1))
          & k1_goboard1(k3_goboard1(A),k3_finseq_1(A)) = k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) ) ) ) )).

fof(t61_jgraph_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(A,k4_finseq_1(B))
           => ( k1_goboard1(k2_goboard1(B),A) = k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A))
              & k1_goboard1(k3_goboard1(B),A) = k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) )).

fof(t62_jgraph_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r1_topreal1(k15_euclid(np__2),C,D,A)
                              & r1_topreal1(k15_euclid(np__2),E,F,B)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(G,A)
                                   => ( r1_xreal_0(k21_euclid(C),k21_euclid(G))
                                      & r1_xreal_0(k21_euclid(G),k21_euclid(D)) ) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(G,B)
                                   => ( r1_xreal_0(k21_euclid(C),k21_euclid(G))
                                      & r1_xreal_0(k21_euclid(G),k21_euclid(D)) ) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(G,A)
                                   => ( r1_xreal_0(k22_euclid(E),k22_euclid(G))
                                      & r1_xreal_0(k22_euclid(G),k22_euclid(F)) ) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k15_euclid(np__2)))
                                 => ( r2_hidden(G,B)
                                   => ( r1_xreal_0(k22_euclid(E),k22_euclid(G))
                                      & r1_xreal_0(k22_euclid(G),k22_euclid(F)) ) ) )
                              & r2_subset_1(A,B) ) ) ) ) ) ) ) )).

fof(t63_jgraph_1,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)) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
                     => ( ( C = E
                          & v5_pre_topc(C,A,B) )
                       => v5_pre_topc(E,A,k3_pre_topc(B,D)) ) ) ) ) ) ) )).

fof(t64_jgraph_1,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)) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ~ ( v2_compts_1(A)
                      & v3_compts_1(B)
                      & v5_pre_topc(C,A,B)
                      & v2_funct_1(C)
                      & D = k1_pscomp_1(u1_struct_0(A),u1_struct_0(B),C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D)))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) )
                         => ~ ( C = E
                              & v3_tops_2(E,A,k3_pre_topc(B,D)) ) ) ) ) ) ) ) )).

fof(t65_jgraph_1,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
                                      & 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
                                      & ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(k5_topmetr))
                                         => ( r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)))
                                            & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),A,I)),D)
                                            & r1_xreal_0(C,k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)))
                                            & r1_xreal_0(k21_euclid(k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),B,I)),D)
                                            & r1_xreal_0(E,k22_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)),F)
                                            & r1_xreal_0(E,k22_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)),F) ) )
                                      & 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_1,axiom,(
    ! [A] : l1_graph_1(k1_jgraph_1(A)) )).

fof(dt_k2_jgraph_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k2_jgraph_1(A))
        & v1_funct_1(k2_jgraph_1(A))
        & v1_finseq_1(k2_jgraph_1(A)) ) ) )).

fof(dt_k3_jgraph_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => m2_finseq_1(k3_jgraph_1(A,B),u2_graph_1(k1_jgraph_1(A))) ) )).

fof(redefinition_k3_jgraph_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => k3_jgraph_1(A,B) = k2_jgraph_1(B) ) )).

fof(dt_k4_jgraph_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => ( v8_graph_1(k4_jgraph_1(A,B),k1_jgraph_1(A))
        & m2_graph_1(k4_jgraph_1(A,B),k1_jgraph_1(A)) ) ) )).

fof(redefinition_k4_jgraph_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => k4_jgraph_1(A,B) = k2_jgraph_1(B) ) )).
%------------------------------------------------------------------------------