SET007 Axioms: SET007+519.ax


%------------------------------------------------------------------------------
% File     : SET007+519 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Euler Circuits and Paths
% 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    : graph_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  113 (   5 unit)
%            Number of atoms       :  855 ( 135 equality)
%            Maximal formula depth :   18 (  10 average)
%            Number of connectives :  814 (  72 ~  ;  23  |; 396  &)
%                                         (  23 <=>; 300 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-4 arity)
%            Number of functors    :   57 (   5 constant; 0-4 arity)
%            Number of variables   :  384 (   0 singleton; 366 !;  18 ?)
%            Maximal term depth    :    5 (   1 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_graph_3,axiom,(
    ! [A,B] :
      ( ( v1_int_1(A)
        & v1_abian(A)
        & v1_int_1(B)
        & v1_abian(B) )
     => ( v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_abian(k6_xcmplx_0(A,B)) ) ) )).

fof(rc1_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] :
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v1_msscyc_1(B,A) ) ) )).

fof(fc2_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => v1_finset_1(k2_graph_3(A,B,C)) ) )).

fof(fc3_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => v1_finset_1(k3_graph_3(A,B,C)) ) )).

fof(fc4_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => v1_finset_1(k4_graph_3(A,B,C)) ) )).

fof(fc5_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & v1_xboole_0(C) )
     => ( v1_xboole_0(k2_graph_3(A,B,C))
        & v1_finset_1(k2_graph_3(A,B,C))
        & v1_membered(k2_graph_3(A,B,C))
        & v2_membered(k2_graph_3(A,B,C))
        & v3_membered(k2_graph_3(A,B,C))
        & v4_membered(k2_graph_3(A,B,C))
        & v5_membered(k2_graph_3(A,B,C)) ) ) )).

fof(fc6_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & v1_xboole_0(C) )
     => ( v1_xboole_0(k3_graph_3(A,B,C))
        & v1_finset_1(k3_graph_3(A,B,C))
        & v1_membered(k3_graph_3(A,B,C))
        & v2_membered(k3_graph_3(A,B,C))
        & v3_membered(k3_graph_3(A,B,C))
        & v4_membered(k3_graph_3(A,B,C))
        & v5_membered(k3_graph_3(A,B,C)) ) ) )).

fof(fc7_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & v1_xboole_0(C) )
     => ( v1_xboole_0(k4_graph_3(A,B,C))
        & v1_finset_1(k4_graph_3(A,B,C))
        & v1_membered(k4_graph_3(A,B,C))
        & v2_membered(k4_graph_3(A,B,C))
        & v3_membered(k4_graph_3(A,B,C))
        & v4_membered(k4_graph_3(A,B,C))
        & v5_membered(k4_graph_3(A,B,C)) ) ) )).

fof(fc8_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => v1_finset_1(k5_graph_3(A,B)) ) )).

fof(fc9_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => v1_finset_1(k6_graph_3(A,B)) ) )).

fof(fc10_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A)) )
     => ( v1_graph_1(k8_graph_3(A,B,C))
        & v2_graph_1(k8_graph_3(A,B,C))
        & v7_graph_1(k8_graph_3(A,B,C)) ) ) )).

fof(fc11_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A)) )
     => ( v1_graph_1(k8_graph_3(A,B,C))
        & v2_graph_1(k8_graph_3(A,B,C))
        & v6_graph_1(k8_graph_3(A,B,C)) ) ) )).

fof(t1_graph_3,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ( ( v1_abian(A)
            <=> v1_abian(B) )
          <=> v1_abian(k6_xcmplx_0(A,B)) ) ) ) )).

fof(t2_graph_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(D,k4_finseq_1(k1_graph_2(A,B,C)))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(E,k4_finseq_1(A))
                              & k1_funct_1(A,E) = k1_funct_1(k1_graph_2(A,B,C),D)
                              & k1_nat_1(E,np__1) = k1_nat_1(B,D)
                              & r1_xreal_0(B,E)
                              & r1_xreal_0(E,C) ) ) ) ) ) ) ) )).

fof(t3_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ~ ( r1_graph_2(A,C,B)
                  & v1_xboole_0(C) ) ) ) ) )).

fof(t4_graph_3,axiom,(
    $true )).

fof(t5_graph_3,axiom,(
    $true )).

fof(t6_graph_3,axiom,(
    $true )).

fof(t7_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( r2_hidden(B,u2_graph_1(A))
         => ( v2_funct_1(k9_finseq_1(B))
            & m2_graph_1(k9_finseq_1(B),A) ) ) ) )).

fof(t8_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v2_funct_1(k2_graph_2(u2_graph_1(A),B,C,D))
                    & m2_graph_1(k2_graph_2(u2_graph_1(A),B,C,D),A) ) ) ) ) ) )).

fof(t9_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( ( v2_funct_1(C)
                & m2_graph_1(C,A) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_graph_1(A))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_graph_1(A))
                     => ( ( r1_xboole_0(k2_relat_1(B),k2_relat_1(C))
                          & r1_graph_2(A,D,B)
                          & r1_graph_2(A,E,C)
                          & k1_funct_1(D,k3_finseq_1(D)) = k1_funct_1(E,np__1) )
                       => ( v2_funct_1(k8_finseq_1(u2_graph_1(A),B,C))
                          & m2_graph_1(k8_finseq_1(u2_graph_1(A),B,C),A) ) ) ) ) ) ) ) )).

fof(t10_graph_3,axiom,(
    $true )).

fof(t11_graph_3,axiom,(
    $true )).

fof(t12_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ( B = k1_xboole_0
           => v1_msscyc_1(B,A) ) ) ) )).

fof(t13_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v2_funct_1(C)
                & v1_msscyc_1(C,A)
                & m2_graph_1(C,A) )
             => ( v2_funct_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),C,k1_nat_1(B,np__1),k3_finseq_1(C)),k2_graph_2(u2_graph_1(A),C,np__1,B)))
                & v1_msscyc_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),C,k1_nat_1(B,np__1),k3_finseq_1(C)),k2_graph_2(u2_graph_1(A),C,np__1,B)),A)
                & m2_graph_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),C,k1_nat_1(B,np__1),k3_finseq_1(C)),k2_graph_2(u2_graph_1(A),C,np__1,B)),A) ) ) ) ) )).

fof(t14_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(B))
               => ( k3_finseq_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),B,k1_nat_1(C,np__1),k3_finseq_1(B)),k2_graph_2(u2_graph_1(A),B,np__1,C))) = k3_finseq_1(B)
                  & k2_relat_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),B,k1_nat_1(C,np__1),k3_finseq_1(B)),k2_graph_2(u2_graph_1(A),B,np__1,C))) = k2_relat_1(B)
                  & k1_funct_1(k8_finseq_1(u2_graph_1(A),k2_graph_2(u2_graph_1(A),B,k1_nat_1(C,np__1),k3_finseq_1(B)),k2_graph_2(u2_graph_1(A),B,np__1,C)),np__1) = k1_funct_1(B,k1_nat_1(C,np__1)) ) ) ) ) ) )).

fof(t15_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v2_funct_1(C)
                & v1_msscyc_1(C,A)
                & m2_graph_1(C,A) )
             => ~ ( r2_hidden(B,k4_finseq_1(C))
                  & ! [D] :
                      ( ( v2_funct_1(D)
                        & v1_msscyc_1(D,A)
                        & m2_graph_1(D,A) )
                     => ~ ( k1_funct_1(D,np__1) = k1_funct_1(C,B)
                          & k3_finseq_1(D) = k3_finseq_1(C)
                          & k2_relat_1(D) = k2_relat_1(C) ) ) ) ) ) ) )).

fof(t16_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B,C] :
          ( m1_subset_1(C,u1_graph_1(A))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(A))
             => ( ( C = k1_funct_1(u3_graph_1(A),B)
                  & D = k1_funct_1(u4_graph_1(A),B) )
               => r1_graph_2(A,k2_finseq_4(u1_graph_1(A),D,C),k9_finseq_1(B)) ) ) ) ) )).

fof(t17_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( r2_hidden(D,u2_graph_1(A))
                    & r1_graph_2(A,C,B)
                    & k1_funct_1(C,k3_finseq_1(C)) = k1_funct_1(u3_graph_1(A),D) )
                 => ( m1_graph_1(k7_finseq_1(B,k9_finseq_1(D)),A)
                    & ? [E] :
                        ( m2_finseq_1(E,u1_graph_1(A))
                        & E = k3_graph_2(C,k10_finseq_1(k1_funct_1(u3_graph_1(A),D),k1_funct_1(u4_graph_1(A),D)))
                        & r1_graph_2(A,E,k7_finseq_1(B,k9_finseq_1(D)))
                        & k1_funct_1(E,np__1) = k1_funct_1(C,np__1)
                        & k1_funct_1(E,k3_finseq_1(E)) = k1_funct_1(u4_graph_1(A),D) ) ) ) ) ) ) )).

fof(t18_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( r2_hidden(D,u2_graph_1(A))
                    & r1_graph_2(A,C,B)
                    & k1_funct_1(C,k3_finseq_1(C)) = k1_funct_1(u4_graph_1(A),D) )
                 => ( m1_graph_1(k7_finseq_1(B,k9_finseq_1(D)),A)
                    & ? [E] :
                        ( m2_finseq_1(E,u1_graph_1(A))
                        & E = k3_graph_2(C,k10_finseq_1(k1_funct_1(u4_graph_1(A),D),k1_funct_1(u3_graph_1(A),D)))
                        & r1_graph_2(A,E,k7_finseq_1(B,k9_finseq_1(D)))
                        & k1_funct_1(E,np__1) = k1_funct_1(C,np__1)
                        & k1_funct_1(E,k3_finseq_1(E)) = k1_funct_1(u3_graph_1(A),D) ) ) ) ) ) ) )).

fof(t19_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ( r1_graph_2(A,C,B)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r2_hidden(D,k4_finseq_1(B))
                        & ~ ( k1_funct_1(C,D) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,D))
                            & k1_funct_1(C,k1_nat_1(D,np__1)) = k1_funct_1(u3_graph_1(A),k1_funct_1(B,D)) )
                        & ~ ( k1_funct_1(C,D) = k1_funct_1(u3_graph_1(A),k1_funct_1(B,D))
                            & k1_funct_1(C,k1_nat_1(D,np__1)) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,D)) ) ) ) ) ) ) ) )).

fof(t20_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_graph_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( r1_graph_2(A,C,B)
                    & r2_hidden(D,k2_relat_1(B)) )
                 => ( r2_hidden(k1_funct_1(u4_graph_1(A),D),k2_relat_1(C))
                    & r2_hidden(k1_funct_1(u3_graph_1(A),D),k2_relat_1(C)) ) ) ) ) ) )).

fof(t21_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => k1_graph_3(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t22_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B,C] :
          ~ ( r2_hidden(B,u2_graph_1(A))
            & r2_hidden(B,C)
            & v1_xboole_0(k1_graph_3(A,C)) ) ) )).

fof(t23_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ( v6_graph_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_graph_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_graph_1(A))
               => ~ ( B != C
                    & ! [D] :
                        ( m1_graph_1(D,A)
                       => ! [E] :
                            ( m2_finseq_1(E,u1_graph_1(A))
                           => ~ ( ~ v1_xboole_0(D)
                                & r1_graph_2(A,E,D)
                                & k1_funct_1(E,np__1) = B
                                & k1_funct_1(E,k3_finseq_1(E)) = C ) ) ) ) ) ) ) ) )).

fof(t24_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & l1_graph_1(A) )
     => ! [B,C] :
          ( m1_subset_1(C,u1_graph_1(A))
         => ~ ( ~ r1_xboole_0(B,u2_graph_1(A))
              & ~ r2_hidden(C,k1_graph_3(A,B))
              & ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u2_graph_1(A))
                     => ~ ( r2_hidden(D,k1_graph_3(A,B))
                          & ~ r2_hidden(E,B)
                          & ( D = k1_funct_1(u4_graph_1(A),E)
                            | D = k1_funct_1(u3_graph_1(A),E) ) ) ) ) ) ) ) )).

fof(d1_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C,D] :
              ( m1_subset_1(D,k1_zfmisc_1(u2_graph_1(A)))
             => ( D = k2_graph_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,D)
                  <=> ( r2_hidden(E,u2_graph_1(A))
                      & r2_hidden(E,C)
                      & k1_funct_1(u4_graph_1(A),E) = B ) ) ) ) ) ) )).

fof(d2_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C,D] :
              ( m1_subset_1(D,k1_zfmisc_1(u2_graph_1(A)))
             => ( D = k3_graph_3(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,D)
                  <=> ( r2_hidden(E,u2_graph_1(A))
                      & r2_hidden(E,C)
                      & k1_funct_1(u3_graph_1(A),E) = B ) ) ) ) ) ) )).

fof(d3_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] : k4_graph_3(A,B,C) = k4_subset_1(u2_graph_1(A),k2_graph_3(A,B,C),k3_graph_3(A,B,C)) ) ) )).

fof(d4_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k5_graph_3(A,B) = k2_graph_3(A,B,u2_graph_1(A)) ) ) )).

fof(d5_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k6_graph_3(A,B) = k3_graph_3(A,B,u2_graph_1(A)) ) ) )).

fof(t25_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] : r1_tarski(k2_graph_3(A,B,C),k5_graph_3(A,B)) ) ) )).

fof(t26_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] : r1_tarski(k3_graph_3(A,B,C),k6_graph_3(A,B)) ) ) )).

fof(t27_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k4_card_1(k5_graph_3(A,B)) = k4_graph_1(A,B) ) ) )).

fof(t28_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k4_card_1(k6_graph_3(A,B)) = k5_graph_1(A,B) ) ) )).

fof(d6_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] : k7_graph_3(A,B,C) = k1_nat_1(k4_card_1(k2_graph_3(A,B,C)),k4_card_1(k3_graph_3(A,B,C))) ) ) )).

fof(t29_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k6_graph_1(A,B) = k7_graph_3(A,B,u2_graph_1(A)) ) ) )).

fof(t30_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ~ ( k7_graph_3(B,C,A) != np__0
              & v1_xboole_0(k4_graph_3(B,C,A)) ) ) ) )).

fof(t31_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & v7_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_graph_1(C))
         => ~ ( r2_hidden(A,u2_graph_1(C))
              & ~ r2_hidden(A,B)
              & ( D = k1_funct_1(u4_graph_1(C),A)
                | D = k1_funct_1(u3_graph_1(C),A) )
              & k6_graph_1(C,D) = k7_graph_3(C,D,B) ) ) ) )).

fof(t32_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C,D] :
              ( r1_tarski(C,D)
             => k4_card_1(k2_graph_3(A,B,k4_xboole_0(D,C))) = k6_xcmplx_0(k4_card_1(k2_graph_3(A,B,D)),k4_card_1(k2_graph_3(A,B,C))) ) ) ) )).

fof(t33_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C,D] :
              ( r1_tarski(C,D)
             => k4_card_1(k3_graph_3(A,B,k4_xboole_0(D,C))) = k6_xcmplx_0(k4_card_1(k3_graph_3(A,B,D)),k4_card_1(k3_graph_3(A,B,C))) ) ) ) )).

fof(t34_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C,D] :
              ( r1_tarski(C,D)
             => k7_graph_3(A,B,k4_xboole_0(D,C)) = k6_xcmplx_0(k7_graph_3(A,B,D),k7_graph_3(A,B,C)) ) ) ) )).

fof(t35_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ( k2_graph_3(B,C,A) = k2_graph_3(B,C,k3_xboole_0(A,u2_graph_1(B)))
            & k3_graph_3(B,C,A) = k3_graph_3(B,C,k3_xboole_0(A,u2_graph_1(B))) ) ) ) )).

fof(t36_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => k7_graph_3(B,C,A) = k7_graph_3(B,C,k3_xboole_0(A,u2_graph_1(B))) ) ) )).

fof(t37_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_graph_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,u1_graph_1(A))
                 => ( r1_graph_2(A,D,C)
                   => ( v1_xboole_0(C)
                      | ( r2_hidden(B,k2_relat_1(D))
                      <=> k7_graph_3(A,B,k2_relat_1(C)) != np__0 ) ) ) ) ) ) ) )).

fof(t38_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & ~ v2_msscyc_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => k6_graph_1(A,B) != np__0 ) ) )).

fof(d7_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( v1_graph_1(D)
                    & v2_graph_1(D)
                    & l1_graph_1(D) )
                 => ( D = k8_graph_3(A,B,C)
                  <=> ( u1_graph_1(D) = u1_graph_1(A)
                      & u2_graph_1(D) = k2_xboole_0(u2_graph_1(A),k1_tarski(u2_graph_1(A)))
                      & u3_graph_1(D) = k1_funct_4(u3_graph_1(A),k3_cqc_lang(u2_graph_1(A),B))
                      & u4_graph_1(D) = k1_funct_4(u4_graph_1(A),k3_cqc_lang(u2_graph_1(A),C)) ) ) ) ) ) ) )).

fof(t39_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ( r2_hidden(u2_graph_1(A),u2_graph_1(k8_graph_3(A,B,C)))
                & u2_graph_1(A) = k4_xboole_0(u2_graph_1(k8_graph_3(A,B,C)),k1_tarski(u2_graph_1(A)))
                & k1_funct_1(u3_graph_1(k8_graph_3(A,B,C)),u2_graph_1(A)) = B
                & k1_funct_1(u4_graph_1(k8_graph_3(A,B,C)),u2_graph_1(A)) = C ) ) ) ) )).

fof(t40_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ( r2_hidden(A,u2_graph_1(B))
               => ( k1_funct_1(u3_graph_1(k8_graph_3(B,C,D)),A) = k1_funct_1(u3_graph_1(B),A)
                  & k1_funct_1(u4_graph_1(k8_graph_3(B,C,D)),A) = k1_funct_1(u4_graph_1(B),A) ) ) ) ) ) )).

fof(t41_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_graph_1(D,A)
                 => ! [E] :
                      ( m2_finseq_1(E,u1_graph_1(A))
                     => ! [F] :
                          ( m2_finseq_1(F,u1_graph_1(k8_graph_3(A,B,C)))
                         => ( ( F = E
                              & r1_graph_2(A,E,D) )
                           => r1_graph_2(k8_graph_3(A,B,C),F,D) ) ) ) ) ) ) ) )).

fof(t42_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_graph_1(D,A)
                 => m1_graph_1(D,k8_graph_3(A,B,C)) ) ) ) ) )).

fof(t43_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( v2_funct_1(D)
                    & m2_graph_1(D,A) )
                 => ( v2_funct_1(D)
                    & m2_graph_1(D,k8_graph_3(A,B,C)) ) ) ) ) ) )).

fof(t44_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(k8_graph_3(B,C,D)))
                 => ( E = C
                   => ( C = D
                      | k2_graph_3(k8_graph_3(B,C,D),E,A) = k2_graph_3(B,C,A) ) ) ) ) ) ) )).

fof(t45_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(k8_graph_3(B,D,C)))
                 => ( E = C
                   => ( D = C
                      | k3_graph_3(k8_graph_3(B,D,C),E,A) = k3_graph_3(B,C,A) ) ) ) ) ) ) )).

fof(t46_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(k8_graph_3(B,C,D)))
                 => ( ( E = C
                      & r2_hidden(u2_graph_1(B),A) )
                   => ( C = D
                      | ( k3_graph_3(k8_graph_3(B,C,D),E,A) = k2_xboole_0(k3_graph_3(B,C,A),k1_tarski(u2_graph_1(B)))
                        & r1_xboole_0(k3_graph_3(B,C,A),k1_tarski(u2_graph_1(B))) ) ) ) ) ) ) ) )).

fof(t47_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(k8_graph_3(B,D,C)))
                 => ( ( E = C
                      & r2_hidden(u2_graph_1(B),A) )
                   => ( D = C
                      | ( k2_graph_3(k8_graph_3(B,D,C),E,A) = k2_xboole_0(k2_graph_3(B,C,A),k1_tarski(u2_graph_1(B)))
                        & r1_xboole_0(k2_graph_3(B,C,A),k1_tarski(u2_graph_1(B))) ) ) ) ) ) ) ) )).

fof(t48_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E)))
                     => ( F = C
                       => ( C = D
                          | C = E
                          | k2_graph_3(k8_graph_3(B,D,E),F,A) = k2_graph_3(B,C,A) ) ) ) ) ) ) ) )).

fof(t49_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E)))
                     => ( F = C
                       => ( C = D
                          | C = E
                          | k3_graph_3(k8_graph_3(B,D,E),F,A) = k3_graph_3(B,C,A) ) ) ) ) ) ) ) )).

fof(t50_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( v2_funct_1(D)
                    & m2_graph_1(D,k8_graph_3(A,B,C)) )
                 => ( ~ r2_hidden(u2_graph_1(A),k2_relat_1(D))
                   => ( v2_funct_1(D)
                      & m2_graph_1(D,A) ) ) ) ) ) ) )).

fof(t51_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_graph_1(A))
                 => ! [E] :
                      ( ( v2_funct_1(E)
                        & m2_graph_1(E,k8_graph_3(A,B,C)) )
                     => ! [F] :
                          ( m2_finseq_1(F,u1_graph_1(k8_graph_3(A,B,C)))
                         => ( ( D = F
                              & r1_graph_2(k8_graph_3(A,B,C),F,E) )
                           => ( r2_hidden(u2_graph_1(A),k2_relat_1(E))
                              | r1_graph_2(A,D,E) ) ) ) ) ) ) ) ) )).

fof(t52_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E)))
                     => ( ( F = C
                          & r2_hidden(u2_graph_1(B),A) )
                       => ( D = E
                          | ( C != D
                            & C != E )
                          | k7_graph_3(k8_graph_3(B,D,E),F,A) = k1_nat_1(k7_graph_3(B,C,A),np__1) ) ) ) ) ) ) ) )).

fof(t53_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(k8_graph_3(B,D,E)))
                     => ( F = C
                       => ( C = D
                          | C = E
                          | k7_graph_3(k8_graph_3(B,D,E),F,A) = k7_graph_3(B,C,A) ) ) ) ) ) ) ) )).

fof(t54_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( ( v2_funct_1(C)
                & v1_msscyc_1(C,A)
                & m2_graph_1(C,A) )
             => v1_abian(k7_graph_3(A,B,k2_relat_1(C))) ) ) ) )).

fof(t55_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ! [D] :
                  ( ( v2_funct_1(D)
                    & m2_graph_1(D,A) )
                 => ( r1_graph_2(A,C,D)
                   => ( v1_msscyc_1(D,A)
                      | ( v1_abian(k7_graph_3(A,B,k2_relat_1(D)))
                      <=> ( B != k1_funct_1(C,np__1)
                          & B != k1_funct_1(C,k3_finseq_1(C)) ) ) ) ) ) ) ) ) )).

fof(d8_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_finseq_2(B,u2_graph_1(A)) )
         => ( B = k9_graph_3(A)
          <=> ! [C] :
                ( r2_hidden(C,B)
              <=> ( v2_funct_1(C)
                  & v1_msscyc_1(C,A)
                  & m2_graph_1(C,A) ) ) ) ) ) )).

fof(t56_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => m2_finseq_2(k1_xboole_0,u2_graph_1(A),k9_graph_3(A)) ) )).

fof(d10_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u2_graph_1(A),k9_graph_3(A))
         => ! [C] :
              ( m2_finseq_2(C,u2_graph_1(A),k9_graph_3(A))
             => ( r1_xboole_0(k2_relat_1(B),k2_relat_1(C))
               => ( r1_xboole_0(k1_graph_3(A,k2_relat_1(B)),k1_graph_3(A,k2_relat_1(C)))
                  | ! [D] :
                      ( m2_finseq_2(D,u2_graph_1(A),k9_graph_3(A))
                     => ( D = k11_graph_3(A,B,C)
                      <=> ? [E] :
                            ( m1_subset_1(E,u1_graph_1(A))
                            & E = k8_subset_1(k5_subset_1(u1_graph_1(A),k1_graph_3(A,k2_relat_1(B)),k1_graph_3(A,k2_relat_1(C))))
                            & D = k8_finseq_1(u2_graph_1(A),k10_graph_3(A,E,B),k10_graph_3(A,E,C)) ) ) ) ) ) ) ) ) )).

fof(t58_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u2_graph_1(A),k9_graph_3(A))
         => ! [C] :
              ( m2_finseq_2(C,u2_graph_1(A),k9_graph_3(A))
             => ~ ( ~ r1_xboole_0(k1_graph_3(A,k2_relat_1(B)),k1_graph_3(A,k2_relat_1(C)))
                  & r1_xboole_0(k2_relat_1(B),k2_relat_1(C))
                  & ~ ( B = k1_xboole_0
                      & C = k1_xboole_0 )
                  & v1_xboole_0(k11_graph_3(A,B,C)) ) ) ) ) )).

fof(t59_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ! [D] :
              ( m2_finseq_2(D,u2_graph_1(B),k12_graph_3(B,C,A))
             => ! [E] :
                  ( v1_finset_1(E)
                 => ( E = u2_graph_1(B)
                   => ( k7_graph_3(B,C,A) = np__0
                      | r1_xreal_0(k3_finseq_1(D),k4_card_1(E)) ) ) ) ) ) ) )).

fof(t60_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_graph_1(B))
         => ( ! [D] :
                ( m1_subset_1(D,u1_graph_1(B))
               => v1_abian(k7_graph_3(B,D,A)) )
           => ( k7_graph_3(B,C,A) = np__0
              | ! [D] :
                  ( m1_graph_3(D,u2_graph_1(B),k9_graph_3(B),k13_graph_3(B,C,A))
                 => ( ~ v1_xboole_0(D)
                    & r1_tarski(k2_relat_1(D),A)
                    & r2_hidden(C,k1_graph_3(B,k2_relat_1(D))) ) ) ) ) ) ) )).

fof(t62_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u2_graph_1(A),k9_graph_3(A))
         => ( ! [C] :
                ( m1_subset_1(C,u1_graph_1(A))
               => v1_abian(k6_graph_1(A,C)) )
           => ( k2_relat_1(B) = u2_graph_1(A)
              | v1_xboole_0(B)
              | ( ~ v1_xboole_0(k14_graph_3(A,B))
                & ~ r1_xreal_0(k4_card_1(k2_relat_1(k14_graph_3(A,B))),k4_card_1(k2_relat_1(B))) ) ) ) ) ) )).

fof(d14_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & m2_graph_1(B,A) )
         => ( v1_graph_3(B,A)
          <=> k2_relat_1(B) = u2_graph_1(A) ) ) ) )).

fof(t63_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_graph_1(A))
             => ( ( v1_graph_3(B,A)
                  & r1_graph_2(A,C,B) )
               => k2_relat_1(C) = u1_graph_1(A) ) ) ) ) )).

fof(t64_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ( ? [B] :
            ( v2_funct_1(B)
            & v1_msscyc_1(B,A)
            & m2_graph_1(B,A)
            & v1_graph_3(B,A) )
      <=> ! [B] :
            ( m1_subset_1(B,u1_graph_1(A))
           => v1_abian(k6_graph_1(A,B)) ) ) ) )).

fof(t65_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ( ~ ( ? [B] :
                ( v2_funct_1(B)
                & m2_graph_1(B,A)
                & ~ v1_msscyc_1(B,A)
                & v1_graph_3(B,A) )
            & ! [B] :
                ( m1_subset_1(B,u1_graph_1(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_graph_1(A))
                   => ~ ( B != C
                        & ! [D] :
                            ( m1_subset_1(D,u1_graph_1(A))
                           => ( v1_abian(k6_graph_1(A,D))
                            <=> ( D != B
                                & D != C ) ) ) ) ) ) )
        & ~ ( ? [B] :
                ( m1_subset_1(B,u1_graph_1(A))
                & ? [C] :
                    ( m1_subset_1(C,u1_graph_1(A))
                    & B != C
                    & ! [D] :
                        ( m1_subset_1(D,u1_graph_1(A))
                       => ( v1_abian(k6_graph_1(A,D))
                        <=> ( D != B
                            & D != C ) ) ) ) )
            & ! [B] :
                ( ( v2_funct_1(B)
                  & m2_graph_1(B,A) )
               => ~ ( ~ v1_msscyc_1(B,A)
                    & v1_graph_3(B,A) ) ) ) ) ) )).

fof(dt_m1_graph_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] :
          ( m1_graph_3(D,A,B,C)
         => m2_finseq_1(D,A) ) ) )).

fof(existence_m1_graph_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ? [D] : m1_graph_3(D,A,B,C) ) )).

fof(redefinition_m1_graph_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] :
          ( m1_graph_3(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_k1_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => m1_subset_1(k1_graph_3(A,B),k1_zfmisc_1(u1_graph_1(A))) ) )).

fof(redefinition_k1_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => k1_graph_3(A,B) = k5_graph_2(A,B) ) )).

fof(dt_k2_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m1_subset_1(k2_graph_3(A,B,C),k1_zfmisc_1(u2_graph_1(A))) ) )).

fof(dt_k3_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m1_subset_1(k3_graph_3(A,B,C),k1_zfmisc_1(u2_graph_1(A))) ) )).

fof(dt_k4_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m1_subset_1(k4_graph_3(A,B,C),k1_zfmisc_1(u2_graph_1(A))) ) )).

fof(dt_k5_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m1_subset_1(k5_graph_3(A,B),k1_zfmisc_1(u2_graph_1(A))) ) )).

fof(dt_k6_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m1_subset_1(k6_graph_3(A,B),k1_zfmisc_1(u2_graph_1(A))) ) )).

fof(dt_k7_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => m2_subset_1(k7_graph_3(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k8_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A)) )
     => ( v1_graph_1(k8_graph_3(A,B,C))
        & v2_graph_1(k8_graph_3(A,B,C))
        & l1_graph_1(k8_graph_3(A,B,C)) ) ) )).

fof(dt_k9_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ( ~ v1_xboole_0(k9_graph_3(A))
        & m1_finseq_2(k9_graph_3(A),u2_graph_1(A)) ) ) )).

fof(dt_k10_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,k9_graph_3(A)) )
     => m2_finseq_2(k10_graph_3(A,B,C),u2_graph_1(A),k9_graph_3(A)) ) )).

fof(dt_k11_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,k9_graph_3(A))
        & m1_subset_1(C,k9_graph_3(A)) )
     => m2_finseq_2(k11_graph_3(A,B,C),u2_graph_1(A),k9_graph_3(A)) ) )).

fof(dt_k12_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => ( ~ v1_xboole_0(k12_graph_3(A,B,C))
        & m1_finseq_2(k12_graph_3(A,B,C),u2_graph_1(A)) ) ) )).

fof(dt_k13_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A)) )
     => ( ~ v1_xboole_0(k13_graph_3(A,B,C))
        & m1_subset_1(k13_graph_3(A,B,C),k1_zfmisc_1(k9_graph_3(A))) ) ) )).

fof(dt_k14_graph_3,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,k9_graph_3(A)) )
     => m2_finseq_2(k14_graph_3(A,B),u2_graph_1(A),k9_graph_3(A)) ) )).

fof(t57_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u2_graph_1(A),k9_graph_3(A))
             => ( r2_hidden(B,k1_graph_3(A,k2_relat_1(C)))
               => ( ~ v1_xboole_0(a_3_0_graph_3(A,B,C))
                  & m1_subset_1(a_3_0_graph_3(A,B,C),k1_zfmisc_1(k9_graph_3(A))) ) ) ) ) ) )).

fof(d9_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u2_graph_1(A),k9_graph_3(A))
             => ( r2_hidden(B,k1_graph_3(A,k2_relat_1(C)))
               => k10_graph_3(A,B,C) = k8_subset_1(a_3_0_graph_3(A,B,C)) ) ) ) ) )).

fof(d11_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( k7_graph_3(A,B,C) != np__0
             => k12_graph_3(A,B,C) = a_3_1_graph_3(A,B,C) ) ) ) )).

fof(d12_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => v1_abian(k7_graph_3(A,D,C)) )
             => ( k7_graph_3(A,B,C) = np__0
                | k13_graph_3(A,B,C) = a_3_2_graph_3(A,B,C) ) ) ) ) )).

fof(t61_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u2_graph_1(A),k9_graph_3(A))
         => ~ ( k2_relat_1(B) != u2_graph_1(A)
              & ~ v1_xboole_0(B)
              & ~ ( ~ v1_xboole_0(a_2_0_graph_3(A,B))
                  & m1_subset_1(a_2_0_graph_3(A,B),k1_zfmisc_1(u1_graph_1(A))) ) ) ) ) )).

fof(d13_graph_3,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v6_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u2_graph_1(A),k9_graph_3(A))
         => ~ ( k2_relat_1(B) != u2_graph_1(A)
              & ~ v1_xboole_0(B)
              & ~ ! [C] :
                    ( m2_finseq_2(C,u2_graph_1(A),k9_graph_3(A))
                   => ( C = k14_graph_3(A,B)
                    <=> ? [D] :
                          ( m2_finseq_2(D,u2_graph_1(A),k9_graph_3(A))
                          & ? [E] :
                              ( m1_subset_1(E,u1_graph_1(A))
                              & E = k8_subset_1(a_2_0_graph_3(A,B))
                              & D = k8_subset_1(k13_graph_3(A,E,k4_xboole_0(u2_graph_1(A),k2_relat_1(B))))
                              & C = k11_graph_3(A,B,D) ) ) ) ) ) ) ) )).

fof(fraenkel_a_3_0_graph_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B))
        & m2_finseq_2(D,u2_graph_1(B),k9_graph_3(B)) )
     => ( r2_hidden(A,a_3_0_graph_3(B,C,D))
      <=> ? [E] :
            ( m2_finseq_2(E,u2_graph_1(B),k9_graph_3(B))
            & A = E
            & k2_relat_1(E) = k2_relat_1(D)
            & ? [F] :
                ( m2_finseq_1(F,u1_graph_1(B))
                & r1_graph_2(B,F,E)
                & k1_funct_1(F,np__1) = C ) ) ) ) )).

fof(fraenkel_a_3_1_graph_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B)) )
     => ( r2_hidden(A,a_3_1_graph_3(B,C,D))
      <=> ? [E] :
            ( m2_finseq_2(E,D,k3_finseq_2(D))
            & A = E
            & v2_funct_1(E)
            & m2_graph_1(E,B)
            & ~ v1_xboole_0(E)
            & ? [F] :
                ( m2_finseq_1(F,u1_graph_1(B))
                & r1_graph_2(B,F,E)
                & k1_funct_1(F,np__1) = C ) ) ) ) )).

fof(fraenkel_a_3_2_graph_3,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B)) )
     => ( r2_hidden(A,a_3_2_graph_3(B,C,D))
      <=> ? [E] :
            ( m2_finseq_2(E,u2_graph_1(B),k9_graph_3(B))
            & A = E
            & r1_tarski(k2_relat_1(E),D)
            & ~ v1_xboole_0(E)
            & ? [F] :
                ( m2_finseq_1(F,u1_graph_1(B))
                & r1_graph_2(B,F,E)
                & k1_funct_1(F,np__1) = C ) ) ) ) )).

fof(fraenkel_a_2_0_graph_3,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(B)
        & v6_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B)
        & m2_finseq_2(C,u2_graph_1(B),k9_graph_3(B)) )
     => ( r2_hidden(A,a_2_0_graph_3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_graph_1(B))
            & A = D
            & r2_hidden(D,k1_graph_3(B,k2_relat_1(C)))
            & k6_graph_1(B,D) != k7_graph_3(B,D,k2_relat_1(C)) ) ) ) )).
%------------------------------------------------------------------------------