SET007 Axioms: SET007+756.ax


%------------------------------------------------------------------------------
% File     : SET007+756 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Underlying Principle of Dijkstra's Shortest Path Algorithm
% 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  117 (   3 unit)
%            Number of atoms       :  974 (  94 equality)
%            Maximal formula depth :   27 (  10 average)
%            Number of connectives :  920 (  63 ~  ;  11  |; 424  &)
%                                         (  25 <=>; 397 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-6 arity)
%            Number of functors    :   55 (  10 constant; 0-4 arity)
%            Number of variables   :  433 (   0 singleton; 419 !;  14 ?)
%            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_5,axiom,
    ( ~ v1_xboole_0(k8_graph_5)
    & v1_membered(k8_graph_5)
    & v2_membered(k8_graph_5) )).

fof(fc2_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => v1_finset_1(k7_graph_5(A)) ) )).

fof(fc3_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A)
        & v8_graph_1(B,A)
        & m1_graph_1(B,A) )
     => v1_finset_1(k6_graph_5(A,B)) ) )).

fof(fc4_graph_5,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_finset_1(k4_graph_5(A,B,C)) ) )).

fof(fc5_graph_5,axiom,(
    ! [A,B,C,D] :
      ( ( 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_finset_1(k5_graph_5(A,B,C,D)) ) )).

fof(t1_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => r1_xreal_0(k4_card_1(k2_relat_1(A)),k4_card_1(k1_relat_1(A))) ) )).

fof(t2_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ~ ( r1_tarski(k2_relat_1(B),k2_relat_1(C))
              & r2_hidden(A,k1_relat_1(B))
              & ! [D] :
                  ~ ( r2_hidden(D,k1_relat_1(C))
                    & k1_funct_1(B,A) = k1_funct_1(C,D) ) ) ) ) )).

fof(t5_graph_5,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ( ~ ( k4_card_1(A) != np__0
            & A = k1_xboole_0 )
        & ~ ( A != k1_xboole_0
            & k4_card_1(A) = np__0 ) ) ) )).

fof(t6_graph_5,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( k4_card_1(A) = k1_nat_1(B,np__1)
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(A))
                     => ~ ( A = k2_xboole_0(D,k1_tarski(C))
                          & k4_card_1(D) = B ) ) ) ) ) ) )).

fof(t7_graph_5,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ~ ( k4_card_1(A) = np__1
          & ! [B] :
              ( m1_subset_1(B,A)
             => A != k1_tarski(B) ) ) ) )).

fof(t8_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A != k1_xboole_0
      <=> r1_xreal_0(np__1,k3_finseq_1(A)) ) ) )).

fof(t9_graph_5,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)
               => ~ ( r1_xreal_0(np__1,B)
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(C,k3_finseq_1(A))
                    & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) )
      <=> v2_funct_1(A) ) ) )).

fof(t10_graph_5,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)
               => ~ ( r1_xreal_0(np__1,B)
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(C,k3_finseq_1(A))
                    & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) )
      <=> k4_card_1(k2_relat_1(A)) = k3_finseq_1(A) ) ) )).

fof(t11_graph_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ( r2_hidden(A,k4_finseq_1(C))
               => ( r2_hidden(k1_funct_1(u3_graph_1(B),k1_funct_1(C,A)),u1_graph_1(B))
                  & r2_hidden(k1_funct_1(u4_graph_1(B),k1_funct_1(C,A)),u1_graph_1(B)) ) ) ) ) ) )).

fof(t12_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ~ ( v2_funct_1(k7_finseq_1(B,k9_finseq_1(A)))
              & r1_tarski(k2_relat_1(k7_finseq_1(B,k9_finseq_1(A))),k2_relat_1(C))
              & ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ~ ( C = k7_finseq_1(k7_finseq_1(D,k9_finseq_1(A)),E)
                          & r1_tarski(k2_relat_1(B),k2_relat_1(k7_finseq_1(D,E))) ) ) ) ) ) ) )).

fof(t13_graph_5,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) )
         => ! [C] :
              ( ( v2_graph_1(C)
                & l1_graph_1(C) )
             => ( m2_graph_1(k7_finseq_1(A,B),C)
               => ( m2_graph_1(A,C)
                  & m2_graph_1(B,C) ) ) ) ) ) )).

fof(t14_graph_5,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) )
         => ! [C] :
              ( ( v2_graph_1(C)
                & l1_graph_1(C) )
             => ( ( v8_graph_1(k7_finseq_1(A,B),C)
                  & m2_graph_1(k7_finseq_1(A,B),C) )
               => ( v8_graph_1(A,C)
                  & m2_graph_1(A,C)
                  & v8_graph_1(B,C)
                  & m2_graph_1(B,C) ) ) ) ) ) )).

fof(t15_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ( k1_funct_1(u4_graph_1(A),k1_funct_1(B,k3_finseq_1(B))) = k1_funct_1(u3_graph_1(A),k1_funct_1(C,np__1))
               => ( v8_graph_1(k8_finseq_1(u2_graph_1(A),B,C),A)
                  & m2_graph_1(k8_finseq_1(u2_graph_1(A),B,C),A) ) ) ) ) ) )).

fof(t16_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ( v8_graph_1(k1_xboole_0,A)
        & v1_graph_4(k1_xboole_0,A)
        & m2_graph_1(k1_xboole_0,A) ) ) )).

fof(t17_graph_5,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) )
         => ! [C] :
              ( ( v2_graph_1(C)
                & l1_graph_1(C) )
             => ( ( v8_graph_1(k7_finseq_1(A,B),C)
                  & v1_graph_4(k7_finseq_1(A,B),C)
                  & m2_graph_1(k7_finseq_1(A,B),C) )
               => ( v8_graph_1(A,C)
                  & v1_graph_4(A,C)
                  & m2_graph_1(A,C)
                  & v8_graph_1(B,C)
                  & v1_graph_4(B,C)
                  & m2_graph_1(B,C) ) ) ) ) ) )).

fof(t18_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ( k3_finseq_1(B) = np__1
           => ( v8_graph_1(B,A)
              & v1_graph_4(B,A)
              & m2_graph_1(B,A) ) ) ) ) )).

fof(t19_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & v1_graph_4(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(A))
             => ( ( r1_xreal_0(np__1,k3_finseq_1(B))
                  & k3_finseq_1(C) = np__1
                  & k1_funct_1(u3_graph_1(A),k1_funct_1(C,np__1)) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,k3_finseq_1(B)))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(B))
                          & k1_funct_1(u4_graph_1(A),k1_funct_1(B,D)) = k1_funct_1(u4_graph_1(A),k1_funct_1(C,np__1)) ) ) )
               => ( k1_funct_1(u3_graph_1(A),k1_funct_1(B,np__1)) = k1_funct_1(u4_graph_1(A),k1_funct_1(B,k3_finseq_1(B)))
                  | ( v8_graph_1(k8_finseq_1(u2_graph_1(A),B,C),A)
                    & v1_graph_4(k8_finseq_1(u2_graph_1(A),B,C),A)
                    & m2_graph_1(k8_finseq_1(u2_graph_1(A),B,C),A) ) ) ) ) ) ) )).

fof(t20_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & v1_graph_4(B,A)
            & m2_graph_1(B,A) )
         => v2_funct_1(B) ) ) )).

fof(d1_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_graph_1(A))
         => k1_graph_5(A,B) = k2_tarski(k1_funct_1(u3_graph_1(A),B),k1_funct_1(u4_graph_1(A),B)) ) ) )).

fof(t21_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(A))
             => ! [D] :
                  ( ( v8_graph_1(D,A)
                    & v1_graph_4(D,A)
                    & m2_graph_1(D,A) )
                 => ( ( D = k8_finseq_1(u2_graph_1(A),B,C)
                      & r1_xreal_0(np__1,k3_finseq_1(B))
                      & r1_xreal_0(np__1,k3_finseq_1(C)) )
                   => ( k1_funct_1(u3_graph_1(A),k1_funct_1(D,np__1)) = k1_funct_1(u4_graph_1(A),k1_funct_1(D,k3_finseq_1(D)))
                      | ( ~ r2_hidden(k1_funct_1(u3_graph_1(A),k1_funct_1(D,np__1)),k2_graph_5(A,C))
                        & ~ r2_hidden(k1_funct_1(u4_graph_1(A),k1_funct_1(D,k3_finseq_1(D))),k2_graph_5(A,B)) ) ) ) ) ) ) ) )).

fof(t22_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m2_finseq_1(C,u2_graph_1(B))
         => ( r1_tarski(k2_graph_5(B,C),A)
          <=> ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( r2_hidden(D,k4_finseq_1(C))
                 => r1_tarski(k1_graph_5(B,k4_finseq_4(k5_numbers,u2_graph_1(B),C,D)),A) ) ) ) ) ) )).

fof(t23_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m2_finseq_1(C,u2_graph_1(B))
         => ~ ( ~ r1_tarski(k2_graph_5(B,C),A)
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_1(E,u2_graph_1(B))
                     => ! [F] :
                          ( m2_finseq_1(F,u2_graph_1(B))
                         => ~ ( r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
                              & ~ r1_tarski(k1_graph_5(B,k4_finseq_4(k5_numbers,u2_graph_1(B),C,k1_nat_1(D,np__1))),A)
                              & k3_finseq_1(E) = D
                              & C = k8_finseq_1(u2_graph_1(B),E,F)
                              & r1_tarski(k2_graph_5(B,E),A) ) ) ) ) ) ) ) )).

fof(t24_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(A))
             => ( r1_tarski(k2_relat_1(B),k2_relat_1(C))
               => r1_tarski(k2_graph_5(A,B),k2_graph_5(A,C)) ) ) ) ) )).

fof(t25_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( m2_finseq_1(D,u2_graph_1(C))
         => ! [E] :
              ( m2_finseq_1(E,u2_graph_1(C))
             => ( ( r1_tarski(k2_relat_1(D),k2_relat_1(E))
                  & r1_tarski(k4_xboole_0(k2_graph_5(C,E),A),B) )
               => r1_tarski(k4_xboole_0(k2_graph_5(C,D),A),B) ) ) ) ) )).

fof(t26_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( m2_finseq_1(D,u2_graph_1(C))
         => ! [E] :
              ( m2_finseq_1(E,u2_graph_1(C))
             => ( r1_tarski(k4_xboole_0(k2_graph_5(C,k8_finseq_1(u2_graph_1(C),D,E)),A),B)
               => ( r1_tarski(k4_xboole_0(k2_graph_5(C,D),A),B)
                  & r1_tarski(k4_xboole_0(k2_graph_5(C,E),A),B) ) ) ) ) ) )).

fof(t27_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_graph_1(A))
             => ( ( B = k1_funct_1(u3_graph_1(A),C)
                  | B = k1_funct_1(u4_graph_1(A),C) )
               => r2_hidden(B,k1_graph_5(A,C)) ) ) ) ) )).

fof(t28_graph_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(B))
                 => ( r2_hidden(A,k4_finseq_1(C))
                   => ( ( D != k1_funct_1(u3_graph_1(B),k1_funct_1(C,A))
                        & D != k1_funct_1(u4_graph_1(B),k1_funct_1(C,A)) )
                      | r2_hidden(D,k2_graph_5(B,C)) ) ) ) ) ) ) )).

fof(t29_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ( k3_finseq_1(B) = np__1
           => k2_graph_5(A,B) = k1_graph_5(A,k4_finseq_4(k5_numbers,u2_graph_1(A),B,np__1)) ) ) ) )).

fof(t30_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(A))
             => ( r1_tarski(k2_graph_5(A,B),k2_graph_5(A,k8_finseq_1(u2_graph_1(A),B,C)))
                & r1_tarski(k2_graph_5(A,C),k2_graph_5(A,k8_finseq_1(u2_graph_1(A),B,C))) ) ) ) ) )).

fof(t31_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ! [D] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( ( C = k8_finseq_1(u2_graph_1(A),D,B)
                      & r1_xreal_0(np__1,k3_finseq_1(D))
                      & k3_finseq_1(B) = np__1 )
                   => k2_graph_5(A,C) = k2_xboole_0(k2_graph_5(A,D),k1_tarski(k1_funct_1(u4_graph_1(A),k1_funct_1(B,np__1)))) ) ) ) ) ) )).

fof(t32_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_graph_1(A))
         => ! [C] :
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ~ ( B != k1_funct_1(u3_graph_1(A),k1_funct_1(C,np__1))
                  & r2_hidden(B,k2_graph_5(A,C))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(C))
                          & B = k1_funct_1(u4_graph_1(A),k1_funct_1(C,D)) ) ) ) ) ) ) )).

fof(d3_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => ( r1_graph_5(A,B,C,D)
                  <=> ( B != k1_xboole_0
                      & k1_funct_1(u3_graph_1(A),k1_funct_1(B,np__1)) = C
                      & k1_funct_1(u4_graph_1(A),k1_funct_1(B,k3_finseq_1(B))) = D ) ) ) ) ) ) )).

fof(d4_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ! [E] :
                      ( r2_graph_5(A,B,C,D,E)
                    <=> ( r1_graph_5(A,D,B,C)
                        & r1_tarski(k4_xboole_0(k2_graph_5(A,D),k1_tarski(C)),E) ) ) ) ) ) ) )).

fof(t33_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( r1_graph_5(A,D,B,C)
                   => ( r2_hidden(B,k2_graph_5(A,D))
                      & r2_hidden(C,k2_graph_5(A,D)) ) ) ) ) ) ) )).

fof(t34_graph_5,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,k3_graph_5(B,C,D))
              <=> ? [E] :
                    ( v8_graph_1(E,B)
                    & m2_graph_1(E,B)
                    & E = A
                    & r1_graph_5(B,E,C,D) ) ) ) ) ) )).

fof(t35_graph_5,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] :
                  ( ( v8_graph_1(E,B)
                    & m2_graph_1(E,B) )
                 => ( r2_graph_5(B,C,D,E,A)
                   => ( C = D
                      | r2_hidden(C,A) ) ) ) ) ) ) )).

fof(t36_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_graph_1(C))
         => ! [E] :
              ( m1_subset_1(E,u1_graph_1(C))
             => ! [F] :
                  ( ( v8_graph_1(F,C)
                    & m2_graph_1(F,C) )
                 => ( ( r2_graph_5(C,D,E,F,A)
                      & r1_tarski(A,B) )
                   => r2_graph_5(C,D,E,F,B) ) ) ) ) ) )).

fof(t37_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_graph_1(A))
                     => ! [F] :
                          ( ( v8_graph_1(F,A)
                            & m2_graph_1(F,A) )
                         => ~ ( r1_xreal_0(np__1,k3_finseq_1(F))
                              & r1_graph_5(A,F,C,D)
                              & r1_graph_4(A,D,E,k1_funct_1(B,np__1))
                              & k3_finseq_1(B) = np__1
                              & ! [G] :
                                  ( ( v8_graph_1(G,A)
                                    & m2_graph_1(G,A) )
                                 => ~ ( G = k8_finseq_1(u2_graph_1(A),F,B)
                                      & r1_graph_5(A,G,C,E) ) ) ) ) ) ) ) ) ) )).

fof(t38_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( m2_finseq_1(C,u2_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(B))
                     => ! [G] :
                          ( ( v8_graph_1(G,B)
                            & m2_graph_1(G,B) )
                         => ! [H] :
                              ( ( v8_graph_1(H,B)
                                & m2_graph_1(H,B) )
                             => ( ( G = k8_finseq_1(u2_graph_1(B),H,C)
                                  & r1_xreal_0(np__1,k3_finseq_1(H))
                                  & k3_finseq_1(C) = np__1
                                  & r2_graph_5(B,D,E,H,A)
                                  & r1_graph_4(B,E,F,k1_funct_1(C,np__1)) )
                               => r2_graph_5(B,D,F,G,k2_xboole_0(A,k1_tarski(E))) ) ) ) ) ) ) ) ) )).

fof(d6_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => ( r3_graph_5(A,B,C,D)
                  <=> ( v1_graph_4(B,A)
                      & r1_graph_5(A,B,C,D) ) ) ) ) ) ) )).

fof(d7_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_graph_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(A))
                 => ! [E] :
                      ( r4_graph_5(A,B,C,D,E)
                    <=> ( v1_graph_4(B,A)
                        & r2_graph_5(A,C,D,B,E) ) ) ) ) ) ) )).

fof(t39_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ~ ( D = k1_xboole_0
                      & r3_graph_5(A,D,B,C) ) ) ) ) ) )).

fof(t40_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( r3_graph_5(A,D,B,C)
                   => r1_graph_5(A,D,B,C) ) ) ) ) ) )).

fof(t41_graph_5,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))
             => r1_tarski(k4_graph_5(A,B,C),k3_graph_5(A,B,C)) ) ) ) )).

fof(t42_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => r1_tarski(k6_graph_5(A,B),k7_graph_5(A)) ) ) )).

fof(t43_graph_5,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))
             => r1_tarski(k4_graph_5(A,B,C),k7_graph_5(A)) ) ) ) )).

fof(t44_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( r1_graph_5(A,D,B,C)
                   => r1_tarski(k6_graph_5(A,D),k4_graph_5(A,B,C)) ) ) ) ) ) )).

fof(t45_graph_5,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] :
                  ( ( v8_graph_1(E,B)
                    & m2_graph_1(E,B) )
                 => ( r2_graph_5(B,C,D,E,A)
                   => r1_tarski(k6_graph_5(B,E),k5_graph_5(B,C,D,A)) ) ) ) ) ) )).

fof(t46_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ( r2_hidden(B,k6_graph_5(A,C))
               => r1_xreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) )).

fof(t47_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( r1_graph_5(A,D,B,C)
                   => ( k6_graph_5(A,D) != k1_xboole_0
                      & k4_graph_5(A,B,C) != k1_xboole_0 ) ) ) ) ) ) )).

fof(t48_graph_5,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] :
                  ( ( v8_graph_1(E,B)
                    & m2_graph_1(E,B) )
                 => ( r2_graph_5(B,C,D,E,A)
                   => ( k6_graph_5(B,E) != k1_xboole_0
                      & k5_graph_5(B,C,D,A) != k1_xboole_0 ) ) ) ) ) ) )).

fof(t49_graph_5,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))
             => r1_tarski(k5_graph_5(B,C,D,A),k7_graph_5(B)) ) ) ) )).

fof(d13_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r5_graph_5(A,B)
          <=> ( v1_funct_1(B)
              & v1_funct_2(B,u2_graph_1(A),k8_graph_5)
              & m2_relset_1(B,u2_graph_1(A),k8_graph_5) ) ) ) ) )).

fof(d14_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r6_graph_5(A,B)
          <=> ( v1_funct_1(B)
              & v1_funct_2(B,u2_graph_1(A),k1_numbers)
              & m2_relset_1(B,u2_graph_1(A),k1_numbers) ) ) ) ) )).

fof(d15_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r6_graph_5(A,C)
               => ! [D] :
                    ( m2_finseq_1(D,k1_numbers)
                   => ( D = k9_graph_5(A,B,C)
                    <=> ( k4_finseq_1(B) = k4_finseq_1(D)
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k4_finseq_1(B))
                             => k1_goboard1(D,E) = k1_funct_1(C,k1_funct_1(B,E)) ) ) ) ) ) ) ) ) ) )).

fof(d16_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k10_graph_5(A,B,C) = k15_rvsum_1(k9_graph_5(A,B,C)) ) ) ) )).

fof(t50_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ( r5_graph_5(B,A)
           => r6_graph_5(B,A) ) ) ) )).

fof(t51_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( m2_finseq_1(D,k1_numbers)
                 => ( ( r5_graph_5(B,A)
                      & D = k9_graph_5(B,C,A) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k4_finseq_1(D))
                         => r1_xreal_0(np__0,k1_goboard1(D,E)) ) ) ) ) ) ) ) )).

fof(t52_graph_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v2_graph_1(C)
                & l1_graph_1(C) )
             => ! [D] :
                  ( m2_finseq_1(D,u2_graph_1(C))
                 => ! [E] :
                      ( m2_finseq_1(E,u2_graph_1(C))
                     => ~ ( r1_tarski(k2_relat_1(D),k2_relat_1(E))
                          & r6_graph_5(C,B)
                          & r2_hidden(A,k4_finseq_1(D))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(F,k4_finseq_1(E))
                                  & k1_goboard1(k9_graph_5(C,E,B),F) = k1_goboard1(k9_graph_5(C,D,B),A) ) ) ) ) ) ) ) ) )).

fof(t53_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( m2_finseq_1(D,u2_graph_1(B))
                 => ( ( k3_finseq_1(C) = np__1
                      & r1_tarski(k2_relat_1(C),k2_relat_1(D))
                      & r5_graph_5(B,A) )
                   => r1_xreal_0(k10_graph_5(B,C,A),k10_graph_5(B,D,A)) ) ) ) ) ) )).

fof(t54_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ( r5_graph_5(B,A)
               => r1_xreal_0(np__0,k10_graph_5(B,C,A)) ) ) ) ) )).

fof(t55_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ( ( C = k1_xboole_0
                  & r6_graph_5(B,A) )
               => k10_graph_5(B,C,A) = np__0 ) ) ) ) )).

fof(t56_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(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] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_finset_1(E)
                        & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(u2_graph_1(B)))) )
                     => ~ ( E = k4_graph_5(B,C,D)
                          & ! [F] :
                              ( m2_finseq_1(F,u2_graph_1(B))
                             => ~ ( r2_hidden(F,E)
                                  & ! [G] :
                                      ( m2_finseq_1(G,u2_graph_1(B))
                                     => ( r2_hidden(G,E)
                                       => r1_xreal_0(k10_graph_5(B,F,A),k10_graph_5(B,G,A)) ) ) ) ) ) ) ) ) ) ) )).

fof(t57_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v2_graph_1(C)
            & l1_graph_1(C) )
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(C))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(C))
                 => ! [F] :
                      ( ( ~ v1_xboole_0(F)
                        & v1_finset_1(F)
                        & m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(u2_graph_1(C)))) )
                     => ~ ( F = k5_graph_5(C,D,E,A)
                          & ! [G] :
                              ( m2_finseq_1(G,u2_graph_1(C))
                             => ~ ( r2_hidden(G,F)
                                  & ! [H] :
                                      ( m2_finseq_1(H,u2_graph_1(C))
                                     => ( r2_hidden(H,F)
                                       => r1_xreal_0(k10_graph_5(C,G,B),k10_graph_5(C,H,B)) ) ) ) ) ) ) ) ) ) ) )).

fof(t58_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( m2_finseq_1(D,u2_graph_1(B))
                 => ( r6_graph_5(B,A)
                   => k10_graph_5(B,k8_finseq_1(u2_graph_1(B),C,D),A) = k3_real_1(k10_graph_5(B,C,A),k10_graph_5(B,D,A)) ) ) ) ) ) )).

fof(t59_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( m2_finseq_1(D,u2_graph_1(B))
                 => ( ( v2_funct_1(C)
                      & r1_tarski(k2_relat_1(C),k2_relat_1(D))
                      & r5_graph_5(B,A) )
                   => r1_xreal_0(k10_graph_5(B,C,A),k10_graph_5(B,D,A)) ) ) ) ) ) )).

fof(t60_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u2_graph_1(B))
             => ! [D] :
                  ( ( v8_graph_1(D,B)
                    & m2_graph_1(D,B) )
                 => ( ( r2_hidden(C,k6_graph_5(B,D))
                      & r5_graph_5(B,A) )
                   => r1_xreal_0(k10_graph_5(B,C,A),k10_graph_5(B,D,A)) ) ) ) ) ) )).

fof(d17_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r7_graph_5(A,B,C,D,E)
                      <=> ( r1_graph_5(A,D,B,C)
                          & ! [F] :
                              ( ( v8_graph_1(F,A)
                                & m2_graph_1(F,A) )
                             => ( r1_graph_5(A,F,B,C)
                               => r1_xreal_0(k10_graph_5(A,D,E),k10_graph_5(A,F,E)) ) ) ) ) ) ) ) ) ) )).

fof(d18_graph_5,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] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ! [E,F] :
                      ( ( v1_relat_1(F)
                        & v1_funct_1(F) )
                     => ( r8_graph_5(A,B,C,D,E,F)
                      <=> ( r2_graph_5(A,B,C,D,E)
                          & ! [G] :
                              ( ( v8_graph_1(G,A)
                                & m2_graph_1(G,A) )
                             => ( r2_graph_5(A,B,C,G,E)
                               => r1_xreal_0(k10_graph_5(A,D,F),k10_graph_5(A,G,F)) ) ) ) ) ) ) ) ) ) )).

fof(t61_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & v1_graph_4(B,A)
            & m2_graph_1(B,A) )
         => r1_xreal_0(k3_finseq_1(B),k2_graph_1(A)) ) ) )).

fof(t62_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v7_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & v1_graph_4(B,A)
            & m2_graph_1(B,A) )
         => r1_xreal_0(k3_finseq_1(B),k3_graph_1(A)) ) ) )).

fof(t63_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(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))
                 => ~ ( k4_graph_5(B,C,D) != k1_xboole_0
                      & ! [E] :
                          ( m2_finseq_1(E,u2_graph_1(B))
                         => ~ ( r2_hidden(E,k4_graph_5(B,C,D))
                              & ! [F] :
                                  ( m2_finseq_1(F,u2_graph_1(B))
                                 => ( r2_hidden(F,k4_graph_5(B,C,D))
                                   => r1_xreal_0(k10_graph_5(B,E,A),k10_graph_5(B,F,A)) ) ) ) ) ) ) ) ) ) )).

fof(t64_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v2_graph_1(C)
            & v7_graph_1(C)
            & l1_graph_1(C) )
         => ! [D] :
              ( m1_subset_1(D,u1_graph_1(C))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(C))
                 => ~ ( k5_graph_5(C,D,E,A) != k1_xboole_0
                      & ! [F] :
                          ( m2_finseq_1(F,u2_graph_1(C))
                         => ~ ( r2_hidden(F,k5_graph_5(C,D,E,A))
                              & ! [G] :
                                  ( m2_finseq_1(G,u2_graph_1(C))
                                 => ( r2_hidden(G,k5_graph_5(C,D,E,A))
                                   => r1_xreal_0(k10_graph_5(C,F,B),k10_graph_5(C,G,B)) ) ) ) ) ) ) ) ) ) )).

fof(t65_graph_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v2_graph_1(B)
            & v7_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( ( v8_graph_1(C,B)
                & m2_graph_1(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_graph_1(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_graph_1(B))
                     => ~ ( r1_graph_5(B,C,D,E)
                          & r5_graph_5(B,A)
                          & ! [F] :
                              ( ( v8_graph_1(F,B)
                                & v1_graph_4(F,B)
                                & m2_graph_1(F,B) )
                             => ~ r7_graph_5(B,D,E,F,A) ) ) ) ) ) ) ) )).

fof(t66_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v2_graph_1(C)
            & v7_graph_1(C)
            & l1_graph_1(C) )
         => ! [D] :
              ( ( v8_graph_1(D,C)
                & m2_graph_1(D,C) )
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(C))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(C))
                     => ~ ( r2_graph_5(C,E,F,D,A)
                          & r5_graph_5(C,B)
                          & ! [G] :
                              ( ( v8_graph_1(G,C)
                                & v1_graph_4(G,C)
                                & m2_graph_1(G,C) )
                             => ~ r8_graph_5(C,E,F,G,A,B) ) ) ) ) ) ) ) )).

fof(t67_graph_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v2_graph_1(C)
            & v7_graph_1(C)
            & l1_graph_1(C) )
         => ! [D] :
              ( ( v8_graph_1(D,C)
                & m2_graph_1(D,C) )
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(C))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(C))
                     => ( ( r5_graph_5(C,B)
                          & r8_graph_5(C,E,F,D,A,B)
                          & ! [G] :
                              ( ( v8_graph_1(G,C)
                                & m2_graph_1(G,C) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_graph_1(C))
                                 => ( r8_graph_5(C,E,H,G,A,B)
                                   => ( r2_hidden(H,A)
                                      | r1_xreal_0(k10_graph_5(C,D,B),k10_graph_5(C,G,B)) ) ) ) ) )
                       => ( E = F
                          | r7_graph_5(C,E,F,D,B) ) ) ) ) ) ) ) )).

fof(t68_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v2_graph_1(D)
            & v7_graph_1(D)
            & l1_graph_1(D) )
         => ! [E] :
              ( ( v8_graph_1(E,D)
                & m2_graph_1(E,D) )
             => ! [F] :
                  ( m1_subset_1(F,u1_graph_1(D))
                 => ! [G] :
                      ( m1_subset_1(G,u1_graph_1(D))
                     => ( ( r5_graph_5(D,C)
                          & r8_graph_5(D,F,G,E,A,C)
                          & r1_tarski(A,B)
                          & ! [H] :
                              ( ( v8_graph_1(H,D)
                                & m2_graph_1(H,D) )
                             => ! [I] :
                                  ( m1_subset_1(I,u1_graph_1(D))
                                 => ( r8_graph_5(D,F,I,H,A,C)
                                   => ( r2_hidden(I,A)
                                      | r1_xreal_0(k10_graph_5(D,E,C),k10_graph_5(D,H,C)) ) ) ) ) )
                       => ( F = G
                          | r8_graph_5(D,F,G,E,B,C) ) ) ) ) ) ) ) )).

fof(d19_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => ! [C,D] :
              ( m1_subset_1(D,u1_graph_1(A))
             => ! [E] :
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( r9_graph_5(A,B,C,D,E)
                  <=> ! [F] :
                        ( m1_subset_1(F,u1_graph_1(A))
                       => ~ ( r2_hidden(F,C)
                            & F != D
                            & ! [G] :
                                ( ( v8_graph_1(G,A)
                                  & m2_graph_1(G,A) )
                               => ~ ( r8_graph_5(A,D,F,G,C,E)
                                    & r1_xreal_0(k10_graph_5(A,G,E),k10_graph_5(A,B,E)) ) ) ) ) ) ) ) ) ) )).

fof(t69_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v2_graph_1(D)
            & v3_graph_1(D)
            & v7_graph_1(D)
            & l1_graph_1(D) )
         => ! [E] :
              ( ( v8_graph_1(E,D)
                & m2_graph_1(E,D) )
             => ! [F] :
                  ( ( v8_graph_1(F,D)
                    & m2_graph_1(F,D) )
                 => ! [G] :
                      ( ( v8_graph_1(G,D)
                        & m2_graph_1(G,D) )
                     => ! [H] :
                          ( m1_subset_1(H,u1_graph_1(D))
                         => ! [I] :
                              ( m1_subset_1(I,u1_graph_1(D))
                             => ! [J] :
                                  ( m1_subset_1(J,u1_graph_1(D))
                                 => ( ( r2_hidden(A,u2_graph_1(D))
                                      & r5_graph_5(D,C)
                                      & r1_xreal_0(np__1,k3_finseq_1(E))
                                      & r8_graph_5(D,H,I,E,B,C)
                                      & G = k7_finseq_1(E,k9_finseq_1(A))
                                      & r8_graph_5(D,H,J,F,B,C)
                                      & r1_graph_4(D,I,J,A)
                                      & r9_graph_5(D,E,B,H,C) )
                                   => ( H = I
                                      | H = J
                                      | ( ( r1_xreal_0(k10_graph_5(D,F,C),k10_graph_5(D,G,C))
                                         => r8_graph_5(D,H,J,F,k2_xboole_0(B,k1_tarski(I)),C) )
                                        & ( r1_xreal_0(k10_graph_5(D,G,C),k10_graph_5(D,F,C))
                                         => r8_graph_5(D,H,J,G,k2_xboole_0(B,k1_tarski(I)),C) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(s1_graph_5,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_graph_5
      & ! [B] :
          ( m1_subset_1(B,f2_s1_graph_5)
         => ( r2_hidden(B,f1_s1_graph_5)
           => k1_funct_1(A,B) = f3_s1_graph_5(B) ) ) ) )).

fof(s2_graph_5,axiom,(
    ? [A] :
      ( m1_subset_1(A,f1_s2_graph_5)
      & ! [B] :
          ( m1_subset_1(B,f1_s2_graph_5)
         => r1_xreal_0(f2_s2_graph_5(A),f2_s2_graph_5(B)) ) ) )).

fof(dt_m1_graph_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_finseq_2(A))) )
     => ! [C] :
          ( m1_graph_5(C,A,B)
         => m2_finseq_1(C,A) ) ) )).

fof(existence_m1_graph_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_finseq_2(A))) )
     => ? [C] : m1_graph_5(C,A,B) ) )).

fof(redefinition_m1_graph_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_finseq_2(A))) )
     => ! [C] :
          ( m1_graph_5(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_k1_graph_5,axiom,(
    $true )).

fof(dt_k2_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_finseq_1(B,u2_graph_1(A)) )
     => m1_subset_1(k2_graph_5(A,B),k1_zfmisc_1(u1_graph_1(A))) ) )).

fof(dt_k3_graph_5,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)) )
     => m1_subset_1(k3_graph_5(A,B,C),k1_zfmisc_1(k3_finseq_2(u2_graph_1(A)))) ) )).

fof(dt_k4_graph_5,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)) )
     => m1_subset_1(k4_graph_5(A,B,C),k1_zfmisc_1(k3_finseq_2(u2_graph_1(A)))) ) )).

fof(dt_k5_graph_5,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A)) )
     => m1_subset_1(k5_graph_5(A,B,C,D),k1_zfmisc_1(k3_finseq_2(u2_graph_1(A)))) ) )).

fof(dt_k6_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & v8_graph_1(B,A)
        & m1_graph_1(B,A) )
     => m1_subset_1(k6_graph_5(A,B),k1_zfmisc_1(k3_finseq_2(u2_graph_1(A)))) ) )).

fof(dt_k7_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => m1_subset_1(k7_graph_5(A),k1_zfmisc_1(k3_finseq_2(u2_graph_1(A)))) ) )).

fof(dt_k8_graph_5,axiom,(
    m1_subset_1(k8_graph_5,k1_zfmisc_1(k1_numbers)) )).

fof(dt_k9_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_finseq_1(B,u2_graph_1(A))
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => m2_finseq_1(k9_graph_5(A,B,C),k1_numbers) ) )).

fof(dt_k10_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m1_finseq_1(B,u2_graph_1(A))
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => m1_subset_1(k10_graph_5(A,B,C),k1_numbers) ) )).

fof(t3_graph_5,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( C = a_2_0_graph_5(A,B)
             => v1_finset_1(C) ) ) ) )).

fof(t4_graph_5,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( C = a_2_1_graph_5(A,B)
             => v1_finset_1(C) ) ) ) )).

fof(d2_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u2_graph_1(A))
         => k2_graph_5(A,B) = a_2_2_graph_5(A,B) ) ) )).

fof(d5_graph_5,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))
             => k3_graph_5(A,B,C) = a_3_0_graph_5(A,B,C) ) ) ) )).

fof(d8_graph_5,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))
             => k4_graph_5(A,B,C) = a_3_1_graph_5(A,B,C) ) ) ) )).

fof(d9_graph_5,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] : k5_graph_5(A,B,C,D) = a_4_0_graph_5(A,B,C,D) ) ) ) )).

fof(d10_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => k6_graph_5(A,B) = a_2_3_graph_5(A,B) ) ) )).

fof(d11_graph_5,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => k7_graph_5(A) = a_1_0_graph_5(A) ) )).

fof(d12_graph_5,axiom,(
    k8_graph_5 = a_0_0_graph_5 )).

fof(fraenkel_a_2_0_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v1_finset_1(B)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_graph_5(B,C))
      <=> ? [D] :
            ( m2_finseq_2(D,B,k3_finseq_2(B))
            & A = D
            & r1_xreal_0(np__1,k3_finseq_1(D))
            & r1_xreal_0(k3_finseq_1(D),C) ) ) ) )).

fof(fraenkel_a_2_1_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v1_finset_1(B)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_1_graph_5(B,C))
      <=> ? [D] :
            ( m2_finseq_2(D,B,k3_finseq_2(B))
            & A = D
            & r1_xreal_0(k3_finseq_1(D),C) ) ) ) )).

fof(fraenkel_a_2_2_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & m2_finseq_1(C,u2_graph_1(B)) )
     => ( r2_hidden(A,a_2_2_graph_5(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_graph_1(B))
            & A = D
            & ? [E] :
                ( m2_subset_1(E,k1_numbers,k5_numbers)
                & r2_hidden(E,k4_finseq_1(C))
                & r2_hidden(D,k1_graph_5(B,k4_finseq_4(k5_numbers,u2_graph_1(B),C,E))) ) ) ) ) )).

fof(fraenkel_a_3_0_graph_5,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B))
        & m1_subset_1(D,u1_graph_1(B)) )
     => ( r2_hidden(A,a_3_0_graph_5(B,C,D))
      <=> ? [E] :
            ( v8_graph_1(E,B)
            & m2_graph_1(E,B)
            & A = E
            & r1_graph_5(B,E,C,D) ) ) ) )).

fof(fraenkel_a_3_1_graph_5,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B))
        & m1_subset_1(D,u1_graph_1(B)) )
     => ( r2_hidden(A,a_3_1_graph_5(B,C,D))
      <=> ? [E] :
            ( v8_graph_1(E,B)
            & v1_graph_4(E,B)
            & m2_graph_1(E,B)
            & A = E
            & r3_graph_5(B,E,C,D) ) ) ) )).

fof(fraenkel_a_4_0_graph_5,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & m1_subset_1(C,u1_graph_1(B))
        & m1_subset_1(D,u1_graph_1(B)) )
     => ( r2_hidden(A,a_4_0_graph_5(B,C,D,E))
      <=> ? [F] :
            ( v8_graph_1(F,B)
            & v1_graph_4(F,B)
            & m2_graph_1(F,B)
            & A = F
            & r4_graph_5(B,F,C,D,E) ) ) ) )).

fof(fraenkel_a_2_3_graph_5,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B)
        & v8_graph_1(C,B)
        & m2_graph_1(C,B) )
     => ( r2_hidden(A,a_2_3_graph_5(B,C))
      <=> ? [D] :
            ( v8_graph_1(D,B)
            & v1_graph_4(D,B)
            & m2_graph_1(D,B)
            & A = D
            & D != k1_xboole_0
            & k1_funct_1(u3_graph_1(B),k1_funct_1(D,np__1)) = k1_funct_1(u3_graph_1(B),k1_funct_1(C,np__1))
            & k1_funct_1(u4_graph_1(B),k1_funct_1(D,k3_finseq_1(D))) = k1_funct_1(u4_graph_1(B),k1_funct_1(C,k3_finseq_1(C)))
            & r1_tarski(k2_relat_1(D),k2_relat_1(C)) ) ) ) )).

fof(fraenkel_a_1_0_graph_5,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & l1_graph_1(B) )
     => ( r2_hidden(A,a_1_0_graph_5(B))
      <=> ? [C] :
            ( v8_graph_1(C,B)
            & v1_graph_4(C,B)
            & m2_graph_1(C,B)
            & A = C ) ) ) )).

fof(fraenkel_a_0_0_graph_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_graph_5)
    <=> ? [B] :
          ( m1_subset_1(B,k1_numbers)
          & A = B
          & r1_xreal_0(np__0,B) ) ) )).
%------------------------------------------------------------------------------