SET007 Axioms: SET007+769.ax


%------------------------------------------------------------------------------
% File     : SET007+769 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : 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    : graphsp [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  108 (   4 unit)
%            Number of atoms       :  830 ( 141 equality)
%            Maximal formula depth :   31 (  10 average)
%            Number of connectives :  760 (  38 ~  ;  18  |; 307  &)
%                                         (  23 <=>; 374 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   46 (   1 propositional; 0-6 arity)
%            Number of functors    :   67 (   8 constant; 0-4 arity)
%            Number of variables   :  404 (   0 singleton; 395 !;   9 ?)
%            Maximal term depth    :   10 (   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_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_finset_1(k15_graphsp(A,B))
        & v1_membered(k15_graphsp(A,B))
        & v2_membered(k15_graphsp(A,B))
        & v3_membered(k15_graphsp(A,B))
        & v4_membered(k15_graphsp(A,B))
        & v5_membered(k15_graphsp(A,B)) ) ) )).

fof(fc2_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_finset_1(k9_graphsp(A,B))
        & v1_membered(k9_graphsp(A,B))
        & v2_membered(k9_graphsp(A,B))
        & v3_membered(k9_graphsp(A,B))
        & v4_membered(k9_graphsp(A,B))
        & v5_membered(k9_graphsp(A,B)) ) ) )).

fof(t1_graphsp,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( ~ r2_hidden(B,k2_relat_1(A))
            & v2_funct_1(A) )
        <=> v2_funct_1(k7_finseq_1(A,k9_finseq_1(B))) ) ) )).

fof(t2_graphsp,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( v1_int_1(C)
         => ( ( r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(B)) )
           => r2_hidden(k1_funct_1(B,C),A) ) ) ) )).

fof(t3_graphsp,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( v1_int_1(C)
         => ( ( r1_xreal_0(np__1,C)
              & r1_xreal_0(C,k3_finseq_1(B)) )
           => k4_finseq_4(k5_numbers,A,B,C) = k1_funct_1(B,C) ) ) ) )).

fof(t4_graphsp,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)
                  & k3_finseq_1(B) = np__1 )
               => k10_graph_5(A,B,C) = k1_funct_1(C,k1_funct_1(B,np__1)) ) ) ) ) )).

fof(t5_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( r2_hidden(B,u2_graph_1(A))
         => ( v8_graph_1(k9_finseq_1(B),A)
            & v1_graph_4(k9_finseq_1(B),A)
            & m2_graph_1(k9_finseq_1(B),A) ) ) ) )).

fof(t6_graphsp,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(u4_graph_1(A),k1_funct_1(D,k3_finseq_1(D))) != 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(D,np__1)) != k1_funct_1(u3_graph_1(A),k1_funct_1(C,np__1)) ) ) ) ) ) ) )).

fof(t7_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C,D] :
              ( m1_subset_1(D,u1_graph_1(A))
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(A))
                 => ( r2_graph_5(A,D,E,B,C)
                  <=> r2_graph_5(A,D,E,B,k2_xboole_0(C,k1_tarski(E))) ) ) ) ) ) )).

fof(t8_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D,E] :
                  ( m1_subset_1(E,u1_graph_1(A))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(A))
                     => ( r8_graph_5(A,E,F,B,D,C)
                      <=> r8_graph_5(A,E,F,B,k2_xboole_0(D,k1_tarski(F)),C) ) ) ) ) ) ) )).

fof(t9_graphsp,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) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E,F] :
                      ( m1_subset_1(F,u1_graph_1(A))
                     => ! [G] :
                          ( m1_subset_1(G,u1_graph_1(A))
                         => ( ( r8_graph_5(A,F,G,B,E,D)
                              & r8_graph_5(A,F,G,C,E,D) )
                           => k10_graph_5(A,B,D) = k10_graph_5(A,C,D) ) ) ) ) ) ) ) )).

fof(t10_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_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,E] :
                  ( ( r2_hidden(D,u2_graph_1(A))
                    & r2_hidden(E,u2_graph_1(A))
                    & r1_graph_4(A,B,C,D)
                    & r1_graph_4(A,B,C,E) )
                 => D = E ) ) ) ) )).

fof(t11_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B,C,D] :
          ( m1_subset_1(D,u1_graph_1(A))
         => ! [E] :
              ( m1_subset_1(E,u1_graph_1(A))
             => ( ( u1_graph_1(A) = k2_xboole_0(B,C)
                  & r2_hidden(D,B)
                  & r2_hidden(E,C)
                  & ! [F] :
                      ( m1_subset_1(F,u1_graph_1(A))
                     => ! [G] :
                          ( m1_subset_1(G,u1_graph_1(A))
                         => ( ( r2_hidden(F,B)
                              & r2_hidden(G,C) )
                           => ! [H] :
                                ~ ( r2_hidden(H,u2_graph_1(A))
                                  & r1_graph_4(A,F,G,H) ) ) ) ) )
               => ! [F] :
                    ( ( v8_graph_1(F,A)
                      & m2_graph_1(F,A) )
                   => ~ r1_graph_5(A,F,D,E) ) ) ) ) ) )).

fof(t12_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v8_graph_1(B,A)
            & m2_graph_1(B,A) )
         => ! [C,D,E] :
              ( m1_subset_1(E,u1_graph_1(A))
             => ! [F] :
                  ( m1_subset_1(F,u1_graph_1(A))
                 => ( ( u1_graph_1(A) = k2_xboole_0(C,D)
                      & r2_hidden(E,C)
                      & ! [G] :
                          ( m1_subset_1(G,u1_graph_1(A))
                         => ! [H] :
                              ( m1_subset_1(H,u1_graph_1(A))
                             => ( ( r2_hidden(G,C)
                                  & r2_hidden(H,D) )
                               => ! [I] :
                                    ~ ( r2_hidden(I,u2_graph_1(A))
                                      & r1_graph_4(A,G,H,I) ) ) ) )
                      & r1_graph_5(A,B,E,F) )
                   => r2_graph_5(A,E,F,B,C) ) ) ) ) ) )).

fof(t13_graphsp,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [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] :
                  ( ( v8_graph_1(E,C)
                    & m2_graph_1(E,C) )
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(C))
                     => ! [G] :
                          ( m1_subset_1(G,u1_graph_1(C))
                         => ! [H] :
                              ( m1_subset_1(H,u1_graph_1(C))
                             => ( ( r5_graph_5(C,A)
                                  & r8_graph_5(C,F,G,D,B,A)
                                  & r8_graph_5(C,F,H,E,B,A)
                                  & ! [I] :
                                      ~ ( r2_hidden(I,u2_graph_1(C))
                                        & r1_graph_4(C,G,H,I) )
                                  & r9_graph_5(C,D,B,F,A) )
                               => ( F = G
                                  | F = H
                                  | r8_graph_5(C,F,H,E,k2_xboole_0(B,k1_tarski(G)),A) ) ) ) ) ) ) ) ) ) )).

fof(t14_graphsp,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v3_graph_1(B)
        & v7_graph_1(B)
        & l1_graph_1(B) )
     => ! [C] :
          ( ( v8_graph_1(C,B)
            & m2_graph_1(C,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,u2_graph_1(B),k8_graph_5)
                & m2_relset_1(D,u2_graph_1(B),k8_graph_5) )
             => ! [E] :
                  ( m1_subset_1(E,u1_graph_1(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_graph_1(B))
                     => ( ( r2_hidden(A,u2_graph_1(B))
                          & C = k9_finseq_1(A)
                          & r1_graph_4(B,E,F,A) )
                       => ( E = F
                          | r8_graph_5(B,E,F,C,k1_tarski(E),D) ) ) ) ) ) ) ) )).

fof(t15_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & v3_graph_1(C)
        & v7_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( ( v8_graph_1(D,C)
            & m2_graph_1(D,C) )
         => ! [E] :
              ( ( v8_graph_1(E,C)
                & m2_graph_1(E,C) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & v1_funct_2(F,u2_graph_1(C),k8_graph_5)
                    & m2_relset_1(F,u2_graph_1(C),k8_graph_5) )
                 => ! [G] :
                      ( m1_subset_1(G,u1_graph_1(C))
                     => ! [H] :
                          ( m1_subset_1(H,u1_graph_1(C))
                         => ! [I] :
                              ( m1_subset_1(I,u1_graph_1(C))
                             => ( ( r2_hidden(A,u2_graph_1(C))
                                  & r8_graph_5(C,G,H,D,B,F)
                                  & E = k7_finseq_1(D,k9_finseq_1(A))
                                  & r1_graph_4(C,H,I,A)
                                  & r2_hidden(G,B)
                                  & ! [J] :
                                      ( m1_subset_1(J,u1_graph_1(C))
                                     => ( r2_hidden(J,B)
                                       => ! [K] :
                                            ~ ( r2_hidden(K,u2_graph_1(C))
                                              & r1_graph_4(C,J,I,K) ) ) ) )
                               => ( G = I
                                  | r8_graph_5(C,G,I,E,k2_xboole_0(B,k1_tarski(H)),F) ) ) ) ) ) ) ) ) ) )).

fof(t16_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v2_graph_1(C)
        & v3_graph_1(C)
        & v7_graph_1(C)
        & l1_graph_1(C) )
     => ! [D] :
          ( ( v8_graph_1(D,C)
            & m2_graph_1(D,C) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & v1_funct_2(E,u2_graph_1(C),k8_graph_5)
                & m2_relset_1(E,u2_graph_1(C),k8_graph_5) )
             => ! [F] :
                  ( m1_subset_1(F,u1_graph_1(C))
                 => ! [G] :
                      ( m1_subset_1(G,u1_graph_1(C))
                     => ( ( u1_graph_1(C) = k2_xboole_0(A,B)
                          & r2_hidden(F,A)
                          & ! [H] :
                              ( m1_subset_1(H,u1_graph_1(C))
                             => ! [I] :
                                  ( m1_subset_1(I,u1_graph_1(C))
                                 => ( ( r2_hidden(H,A)
                                      & r2_hidden(I,B) )
                                   => ! [J] :
                                        ~ ( r2_hidden(J,u2_graph_1(C))
                                          & r1_graph_4(C,H,I,J) ) ) ) ) )
                       => ( r8_graph_5(C,F,G,D,A,E)
                        <=> r7_graph_5(C,F,G,D,E) ) ) ) ) ) ) ) )).

fof(t17_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_tarski(k2_relat_1(k2_funct_7(C,A,B)),k2_xboole_0(k2_relat_1(C),k1_tarski(B))) ) )).

fof(d1_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k2_graphsp(A,B,C,D) = k1_graphsp(k1_graphsp(C,A,B),B,D) ) ) ) ) )).

fof(t18_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r2_hidden(A,k4_finseq_1(C))
                   => ( A = B
                      | k1_goboard1(k2_graphsp(A,B,C,D),A) = B ) ) ) ) ) ) )).

fof(t19_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( r2_hidden(A,k4_finseq_1(D))
                       => ( A = B
                          | A = C
                          | k1_goboard1(k2_graphsp(B,C,D,E),A) = k1_goboard1(D,A) ) ) ) ) ) ) ) )).

fof(t20_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r2_hidden(A,k4_finseq_1(C))
                   => k1_goboard1(k2_graphsp(B,A,C,D),A) = D ) ) ) ) ) )).

fof(t21_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k4_finseq_1(k2_graphsp(A,B,C,D)) = k4_finseq_1(C) ) ) ) ) )).

fof(d2_graphsp,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_funct_2(A,A))
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_funct_2(A,A))
            & m2_relset_1(C,k5_numbers,k1_funct_2(A,A)) )
         => ( C = k7_graphsp(A,B)
          <=> ( k8_funct_2(k5_numbers,k1_funct_2(A,A),C,np__0) = k3_graphsp(A)
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k8_funct_2(k5_numbers,k1_funct_2(A,A),C,k1_nat_1(D,np__1)) = k5_graphsp(A,k8_funct_2(k5_numbers,k1_funct_2(A,A),C,D),B) ) ) ) ) ) )).

fof(t22_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),np__0),B) = B ) ) ) ) )).

fof(t23_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
     => ! [B] :
          ( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),B,A)),k1_nat_1(D,np__1)),C) = k6_graphsp(k3_finseq_2(k1_numbers),A,k6_graphsp(k3_finseq_2(k1_numbers),B,k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),B,A)),D),C))) ) ) ) ) )).

fof(d4_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( D = k10_graphsp(A,B,C)
                    <=> ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),E),B),C) = k1_xboole_0
                             => r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) )).

fof(d5_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
             => ( C = k11_graphsp(A,B)
              <=> ( k1_relat_1(C) = k3_finseq_2(k1_numbers)
                  & ! [D] :
                      ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                     => k8_graphsp(C,D) = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),k10_graphsp(A,D,B)),D) ) ) ) ) ) ) )).

fof(d6_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_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] :
                    ( r2_hidden(D,u2_graph_1(A))
                    & r1_graph_4(A,B,C,D) )
               => ! [D] :
                    ( D = k12_graphsp(A,B,C)
                  <=> ? [E] :
                        ( D = E
                        & r2_hidden(E,u2_graph_1(A))
                        & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).

fof(d7_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_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_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( ? [E] :
                          ( r2_hidden(E,u2_graph_1(A))
                          & r1_graph_4(A,B,C,E) )
                     => k13_graphsp(A,B,C,D) = k1_funct_1(D,k12_graphsp(A,B,C)) )
                    & ( ! [E] :
                          ~ ( r2_hidden(E,u2_graph_1(A))
                            & r1_graph_4(A,B,C,E) )
                     => k13_graphsp(A,B,C,D) = k1_real_1(np__1) ) ) ) ) ) ) )).

fof(t24_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_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_funct_1(D)
                    & v1_funct_2(D,u2_graph_1(A),k8_graph_5)
                    & m2_relset_1(D,u2_graph_1(A),k8_graph_5) )
                 => ( r1_xreal_0(np__0,k14_graphsp(A,B,C,D))
                  <=> ? [E] :
                        ( r2_hidden(E,u2_graph_1(A))
                        & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).

fof(t25_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_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_funct_1(D)
                    & v1_funct_2(D,u2_graph_1(A),k8_graph_5)
                    & m2_relset_1(D,u2_graph_1(A),k8_graph_5) )
                 => ( k14_graphsp(A,B,C,D) = k1_real_1(np__1)
                  <=> ! [E] :
                        ~ ( r2_hidden(E,u2_graph_1(A))
                          & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).

fof(t26_graphsp,axiom,(
    ! [A,B] :
      ( ( v2_graph_1(B)
        & v3_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_funct_1(E)
                    & v1_funct_2(E,u2_graph_1(B),k8_graph_5)
                    & m2_relset_1(E,u2_graph_1(B),k8_graph_5) )
                 => ( ( r2_hidden(A,u2_graph_1(B))
                      & r1_graph_4(B,C,D,A) )
                   => k14_graphsp(B,C,D,E) = k1_funct_1(E,A) ) ) ) ) ) )).

fof(t27_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => r1_tarski(k15_graphsp(B,A),k2_finseq_1(A)) ) ) )).

fof(t28_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => r1_tarski(k9_graphsp(B,A),k15_graphsp(B,A)) ) ) )).

fof(t29_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => r1_tarski(k9_graphsp(B,A),k2_finseq_1(A)) ) ) )).

fof(d10_graphsp,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( D = k17_graphsp(A,B,C)
                  <=> ( ~ ( A != k1_xboole_0
                          & ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ ( E = D
                                  & r2_hidden(E,A)
                                  & ! [F] :
                                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                                     => ( r2_hidden(F,A)
                                       => r1_xreal_0(k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),E)),k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),F))) ) )
                                  & ! [F] :
                                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                                     => ( ( r2_hidden(F,A)
                                          & k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),E)) = k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),F)) )
                                       => r1_xreal_0(E,F) ) ) ) ) )
                      & ( A = k1_xboole_0
                       => D = np__0 ) ) ) ) ) ) ) )).

fof(t30_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( B = k17_graphsp(k9_graphsp(C,A),C,A)
               => ( k9_graphsp(C,A) = k1_xboole_0
                  | ( r2_hidden(B,k4_finseq_1(C))
                    & r1_xreal_0(np__1,B)
                    & r1_xreal_0(B,A)
                    & k1_goboard1(C,B) != k1_real_1(np__1)
                    & k1_goboard1(C,k1_nat_1(A,B)) != k1_real_1(np__1) ) ) ) ) ) ) )).

fof(t31_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => r1_xreal_0(k17_graphsp(k9_graphsp(B,A),B,A),A) ) ) )).

fof(d11_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
         => ( B = k18_graphsp(A)
          <=> ( k1_relat_1(B) = k3_finseq_2(k1_numbers)
              & ! [C] :
                  ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
                 => k8_graphsp(B,C) = k2_graphsp(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A)),np__1),k17_graphsp(k9_graphsp(C,A),C,A),C,k1_real_1(np__1)) ) ) ) ) ) )).

fof(t32_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( r2_hidden(A,k4_finseq_1(C))
               => ( r1_xreal_0(A,B)
                  | A = k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)
                  | k1_goboard1(k8_graphsp(k18_graphsp(B),C),A) = k1_goboard1(C,A) ) ) ) ) ) )).

fof(t33_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( ( r2_hidden(A,k4_finseq_1(C))
                  & k1_goboard1(C,A) = k1_real_1(np__1) )
               => ( A = k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)
                  | k1_goboard1(k8_graphsp(k18_graphsp(B),C),A) = k1_real_1(np__1) ) ) ) ) ) )).

fof(t34_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => k4_finseq_1(k8_graphsp(k18_graphsp(A),B)) = k4_finseq_1(B) ) ) )).

fof(t35_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ~ ( k9_graphsp(B,A) != k1_xboole_0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(C,k9_graphsp(B,A))
                      & r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,A)
                      & k1_goboard1(k8_graphsp(k18_graphsp(A),B),C) = k1_real_1(np__1) ) ) ) ) ) )).

fof(d12_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k19_graphsp(A,B,C) = k3_real_1(k4_finseq_4(k5_numbers,k1_numbers,A,k3_real_1(k2_nat_1(np__2,B),k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)))),k4_finseq_4(k5_numbers,k1_numbers,A,k3_real_1(k3_real_1(k2_nat_1(np__2,B),k4_real_1(B,k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)))),C))) ) ) ) )).

fof(d13_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( r1_graphsp(A,B,C)
              <=> ( ~ ( k1_goboard1(C,k1_nat_1(A,B)) != k1_real_1(np__1)
                      & r1_xreal_0(k4_finseq_4(k5_numbers,k1_numbers,C,k1_nat_1(k2_nat_1(np__2,A),B)),k19_graphsp(C,A,B)) )
                  & r1_xreal_0(np__0,k4_finseq_4(k5_numbers,k1_numbers,C,k3_real_1(k3_real_1(k2_nat_1(np__2,A),k4_real_1(A,k4_finseq_4(k5_numbers,k1_numbers,C,k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A)),np__1)))),B)))
                  & k1_goboard1(C,B) != k1_real_1(np__1) ) ) ) ) ) )).

fof(d14_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( C = k20_graphsp(A,B)
              <=> ( k4_finseq_1(C) = k4_finseq_1(A)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => ( ( r1_xreal_0(D,k2_nat_1(np__2,B))
                           => ( r1_xreal_0(D,B)
                              | ( ( r1_graphsp(B,k5_binarith(D,B),A)
                                 => k1_goboard1(C,D) = k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)) )
                                & ( ~ r1_graphsp(B,k5_binarith(D,B),A)
                                 => k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) )
                          & ( r1_xreal_0(D,k2_nat_1(np__3,B))
                           => ( r1_xreal_0(D,k2_nat_1(np__2,B))
                              | ( ( r1_graphsp(B,k5_binarith(D,k2_nat_1(np__2,B)),A)
                                 => k1_goboard1(C,D) = k19_graphsp(A,B,k5_binarith(D,k2_nat_1(np__2,B))) )
                                & ( ~ r1_graphsp(B,k5_binarith(D,k2_nat_1(np__2,B)),A)
                                 => k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) )
                          & ( ~ ( ~ r1_xreal_0(D,B)
                                & r1_xreal_0(D,k2_nat_1(np__3,B)) )
                           => k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) ) ) ) ) ) ) )).

fof(d15_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
         => ( B = k21_graphsp(A)
          <=> ( k1_relat_1(B) = k3_finseq_2(k1_numbers)
              & ! [C] :
                  ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
                 => k8_graphsp(B,C) = k20_graphsp(C,A) ) ) ) ) ) )).

fof(t36_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => k4_finseq_1(k8_graphsp(k21_graphsp(A),B)) = k4_finseq_1(B) ) ) )).

fof(t37_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( r2_hidden(A,k4_finseq_1(C))
               => ( ( ~ r1_xreal_0(A,B)
                    & r1_xreal_0(A,k2_nat_1(np__3,B)) )
                  | k1_goboard1(k8_graphsp(k21_graphsp(B),C),A) = k1_goboard1(C,A) ) ) ) ) ) )).

fof(t38_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C)) = k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C)) ) ) ) )).

fof(t39_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),A) != k1_xboole_0
               => r2_xboole_0(k15_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C),A),k15_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),A)) ) ) ) ) )).

fof(t40_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                 => ! [E] :
                      ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
                     => ! [F] :
                          ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers))
                         => ( ( D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),E)
                              & F = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),E)
                              & C = k17_graphsp(k9_graphsp(D,A),D,A) )
                           => ( k9_graphsp(D,A) = k1_xboole_0
                              | ( k16_graphsp(F,A) = k4_subset_1(k5_numbers,k16_graphsp(D,A),k6_domain_1(k5_numbers,C))
                                & ~ r2_hidden(C,k16_graphsp(D,A)) ) ) ) ) ) ) ) ) ) )).

fof(t41_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ? [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & r1_xreal_0(C,A)
              & k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),C),B),A) = k1_xboole_0 ) ) ) )).

fof(t42_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => k4_finseq_1(C) = k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C)) ) ) ) )).

fof(d16_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_graphsp(A,B,C,D)
                  <=> ( k4_finseq_1(A) = k4_finseq_1(B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(E,k4_finseq_1(A))
                              & r1_xreal_0(C,E)
                              & r1_xreal_0(E,D) )
                           => k1_goboard1(A,E) = k1_goboard1(B,E) ) ) ) ) ) ) ) ) )).

fof(t43_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => r2_graphsp(C,C,A,B) ) ) ) )).

fof(t44_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                 => ! [E] :
                      ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
                     => ( ( r2_graphsp(C,D,A,B)
                          & r2_graphsp(D,E,A,B) )
                       => r2_graphsp(C,E,A,B) ) ) ) ) ) ) )).

fof(t45_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => r2_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C),k1_nat_1(k2_nat_1(np__3,A),np__1),k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A))) ) ) ) )).

fof(t46_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(k10_graphsp(A,B,C),D)
                      & k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 ) ) ) ) ) )).

fof(t47_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => r2_graphsp(C,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),k1_nat_1(k2_nat_1(np__3,A),np__1),k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A))) ) ) ) )).

fof(t48_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ( ( r1_xreal_0(np__1,A)
              & r2_hidden(np__1,k4_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,A) )
                   => k1_goboard1(B,C) = np__1 ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__2,C)
                      & r1_xreal_0(C,A) )
                   => k1_goboard1(B,k1_nat_1(A,C)) = k1_real_1(np__1) ) ) )
           => ( k1_goboard1(B,k1_nat_1(A,np__1)) = k1_real_1(np__1)
              | ( np__1 = k17_graphsp(k9_graphsp(B,A),B,A)
                & k16_graphsp(B,A) = k1_xboole_0
                & k6_domain_1(k5_numbers,np__1) = k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),np__1),B),A) ) ) ) ) ) )).

fof(t49_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                 => ! [E] :
                      ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
                     => ! [F] :
                          ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers))
                         => ( ( D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),np__1),E)
                              & F = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),E)
                              & r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),E,A))
                              & r2_hidden(C,k16_graphsp(D,A)) )
                           => r2_hidden(C,k16_graphsp(F,A)) ) ) ) ) ) ) ) )).

fof(d17_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r3_graphsp(A,B,C,D)
                  <=> ( k1_funct_1(A,k3_finseq_1(A)) = C
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(np__1,E)
                           => ( r1_xreal_0(k3_finseq_1(A),E)
                              | k1_funct_1(A,k5_real_1(k3_finseq_1(A),E)) = k1_goboard1(B,k1_nat_1(D,k4_finseq_4(k5_numbers,k5_numbers,A,k3_real_1(k5_real_1(k3_finseq_1(A),E),np__1)))) ) ) ) ) ) ) ) ) ) )).

fof(d18_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r4_graphsp(A,B,C,D)
                  <=> ( k1_funct_1(A,np__1) = np__1
                      & ~ r1_xreal_0(k3_finseq_1(A),np__1)
                      & r3_graphsp(A,B,C,D)
                      & v2_funct_1(A) ) ) ) ) ) ) )).

fof(t50_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r4_graphsp(A,C,D,E)
                          & r4_graphsp(B,C,D,E) )
                       => A = B ) ) ) ) ) ) )).

fof(d19_graphsp,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)
                & v1_finseq_1(C) )
             => ( r5_graphsp(A,B,C)
              <=> ( k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),np__1)
                  & ! [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(u3_graph_1(A),k1_funct_1(B,D)) = 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)) ) ) ) ) ) ) ) ) )).

fof(t51_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & v3_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ! [D] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( ( r5_graphsp(A,C,B)
                      & r5_graphsp(A,D,B) )
                   => C = D ) ) ) ) ) )).

fof(t52_graphsp,axiom,(
    ! [A] :
      ( ( v2_graph_1(A)
        & l1_graph_1(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) )
             => ! [D] :
                  ( ( v8_graph_1(D,A)
                    & m2_graph_1(D,A) )
                 => ( ( r5_graphsp(A,D,B)
                      & r5_graphsp(A,D,C)
                      & r1_xreal_0(np__1,k3_finseq_1(D)) )
                   => B = C ) ) ) ) ) )).

fof(d20_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( ( v2_graph_1(B)
            & v3_graph_1(B)
            & l1_graph_1(B) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u2_graph_1(B),k8_graph_5)
                    & m2_relset_1(D,u2_graph_1(B),k8_graph_5) )
                 => ( r6_graphsp(A,B,C,D)
                  <=> ( k3_finseq_1(A) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(np__3,C)),np__1)
                      & k2_finseq_1(C) = u1_graph_1(B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,C) )
                           => ( k1_goboard1(A,E) = np__1
                              & k1_goboard1(A,k1_nat_1(k2_nat_1(np__2,C),E)) = np__0 ) ) )
                      & k1_goboard1(A,k1_nat_1(C,np__1)) = np__0
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__2,E)
                              & r1_xreal_0(E,C) )
                           => k1_goboard1(A,k1_nat_1(C,E)) = k1_real_1(np__1) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_graph_1(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_graph_1(B))
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ( G = E
                                          & H = F )
                                       => k1_goboard1(A,k1_nat_1(k1_nat_1(k2_nat_1(np__2,C),k2_nat_1(C,G)),H)) = k14_graphsp(B,E,F,D) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d21_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k22_graphsp(A) = k11_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),A) ) )).

fof(t53_graphsp,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
             => ! [D] :
                  ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
                 => ! [E] :
                      ( ( v2_graph_1(E)
                        & v3_graph_1(E)
                        & v7_graph_1(E)
                        & l1_graph_1(E) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u2_graph_1(E),k8_graph_5)
                            & m2_relset_1(F,u2_graph_1(E),k8_graph_5) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_graph_1(E))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_graph_1(E))
                                 => ( ( r6_graphsp(C,E,A,F)
                                      & G = np__1
                                      & H = B
                                      & r1_xreal_0(np__1,A)
                                      & D = k8_graphsp(k22_graphsp(A),C) )
                                   => ( np__1 = H
                                      | ( u1_graph_1(E) = k4_subset_1(k5_numbers,k16_graphsp(D,A),k15_graphsp(D,A))
                                        & ~ ( r2_hidden(H,k16_graphsp(D,A))
                                            & ! [I] :
                                                ( m2_finseq_1(I,k5_numbers)
                                               => ! [J] :
                                                    ( ( v8_graph_1(J,E)
                                                      & m2_graph_1(J,E) )
                                                   => ~ ( r4_graphsp(I,D,B,A)
                                                        & r5_graphsp(E,J,I)
                                                        & r7_graph_5(E,G,H,J,F)
                                                        & k10_graph_5(E,J,F) = k1_goboard1(D,k1_nat_1(k2_nat_1(np__2,A),B)) ) ) ) )
                                        & ( r2_hidden(H,k15_graphsp(D,A))
                                         => ! [I] :
                                              ( ( v8_graph_1(I,E)
                                                & m2_graph_1(I,E) )
                                             => ~ r1_graph_5(E,I,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => m2_finseq_1(k1_graphsp(A,B,C),k1_numbers) ) )).

fof(redefinition_k1_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => k1_graphsp(A,B,C) = k2_funct_7(A,B,C) ) )).

fof(dt_k2_graphsp,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_finseq_1(C,k1_numbers)
        & m1_subset_1(D,k1_numbers) )
     => m2_finseq_1(k2_graphsp(A,B,C,D),k1_numbers) ) )).

fof(dt_k3_graphsp,axiom,(
    ! [A] : m1_subset_1(k3_graphsp(A),k1_funct_2(A,A)) )).

fof(redefinition_k3_graphsp,axiom,(
    ! [A] : k3_graphsp(A) = k6_relat_1(A) )).

fof(dt_k4_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k4_graphsp(A,B,C))
        & v1_funct_2(k4_graphsp(A,B,C),A,A)
        & m2_relset_1(k4_graphsp(A,B,C),A,A) ) ) )).

fof(redefinition_k4_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => k4_graphsp(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k5_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_funct_2(A,A))
        & m1_subset_1(C,k1_funct_2(A,A)) )
     => m1_subset_1(k5_graphsp(A,B,C),k1_funct_2(A,A)) ) )).

fof(redefinition_k5_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_funct_2(A,A))
        & m1_subset_1(C,k1_funct_2(A,A)) )
     => k5_graphsp(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k6_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_funct_2(A,A))
        & m1_subset_1(C,A) )
     => m1_subset_1(k6_graphsp(A,B,C),A) ) )).

fof(redefinition_k6_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_funct_2(A,A))
        & m1_subset_1(C,A) )
     => k6_graphsp(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k7_graphsp,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_funct_2(A,A))
     => ( v1_funct_1(k7_graphsp(A,B))
        & v1_funct_2(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A))
        & m2_relset_1(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A)) ) ) )).

fof(dt_k8_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
        & m1_subset_1(B,k3_finseq_2(k1_numbers)) )
     => m2_finseq_2(k8_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) )).

fof(redefinition_k8_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
        & m1_subset_1(B,k3_finseq_2(k1_numbers)) )
     => k8_graphsp(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k9_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k9_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) )).

fof(dt_k10_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
        & m1_subset_1(B,k3_finseq_2(k1_numbers))
        & m1_subset_1(C,k5_numbers) )
     => m2_subset_1(k10_graphsp(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k11_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k11_graphsp(A,B),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) )).

fof(dt_k12_graphsp,axiom,(
    $true )).

fof(dt_k13_graphsp,axiom,(
    $true )).

fof(dt_k14_graphsp,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(A)
        & v3_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,u2_graph_1(A),k8_graph_5)
        & m1_relset_1(D,u2_graph_1(A),k8_graph_5) )
     => m1_subset_1(k14_graphsp(A,B,C,D),k1_numbers) ) )).

fof(redefinition_k14_graphsp,axiom,(
    ! [A,B,C,D] :
      ( ( v2_graph_1(A)
        & v3_graph_1(A)
        & l1_graph_1(A)
        & m1_subset_1(B,u1_graph_1(A))
        & m1_subset_1(C,u1_graph_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,u2_graph_1(A),k8_graph_5)
        & m1_relset_1(D,u2_graph_1(A),k8_graph_5) )
     => k14_graphsp(A,B,C,D) = k13_graphsp(A,B,C,D) ) )).

fof(dt_k15_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k15_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) )).

fof(dt_k16_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k16_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) )).

fof(dt_k17_graphsp,axiom,(
    ! [A,B,C] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers))
        & m1_subset_1(B,k3_finseq_2(k1_numbers))
        & m1_subset_1(C,k5_numbers) )
     => m2_subset_1(k17_graphsp(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k18_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k18_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) )).

fof(dt_k19_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k19_graphsp(A,B,C),k1_numbers) ) )).

fof(dt_k20_graphsp,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => m2_finseq_2(k20_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) )).

fof(dt_k21_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k21_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) )).

fof(dt_k22_graphsp,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k22_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) )).

fof(d3_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k9_graphsp(A,B) = a_2_0_graphsp(A,B) ) ) )).

fof(d8_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k15_graphsp(A,B) = a_2_1_graphsp(A,B) ) ) )).

fof(d9_graphsp,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k16_graphsp(A,B) = a_2_2_graphsp(A,B) ) ) )).

fof(fraenkel_a_2_0_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_graphsp(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & r2_hidden(D,k4_finseq_1(B))
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,C)
            & k1_goboard1(B,D) != k1_real_1(np__1)
            & k1_goboard1(B,k1_nat_1(C,D)) != k1_real_1(np__1) ) ) ) )).

fof(fraenkel_a_2_1_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_1_graphsp(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & r2_hidden(D,k4_finseq_1(B))
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,C)
            & k1_goboard1(B,D) != k1_real_1(np__1) ) ) ) )).

fof(fraenkel_a_2_2_graphsp,axiom,(
    ! [A,B,C] :
      ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_2_graphsp(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = D
            & r2_hidden(D,k4_finseq_1(B))
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,C)
            & k1_goboard1(B,D) = k1_real_1(np__1) ) ) ) )).
%------------------------------------------------------------------------------