SET007 Axioms: SET007+597.ax


%------------------------------------------------------------------------------
% File     : SET007+597 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Cells on Go Board
% 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    : gobrd13 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (   2 unit)
%            Number of atoms       : 1127 ( 189 equality)
%            Maximal formula depth :   30 (  16 average)
%            Number of connectives : 1162 ( 105 ~  ;  11  |; 705  &)
%                                         (   9 <=>; 332 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-4 arity)
%            Number of functors    :   42 (   4 constant; 0-4 arity)
%            Number of variables   :  315 (   0 singleton; 312 !;   3 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_gobrd13,axiom,(
    ! [A,B] :
      ( m1_finseq_1(B,k3_finseq_2(A))
     => v1_matrlin(B) ) )).

fof(cc2_gobrd13,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_matrlin(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) ) ) )).

fof(fc1_gobrd13,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k3_finseq_2(A)) )
     => v1_finset_1(k2_gobrd13(B)) ) )).

fof(d1_gobrd13,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k2_gobrd13(A) = k3_card_3(k3_funct_6(A)) ) )).

fof(t1_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k3_finseq_2(B))
             => m2_finseq_1(k1_funct_1(C,A),B) ) ) ) )).

fof(t2_gobrd13,axiom,(
    $true )).

fof(t4_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(B)) )
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & k1_funct_1(D,A) = C )
                   => k3_finseq_1(C) = k1_matrix_1(D) ) ) ) ) ) )).

fof(t5_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(C)) )
                     => ( ( r2_hidden(A,k4_finseq_1(E))
                          & k1_funct_1(E,A) = D
                          & r2_hidden(B,k4_finseq_1(D)) )
                       => r2_hidden(k4_tarski(A,B),k2_matrix_1(E)) ) ) ) ) ) ) )).

fof(t6_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(C)) )
                     => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
                          & k1_funct_1(E,A) = D )
                       => ( k3_finseq_1(D) = k1_matrix_1(E)
                          & r2_hidden(B,k4_finseq_1(D)) ) ) ) ) ) ) ) )).

fof(t8_gobrd13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => r1_xreal_0(k4_card_1(k2_gobrd13(B)),k2_nat_1(k3_finseq_1(B),k1_matrix_1(B))) ) ) )).

fof(t9_gobrd13,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => r1_tarski(k2_relat_1(A),k2_gobrd13(B)) ) ) ) )).

fof(t10_gobrd13,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] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_tarski(k2_gobrd13(D),k2_gobrd13(E))
                          & r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(E))
                          & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,np__1,C) )
                       => A = np__1 ) ) ) ) ) ) )).

fof(t11_gobrd13,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] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_tarski(k2_gobrd13(D),k2_gobrd13(E))
                          & r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k1_matrix_1(E))
                          & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E),C) )
                       => A = k3_finseq_1(D) ) ) ) ) ) ) )).

fof(t12_gobrd13,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] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_tarski(k2_gobrd13(D),k2_gobrd13(E))
                          & r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(E))
                          & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,np__1) )
                       => B = np__1 ) ) ) ) ) ) )).

fof(t13_gobrd13,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] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_tarski(k2_gobrd13(D),k2_gobrd13(E))
                          & r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
                          & r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(E))
                          & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,k1_matrix_1(E)) )
                       => B = k1_matrix_1(D) ) ) ) ) ) ) )).

fof(t14_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r1_tarski(k2_gobrd13(E),k2_gobrd13(F))
                              & r1_xreal_0(np__1,A)
                              & r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k1_matrix_1(E))
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(np__1,D)
                              & r1_xreal_0(D,k1_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => ( r1_xreal_0(k3_finseq_1(E),A)
                              | r1_xreal_0(k3_finseq_1(F),C)
                              | r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,k1_nat_1(C,np__1),D)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(A,np__1),B))) ) ) ) ) ) ) ) ) )).

fof(t15_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k5_binarith(A,np__1),B),k2_gobrd13(F))
                              & r1_xreal_0(A,k3_finseq_1(E))
                              & r1_xreal_0(np__1,B)
                              & r1_xreal_0(B,k1_matrix_1(E))
                              & r1_xreal_0(C,k3_finseq_1(F))
                              & r1_xreal_0(np__1,D)
                              & r1_xreal_0(D,k1_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => ( r1_xreal_0(A,np__1)
                              | r1_xreal_0(C,np__1)
                              | r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k5_binarith(A,np__1),B)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,k5_binarith(C,np__1),D))) ) ) ) ) ) ) ) ) )).

fof(t16_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k1_nat_1(B,np__1)),k2_gobrd13(F))
                              & r1_xreal_0(np__1,A)
                              & r1_xreal_0(A,k3_finseq_1(E))
                              & r1_xreal_0(np__1,B)
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(C,k3_finseq_1(F))
                              & r1_xreal_0(np__1,D)
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => ( r1_xreal_0(k1_matrix_1(E),B)
                              | r1_xreal_0(k1_matrix_1(F),D)
                              | r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,k1_nat_1(D,np__1))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k1_nat_1(B,np__1)))) ) ) ) ) ) ) ) ) )).

fof(t17_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r1_tarski(k2_gobrd13(E),k2_gobrd13(F))
                              & r1_xreal_0(np__1,A)
                              & r1_xreal_0(A,k3_finseq_1(E))
                              & r1_xreal_0(B,k1_matrix_1(E))
                              & r1_xreal_0(np__1,C)
                              & r1_xreal_0(C,k3_finseq_1(F))
                              & r1_xreal_0(D,k1_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => ( r1_xreal_0(B,np__1)
                              | r1_xreal_0(D,np__1)
                              | r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k5_binarith(B,np__1))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,k5_binarith(D,np__1)))) ) ) ) ) ) ) ) ) )).

fof(t18_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r1_tarski(k2_gobrd13(E),k2_gobrd13(F))
                              & r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
                              & r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => r1_tarski(k3_goboard5(F,C,D),k3_goboard5(E,A,B)) ) ) ) ) ) ) ) )).

fof(t19_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r1_tarski(k2_gobrd13(E),k2_gobrd13(F))
                              & r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
                              & r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => r1_tarski(k3_goboard5(F,k5_binarith(C,np__1),D),k3_goboard5(E,k5_binarith(A,np__1),B)) ) ) ) ) ) ) ) )).

fof(t20_gobrd13,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_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ! [F] :
                          ( ( ~ v3_relat_1(F)
                            & v1_matrix_1(F)
                            & v3_goboard1(F)
                            & v4_goboard1(F)
                            & v5_goboard1(F)
                            & v6_goboard1(F)
                            & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                         => ( ( r1_tarski(k2_gobrd13(E),k2_gobrd13(F))
                              & r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
                              & r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
                              & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
                           => r1_tarski(k3_goboard5(F,C,k5_binarith(D,np__1)),k3_goboard5(E,A,k5_binarith(B,np__1))) ) ) ) ) ) ) ) )).

fof(t21_gobrd13,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
           => r1_tarski(k2_gobrd13(k3_goboard2(B)),k2_gobrd13(A)) ) ) ) )).

fof(d2_gobrd13,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                   => ( D = k3_gobrd13(A,B,C)
                    <=> ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
                                          & r2_hidden(k4_tarski(G,H),k2_matrix_1(B))
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,E,F)
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,G,H)
                                          & ~ ( E = G
                                              & k1_nat_1(F,np__1) = H
                                              & D = k3_goboard5(B,E,F) )
                                          & ~ ( k1_nat_1(E,np__1) = G
                                              & F = H
                                              & D = k3_goboard5(B,E,k5_binarith(F,np__1)) )
                                          & ~ ( E = k1_nat_1(G,np__1)
                                              & F = H
                                              & D = k3_goboard5(B,G,H) )
                                          & ~ ( E = G
                                              & F = k1_nat_1(H,np__1)
                                              & D = k3_goboard5(B,k5_binarith(E,np__1),H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_gobrd13,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                   => ( D = k4_gobrd13(A,B,C)
                    <=> ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
                                          & r2_hidden(k4_tarski(G,H),k2_matrix_1(B))
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,E,F)
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,G,H)
                                          & ~ ( E = G
                                              & k1_nat_1(F,np__1) = H
                                              & D = k3_goboard5(B,k5_binarith(E,np__1),F) )
                                          & ~ ( k1_nat_1(E,np__1) = G
                                              & F = H
                                              & D = k3_goboard5(B,E,F) )
                                          & ~ ( E = k1_nat_1(G,np__1)
                                              & F = H
                                              & D = k3_goboard5(B,G,k5_binarith(H,np__1)) )
                                          & ~ ( E = G
                                              & F = k1_nat_1(H,np__1)
                                              & D = k3_goboard5(B,E,H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
                       => k4_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) )).

fof(t23_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
                       => k3_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) )).

fof(t24_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
                       => k4_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) )).

fof(t25_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
                       => k3_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t26_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k4_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t27_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k3_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) )).

fof(t28_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k4_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) )).

fof(t29_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k3_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) )).

fof(t30_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,C) )
               => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_gobrd13(B,C,A),k3_gobrd13(B,C,A)) = k4_topreal1(np__2,B,A) ) ) ) ) )).

fof(t31_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( ( ~ v3_relat_1(C)
                & v1_matrix_1(C)
                & v3_goboard1(C)
                & v4_goboard1(C)
                & v5_goboard1(C)
                & v6_goboard1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,C) )
               => v4_pre_topc(k3_gobrd13(B,C,A),k15_euclid(np__2)) ) ) ) ) )).

fof(t32_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D)
                      & r1_xreal_0(k1_nat_1(A,np__1),B) )
                   => ( k4_gobrd13(C,D,A) = k4_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
                      & k3_gobrd13(C,D,A) = k3_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) )).

fof(t33_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & r1_xreal_0(B,k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D) )
                   => ( k4_gobrd13(C,D,k1_nat_1(A,B)) = k4_gobrd13(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
                      & k3_gobrd13(C,D,k1_nat_1(A,B)) = k3_gobrd13(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) )).

fof(t34_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B) )
               => ( r1_tarski(k4_gobrd13(C,B,A),k5_goboard5(C,A))
                  & r1_tarski(k3_gobrd13(C,B,A),k4_goboard5(C,A)) ) ) ) ) ) )).

fof(d4_gobrd13,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                   => ( D = k5_gobrd13(A,B,C)
                    <=> ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
                                          & r2_hidden(k4_tarski(G,H),k2_matrix_1(B))
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,E,F)
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,G,H)
                                          & ~ ( E = G
                                              & k1_nat_1(F,np__1) = H
                                              & D = k3_goboard5(B,G,H) )
                                          & ~ ( k1_nat_1(E,np__1) = G
                                              & F = H
                                              & D = k3_goboard5(B,G,k5_binarith(H,np__1)) )
                                          & ~ ( E = k1_nat_1(G,np__1)
                                              & F = H
                                              & D = k3_goboard5(B,k5_binarith(G,np__1),H) )
                                          & ~ ( E = G
                                              & F = k1_nat_1(H,np__1)
                                              & D = k3_goboard5(B,k5_binarith(G,np__1),k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_gobrd13,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                   => ( D = k6_gobrd13(A,B,C)
                    <=> ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
                                          & r2_hidden(k4_tarski(G,H),k2_matrix_1(B))
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,E,F)
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,G,H)
                                          & ~ ( E = G
                                              & k1_nat_1(F,np__1) = H
                                              & D = k3_goboard5(B,k5_binarith(G,np__1),H) )
                                          & ~ ( k1_nat_1(E,np__1) = G
                                              & F = H
                                              & D = k3_goboard5(B,G,H) )
                                          & ~ ( E = k1_nat_1(G,np__1)
                                              & F = H
                                              & D = k3_goboard5(B,k5_binarith(G,np__1),k5_binarith(H,np__1)) )
                                          & ~ ( E = G
                                              & F = k1_nat_1(H,np__1)
                                              & D = k3_goboard5(B,G,k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
                       => k6_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k1_nat_1(C,np__1)) ) ) ) ) ) ) )).

fof(t36_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
                       => k5_gobrd13(D,E,A) = k3_goboard5(E,B,k1_nat_1(C,np__1)) ) ) ) ) ) ) )).

fof(t37_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
                       => k6_gobrd13(D,E,A) = k3_goboard5(E,k1_nat_1(B,np__1),C) ) ) ) ) ) ) )).

fof(t38_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
                       => k5_gobrd13(D,E,A) = k3_goboard5(E,k1_nat_1(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t39_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k6_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t40_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k5_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) )).

fof(t41_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k6_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t42_gobrd13,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_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( ( ~ v3_relat_1(E)
                        & v1_matrix_1(E)
                        & v3_goboard1(E)
                        & v4_goboard1(E)
                        & v5_goboard1(E)
                        & v6_goboard1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                          & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
                          & r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
                       => k5_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) )).

fof(t43_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( ( ~ v3_relat_1(D)
                    & v1_matrix_1(D)
                    & v3_goboard1(D)
                    & v4_goboard1(D)
                    & v5_goboard1(D)
                    & v6_goboard1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D)
                      & r1_xreal_0(k1_nat_1(A,np__1),B) )
                   => ( k6_gobrd13(C,D,A) = k6_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
                      & k5_gobrd13(C,D,A) = k5_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) )).

fof(d6_gobrd13,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( ( v1_matrix_1(C)
            & m2_finseq_1(C,k3_finseq_2(A)) )
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r1_gobrd13(A,B,C,D)
              <=> ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ! [F] :
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ! [G] :
                            ( m2_subset_1(G,k1_numbers,k5_numbers)
                           => ! [H] :
                                ( m2_subset_1(H,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
                                    & r2_hidden(k4_tarski(G,H),k2_matrix_1(C))
                                    & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F)
                                    & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__1)) = k3_matrix_1(A,C,G,H)
                                    & ~ ( E = G
                                        & k1_nat_1(F,np__1) = H
                                        & r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) )
                                    & ~ ( k1_nat_1(E,np__1) = G
                                        & F = H
                                        & r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) )
                                    & ~ ( E = k1_nat_1(G,np__1)
                                        & F = H
                                        & r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
                                    & ~ ( E = G
                                        & F = k1_nat_1(H,np__1)
                                        & r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_gobrd13,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( ( v1_matrix_1(C)
            & m2_finseq_1(C,k3_finseq_2(A)) )
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r2_gobrd13(A,B,C,D)
              <=> ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ! [F] :
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ! [G] :
                            ( m2_subset_1(G,k1_numbers,k5_numbers)
                           => ! [H] :
                                ( m2_subset_1(H,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
                                    & r2_hidden(k4_tarski(G,H),k2_matrix_1(C))
                                    & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F)
                                    & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__1)) = k3_matrix_1(A,C,G,H)
                                    & ~ ( E = G
                                        & k1_nat_1(F,np__1) = H
                                        & r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) )
                                    & ~ ( k1_nat_1(E,np__1) = G
                                        & F = H
                                        & r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
                                    & ~ ( E = k1_nat_1(G,np__1)
                                        & F = H
                                        & r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) )
                                    & ~ ( E = G
                                        & F = k1_nat_1(H,np__1)
                                        & r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_gobrd13,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( ( v1_matrix_1(C)
            & m2_finseq_1(C,k3_finseq_2(A)) )
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r3_gobrd13(A,B,C,D)
              <=> ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ! [F] :
                        ( m2_subset_1(F,k1_numbers,k5_numbers)
                       => ! [G] :
                            ( m2_subset_1(G,k1_numbers,k5_numbers)
                           => ! [H] :
                                ( m2_subset_1(H,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
                                    & r2_hidden(k4_tarski(G,H),k2_matrix_1(C))
                                    & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F)
                                    & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__1)) = k3_matrix_1(A,C,G,H)
                                    & ~ ( E = G
                                        & k1_nat_1(F,np__1) = H
                                        & r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
                                    & ~ ( k1_nat_1(E,np__1) = G
                                        & F = H
                                        & r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) )
                                    & ~ ( E = k1_nat_1(G,np__1)
                                        & F = H
                                        & r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) )
                                    & ~ ( E = G
                                        & F = k1_nat_1(H,np__1)
                                        & r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
                                        & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) )).

fof(t44_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C,D] :
              ( m2_finseq_1(D,C)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(C)) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
                      & r1_xreal_0(k1_nat_1(A,np__2),B)
                      & r1_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
                   => r1_gobrd13(C,D,E,A) ) ) ) ) ) )).

fof(t45_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C,D] :
              ( m2_finseq_1(D,C)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(C)) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
                      & r1_xreal_0(k1_nat_1(A,np__2),B)
                      & r2_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
                   => r2_gobrd13(C,D,E,A) ) ) ) ) ) )).

fof(t46_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C,D] :
              ( m2_finseq_1(D,C)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(C)) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
                      & r1_xreal_0(k1_nat_1(A,np__2),B)
                      & r3_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
                   => r3_gobrd13(C,D,E,A) ) ) ) ) ) )).

fof(t47_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(B)) )
                 => ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                      & r1_goboard1(B,C,E)
                      & k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
                      & r1_gobrd13(B,C,E,k5_binarith(A,np__1))
                      & r1_gobrd13(B,D,E,k5_binarith(A,np__1)) )
                   => ( r1_xreal_0(A,np__1)
                      | k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) )).

fof(t48_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(B)) )
                 => ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                      & r1_goboard1(B,C,E)
                      & k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
                      & r2_gobrd13(B,C,E,k5_binarith(A,np__1))
                      & r2_gobrd13(B,D,E,k5_binarith(A,np__1)) )
                   => ( r1_xreal_0(A,np__1)
                      | k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) )).

fof(t49_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ! [E] :
                  ( ( v1_matrix_1(E)
                    & m2_finseq_1(E,k3_finseq_2(B)) )
                 => ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
                      & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
                      & r1_goboard1(B,C,E)
                      & k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
                      & r3_gobrd13(B,C,E,k5_binarith(A,np__1))
                      & r3_gobrd13(B,D,E,k5_binarith(A,np__1)) )
                   => ( r1_xreal_0(A,np__1)
                      | k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) )).

fof(t50_gobrd13,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(C)) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(A,k3_finseq_1(D))
                      & r1_xreal_0(np__1,B)
                      & r1_xreal_0(B,k1_matrix_1(D)) )
                   => r2_hidden(k3_matrix_1(C,D,A,B),k2_gobrd13(D)) ) ) ) ) ) )).

fof(dt_k1_gobrd13,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_2(B,u1_struct_0(k15_euclid(np__2)))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m2_finseq_1(k1_gobrd13(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) )).

fof(redefinition_k1_gobrd13,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_finseq_2(B,u1_struct_0(k15_euclid(np__2)))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k1_gobrd13(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k2_gobrd13,axiom,(
    $true )).

fof(dt_k3_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & ~ v3_relat_1(B)
        & v1_matrix_1(B)
        & v3_goboard1(B)
        & v4_goboard1(B)
        & v5_goboard1(B)
        & v6_goboard1(B)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k3_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k4_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & ~ v3_relat_1(B)
        & v1_matrix_1(B)
        & v3_goboard1(B)
        & v4_goboard1(B)
        & v5_goboard1(B)
        & v6_goboard1(B)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k4_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k5_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & ~ v3_relat_1(B)
        & v1_matrix_1(B)
        & v3_goboard1(B)
        & v4_goboard1(B)
        & v5_goboard1(B)
        & v6_goboard1(B)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k5_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k6_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & ~ v3_relat_1(B)
        & v1_matrix_1(B)
        & v3_goboard1(B)
        & v4_goboard1(B)
        & v5_goboard1(B)
        & v6_goboard1(B)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k6_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(t3_gobrd13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k3_finseq_2(A))
         => k2_gobrd13(B) = k3_tarski(a_2_0_gobrd13(A,B)) ) ) )).

fof(t7_gobrd13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => k2_gobrd13(B) = a_2_1_gobrd13(A,B) ) ) )).

fof(fraenkel_a_2_0_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & m2_finseq_1(C,k3_finseq_2(B)) )
     => ( r2_hidden(A,a_2_0_gobrd13(B,C))
      <=> ? [D] :
            ( m2_finseq_2(D,B,k3_finseq_2(B))
            & A = k2_relat_1(D)
            & r2_hidden(D,k2_relat_1(C)) ) ) ) )).

fof(fraenkel_a_2_1_gobrd13,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_matrix_1(C)
        & m2_finseq_1(C,k3_finseq_2(B)) )
     => ( r2_hidden(A,a_2_1_gobrd13(B,C))
      <=> ? [D,E] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k3_matrix_1(B,C,D,E)
            & r2_hidden(k4_tarski(D,E),k2_matrix_1(C)) ) ) ) )).
%------------------------------------------------------------------------------