SET007 Axioms: SET007+349.ax


%------------------------------------------------------------------------------
% File     : SET007+349 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Go-Board - Part I
% 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    : goboard1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   75 (  10 unit)
%            Number of atoms       :  962 ( 100 equality)
%            Maximal formula depth :   29 (  12 average)
%            Number of connectives :  995 ( 108 ~  ;  22  |; 524  &)
%                                         (  14 <=>; 327 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-3 arity)
%            Number of functors    :   38 (   8 constant; 0-4 arity)
%            Number of variables   :  282 (   0 singleton; 274 !;   8 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_goboard1,axiom,(
    ? [A] :
      ( m1_finseq_1(A,k1_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_goboard1(A) ) )).

fof(rc2_goboard1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_finseq_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B) ) ) )).

fof(rc3_goboard1,axiom,(
    ? [A] :
      ( m1_finseq_1(A,k1_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v5_seqm_3(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) )).

fof(rc4_goboard1,axiom,(
    ? [A] :
      ( m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
      & v1_relat_1(A)
      & ~ v3_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_matrix_1(A)
      & v3_goboard1(A)
      & v4_goboard1(A)
      & v5_goboard1(A)
      & v6_goboard1(A) ) )).

fof(t1_goboard1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( k18_complex1(k5_real_1(A,B)) = np__1
          <=> ( ( ~ r1_xreal_0(A,B)
                & A = k3_real_1(B,np__1) )
              | ( ~ r1_xreal_0(B,A)
                & B = k3_real_1(A,np__1) ) ) ) ) ) )).

fof(t2_goboard1,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)
                 => ( k3_real_1(k18_complex1(k5_real_1(A,B)),k18_complex1(k5_real_1(C,D))) = np__1
                  <=> ( ( k18_complex1(k5_real_1(A,B)) = np__1
                        & C = D )
                      | ( k18_complex1(k5_real_1(C,D)) = np__1
                        & A = B ) ) ) ) ) ) ) )).

fof(t3_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( ~ ( ~ r1_xreal_0(A,np__1)
            & ! [B] :
                ( m2_subset_1(B,k1_numbers,k5_numbers)
               => ~ ( A = k1_nat_1(B,np__1)
                    & ~ r1_xreal_0(B,np__0) ) ) )
        & ~ ( ? [B] :
                ( m2_subset_1(B,k1_numbers,k5_numbers)
                & A = k1_nat_1(B,np__1)
                & ~ r1_xreal_0(B,np__0) )
            & r1_xreal_0(A,np__1) ) ) ) )).

fof(t4_goboard1,axiom,(
    $true )).

fof(t5_goboard1,axiom,(
    $true )).

fof(t6_goboard1,axiom,(
    $true )).

fof(t7_goboard1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( k3_finseq_1(A) = k1_nat_1(C,np__1)
                      & r2_hidden(B,k4_finseq_1(A))
                      & r2_hidden(D,k2_finseq_1(C))
                      & k1_funct_1(k2_finseq_3(B,A),D) != k1_funct_1(A,D)
                      & k1_funct_1(k2_finseq_3(B,A),D) != k1_funct_1(A,k1_nat_1(D,np__1)) ) ) ) ) ) )).

fof(t8_goboard1,axiom,(
    $true )).

fof(t9_goboard1,axiom,(
    $true )).

fof(d1_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ( v1_goboard1(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r2_hidden(B,k4_finseq_1(A))
                    & r2_hidden(C,k4_finseq_1(A))
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k1_goboard1(A,C),k1_goboard1(A,B)) ) ) ) ) ) )).

fof(d2_goboard1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(B,k4_finseq_1(A))
                    & r2_hidden(C,k4_finseq_1(A)) )
                 => k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ) )).

fof(d3_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ( B = k2_goboard1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => k1_goboard1(B,C) = k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ) )).

fof(d4_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ( B = k3_goboard1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => k1_goboard1(B,C) = k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ) )).

fof(t10_goboard1,axiom,(
    $true )).

fof(t11_goboard1,axiom,(
    $true )).

fof(t12_goboard1,axiom,(
    $true )).

fof(t13_goboard1,axiom,(
    $true )).

fof(t14_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_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)
                 => ( ( r1_tarski(k2_relat_1(A),k2_finseq_1(B))
                      & k1_goboard1(A,k3_finseq_1(A)) = B
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k5_real_1(k3_finseq_1(A),np__1)) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] :
                                    ( m1_subset_1(G,k1_numbers)
                                   => ~ ( F = k1_goboard1(A,E)
                                        & G = k1_goboard1(A,k1_nat_1(E,np__1))
                                        & k18_complex1(k5_real_1(F,G)) != np__1
                                        & F != G ) ) ) ) )
                      & r2_hidden(C,k2_finseq_1(B))
                      & r2_hidden(k1_nat_1(C,np__1),k2_finseq_1(B))
                      & r2_hidden(D,k4_finseq_1(A))
                      & k1_goboard1(A,D) = C
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(E,k4_finseq_1(A))
                              & k1_goboard1(A,E) = C )
                           => r1_xreal_0(E,D) ) ) )
                   => ( A = k1_xboole_0
                      | ( r2_hidden(k1_nat_1(D,np__1),k4_finseq_1(A))
                        & k1_goboard1(A,k1_nat_1(D,np__1)) = k1_nat_1(C,np__1) ) ) ) ) ) ) ) )).

fof(t15_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_tarski(k2_relat_1(A),k2_finseq_1(B))
              & k1_goboard1(A,np__1) = np__1
              & k1_goboard1(A,k3_finseq_1(A)) = B
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k5_real_1(k3_finseq_1(A),np__1)) )
                   => ! [D] :
                        ( m1_subset_1(D,k1_numbers)
                       => ! [E] :
                            ( m1_subset_1(E,k1_numbers)
                           => ~ ( D = k1_goboard1(A,C)
                                & E = k1_goboard1(A,k1_nat_1(C,np__1))
                                & k18_complex1(k5_real_1(D,E)) != np__1
                                & D != E ) ) ) ) ) )
           => ( A = k1_xboole_0
              | ( ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ~ ( r2_hidden(C,k2_finseq_1(B))
                        & ! [D] :
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                           => ~ ( r2_hidden(D,k4_finseq_1(A))
                                & k1_goboard1(A,D) = C ) ) ) )
                & ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ~ ( r2_hidden(C,k4_finseq_1(A))
                                    & k1_goboard1(A,C) = E
                                    & ! [G] :
                                        ( m2_subset_1(G,k1_numbers,k5_numbers)
                                       => ( ( r2_hidden(G,k4_finseq_1(A))
                                            & k1_goboard1(A,G) = E )
                                         => r1_xreal_0(G,C) ) )
                                    & ~ r1_xreal_0(D,C)
                                    & r2_hidden(D,k4_finseq_1(A))
                                    & F = k1_goboard1(A,D)
                                    & r1_xreal_0(F,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r2_hidden(B,k4_finseq_1(A))
              & r1_xreal_0(np__2,k3_finseq_1(A)) )
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k5_topreal1(np__2,A)) ) ) ) )).

fof(t17_goboard1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(D,k4_finseq_1(B))
                      & r2_hidden(C,k2_finseq_1(k1_matrix_1(B))) )
                   => k1_funct_1(k8_matrix_1(A,B,C),D) = k1_funct_1(k7_matrix_1(A,B,D),C) ) ) ) ) ) )).

fof(d5_goboard1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => ( v3_relat_1(B)
          <=> ( np__0 = k3_finseq_1(B)
              | np__0 = k1_matrix_1(B) ) ) ) ) )).

fof(d6_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( v3_goboard1(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k4_finseq_1(A))
             => v5_seqm_3(k2_goboard1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) )).

fof(d7_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( v4_goboard1(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
             => v5_seqm_3(k3_goboard1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) )).

fof(d8_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( v5_goboard1(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k4_finseq_1(A))
             => v1_goboard1(k3_goboard1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) )).

fof(d9_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ( v6_goboard1(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
             => v1_goboard1(k2_goboard1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) )).

fof(t18_goboard1,axiom,(
    $true )).

fof(t19_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & v3_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B,C] :
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
                  & r2_hidden(B,k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
                  & r2_hidden(C,k4_finseq_1(A))
                  & r2_hidden(D,k4_finseq_1(A)) )
               => C = D ) ) ) ) )).

fof(t20_goboard1,axiom,(
    ! [A] :
      ( ( v1_matrix_1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B,C] :
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
                  & r2_hidden(B,k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
                  & r2_hidden(C,k2_finseq_1(k1_matrix_1(A)))
                  & r2_hidden(D,k2_finseq_1(k1_matrix_1(A))) )
               => C = D ) ) ) ) )).

fof(t21_goboard1,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,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)))) )
                     => ( ( E = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,A,B)
                          & E = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D)
                          & r2_hidden(k4_tarski(A,B),k2_matrix_1(F))
                          & r2_hidden(k4_tarski(C,D),k2_matrix_1(F)) )
                       => ( A = C
                          & B = D ) ) ) ) ) ) ) )).

fof(t22_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1))) )
               => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1))) ) ) ) ) )).

fof(t23_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C)))) )
               => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C)))) ) ) ) ) )).

fof(t24_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [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_xboole_0(k2_relat_1(A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),F,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)),F,D,E)
                              & r2_hidden(C,k4_finseq_1(A))
                              & r2_hidden(D,k4_finseq_1(F))
                              & B = E ) ) ) ) ) ) ) )).

fof(d10_goboard1,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
           => ( r1_xreal_0(k1_matrix_1(A),np__1)
              | ! [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)))) )
                 => ( C = k4_goboard1(A,B)
                  <=> ( k3_finseq_1(C) = k3_finseq_1(A)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( r2_hidden(D,k4_finseq_1(A))
                           => k1_funct_1(C,D) = k2_finseq_3(B,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ) ) ) )).

fof(t25_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
                  & r2_hidden(B,k4_finseq_1(C)) )
               => ( r1_xreal_0(k1_matrix_1(C),np__1)
                  | k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,A),B) = k2_finseq_3(A,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)) ) ) ) ) ) )).

fof(t26_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
                  & k1_matrix_1(C) = k1_nat_1(B,np__1) )
               => ( r1_xreal_0(B,np__0)
                  | k1_matrix_1(k4_goboard1(C,A)) = B ) ) ) ) ) )).

fof(t27_goboard1,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)))) )
         => ( r2_hidden(A,k2_finseq_1(k1_matrix_1(B)))
           => ( r1_xreal_0(k1_matrix_1(B),np__1)
              | k1_matrix_1(B) = k1_nat_1(k1_matrix_1(k4_goboard1(B,A)),np__1) ) ) ) ) )).

fof(t28_goboard1,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)))) )
                 => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
                      & r2_hidden(B,k4_finseq_1(D))
                      & r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A)))) )
                   => ( r1_xreal_0(k1_matrix_1(D),np__1)
                      | k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),B,C) = k1_funct_1(k2_finseq_3(A,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B)),C) ) ) ) ) ) ) )).

fof(t29_goboard1,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)))) )
                 => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
                      & k1_matrix_1(D) = k1_nat_1(B,np__1)
                      & r1_xreal_0(np__1,C) )
                   => ( r1_xreal_0(B,np__0)
                      | r1_xreal_0(A,C)
                      | ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),C) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C)
                        & r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A))))
                        & r2_hidden(C,k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) )).

fof(t30_goboard1,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)))) )
                 => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
                      & k1_matrix_1(D) = k1_nat_1(B,np__1)
                      & r1_xreal_0(A,C)
                      & r1_xreal_0(C,B) )
                   => ( r1_xreal_0(B,np__0)
                      | ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),C) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1))
                        & r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A))))
                        & r2_hidden(k1_nat_1(C,np__1),k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) )).

fof(t31_goboard1,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)))) )
                     => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(E)))
                          & k1_matrix_1(E) = k1_nat_1(B,np__1)
                          & r2_hidden(C,k4_finseq_1(E))
                          & r1_xreal_0(np__1,D) )
                       => ( r1_xreal_0(B,np__0)
                          | r1_xreal_0(A,D)
                          | ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,A),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,D)
                            & r2_hidden(D,k2_finseq_1(k1_matrix_1(E))) ) ) ) ) ) ) ) ) )).

fof(t32_goboard1,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)))) )
                     => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(E)))
                          & k1_matrix_1(E) = k1_nat_1(B,np__1)
                          & r2_hidden(C,k4_finseq_1(E))
                          & r1_xreal_0(A,D)
                          & r1_xreal_0(D,B) )
                       => ( r1_xreal_0(B,np__0)
                          | ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,A),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,k1_nat_1(D,np__1))
                            & r2_hidden(k1_nat_1(D,np__1),k2_finseq_1(k1_matrix_1(E))) ) ) ) ) ) ) ) ) )).

fof(t33_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( k1_matrix_1(C) = k1_nat_1(A,np__1)
                  & r2_hidden(B,k2_finseq_1(A)) )
               => ( r1_xreal_0(A,np__0)
                  | ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,np__1),B) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1))
                    & r2_hidden(B,k2_finseq_1(k1_matrix_1(k4_goboard1(C,np__1))))
                    & r2_hidden(k1_nat_1(B,np__1),k2_finseq_1(k1_matrix_1(C))) ) ) ) ) ) ) )).

fof(t34_goboard1,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)))) )
                 => ( ( k1_matrix_1(D) = k1_nat_1(A,np__1)
                      & r2_hidden(B,k2_finseq_1(A))
                      & r2_hidden(C,k4_finseq_1(D)) )
                   => ( r1_xreal_0(A,np__0)
                      | ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,np__1),C,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,k1_nat_1(B,np__1))
                        & r2_hidden(np__1,k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) )).

fof(t35_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ( ( k1_matrix_1(C) = k1_nat_1(A,np__1)
                  & r2_hidden(B,k2_finseq_1(A)) )
               => ( r1_xreal_0(A,np__0)
                  | ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,k1_matrix_1(C)),B) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)
                    & r2_hidden(B,k2_finseq_1(k1_matrix_1(k4_goboard1(C,k1_matrix_1(C))))) ) ) ) ) ) ) )).

fof(t36_goboard1,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)))) )
                 => ( ( k1_matrix_1(D) = k1_nat_1(A,np__1)
                      & r2_hidden(B,k2_finseq_1(A))
                      & r2_hidden(C,k4_finseq_1(D)) )
                   => ( r1_xreal_0(A,np__0)
                      | ( r2_hidden(B,k2_finseq_1(k1_matrix_1(D)))
                        & k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,k1_matrix_1(D)),C,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B)
                        & r2_hidden(k1_matrix_1(D),k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) )).

fof(t37_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [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)))) )
                     => ( ( r1_xboole_0(k2_relat_1(A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B)))
                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),E,D)))
                          & r2_hidden(C,k4_finseq_1(A))
                          & r2_hidden(B,k2_finseq_1(k1_matrix_1(E)))
                          & r2_hidden(D,k4_finseq_1(E)) )
                       => ( r1_xreal_0(k1_matrix_1(E),np__1)
                          | r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,B),D))) ) ) ) ) ) ) ) )).

fof(d11_goboard1,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( ( v1_matrix_1(C)
            & m2_finseq_1(C,k3_finseq_2(A)) )
         => ( r1_goboard1(A,B,C)
          <=> ( ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(D,k4_finseq_1(B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
                                  & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F) ) ) ) ) )
              & ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(D,k4_finseq_1(B))
                      & r2_hidden(k1_nat_1(D,np__1),k4_finseq_1(B)) )
                   => ! [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) )
                                     => k3_real_1(k18_complex1(k5_real_1(E,G)),k18_complex1(k5_real_1(F,H))) = np__1 ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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(C))
                 => r1_xreal_0(np__1,k3_finseq_1(k16_finseq_1(B,C,A))) )
                & ( r1_goboard1(B,C,D)
                 => r1_goboard1(B,k16_finseq_1(B,C,A),D) ) ) ) ) ) )).

fof(t39_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C,D] :
              ( ( v1_matrix_1(D)
                & m2_finseq_1(D,k3_finseq_2(C)) )
             => ( ( ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(E,k4_finseq_1(A))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(C,D,F,G) ) ) ) ) )
                  & ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(E,k4_finseq_1(B))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E) = k3_matrix_1(C,D,F,G) ) ) ) ) ) )
               => ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ~ ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                    & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),E) = k3_matrix_1(C,D,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t40_goboard1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C,D] :
              ( ( v1_matrix_1(D)
                & m2_finseq_1(D,k3_finseq_2(C)) )
             => ( ( ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r2_hidden(E,k4_finseq_1(A))
                          & r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(A)) )
                       => ! [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)
                                   => ! [I] :
                                        ( m2_subset_1(I,k1_numbers,k5_numbers)
                                       => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                            & r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
                                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(C,D,F,G)
                                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
                                         => k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) )
                  & ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r2_hidden(E,k4_finseq_1(B))
                          & r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(B)) )
                       => ! [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)
                                   => ! [I] :
                                        ( m2_subset_1(I,k1_numbers,k5_numbers)
                                       => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                            & r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
                                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E) = k3_matrix_1(C,D,F,G)
                                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
                                         => k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) )
                  & ! [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(D))
                                      & r2_hidden(k4_tarski(G,H),k2_matrix_1(D))
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k3_matrix_1(C,D,E,F)
                                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k3_matrix_1(C,D,G,H)
                                      & r2_hidden(k3_finseq_1(A),k4_finseq_1(A))
                                      & r2_hidden(np__1,k4_finseq_1(B)) )
                                   => k3_real_1(k18_complex1(k5_real_1(E,G)),k18_complex1(k5_real_1(F,H))) = np__1 ) ) ) ) ) )
               => ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
                        & r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))) )
                     => ! [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)
                                 => ! [I] :
                                      ( m2_subset_1(I,k1_numbers,k5_numbers)
                                     => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
                                          & r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),E) = k3_matrix_1(C,D,F,G)
                                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
                                       => k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_goboard1,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] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r2_hidden(A,k2_finseq_1(k1_matrix_1(B)))
                  & r1_xboole_0(k2_relat_1(C),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),B,A))) )
               => ( r1_xreal_0(k1_matrix_1(B),np__1)
                  | r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k4_goboard1(B,A)) ) ) ) ) ) )).

fof(t42_goboard1,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] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r2_hidden(A,k4_finseq_1(C))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(B))
                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D))) ) ) ) ) ) ) )).

fof(t43_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(C))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & ~ r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & ? [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E)))
                          & r2_hidden(E,k4_finseq_1(C))
                          & k18_complex1(k5_real_1(B,E)) != np__1 ) ) ) ) ) ) )).

fof(t44_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(np__1,k3_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & r2_hidden(A,k4_finseq_1(C))
                      & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(C))
                      & r2_hidden(B,k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A)))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(E,k4_finseq_1(D))
                              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
                           => r1_xreal_0(E,B) ) ) )
                   => ( r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1)))) ) ) ) ) ) ) )).

fof(t45_goboard1,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] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r1_xreal_0(np__1,k3_finseq_1(B))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))))
              & r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(D,k4_finseq_1(B))
                              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,D),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) ) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & r1_xreal_0(np__2,k3_finseq_1(B))
                      & r1_xboole_0(k5_topreal1(np__2,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(np__1,C)
                                  & r1_xreal_0(C,k3_finseq_1(A))
                                  & r1_xreal_0(np__1,D)
                                  & r1_xreal_0(D,k3_finseq_1(A))
                                  & r2_hidden(E,k4_finseq_1(B))
                                  & r2_hidden(F,k4_finseq_1(B))
                                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
                                  & ! [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                     => ( ( r2_hidden(G,k4_finseq_1(B))
                                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,G),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) )
                                       => r1_xreal_0(G,E) ) )
                                  & ~ r1_xreal_0(F,E)
                                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
                                  & r1_xreal_0(D,C) ) ) ) ) ) ) ) ) ) )).

fof(t46_goboard1,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] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                  & r2_hidden(A,k4_finseq_1(C))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k2_finseq_1(k1_matrix_1(B)))
                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D))) ) ) ) ) ) ) )).

fof(t47_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(D))
                      & r2_hidden(B,k2_finseq_1(k1_matrix_1(C)))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & ~ r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & ? [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E)))
                          & r2_hidden(E,k2_finseq_1(k1_matrix_1(C)))
                          & k18_complex1(k5_real_1(B,E)) != np__1 ) ) ) ) ) ) )).

fof(t48_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_xreal_0(np__1,k3_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C))))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
                      & r2_hidden(k1_nat_1(A,np__1),k2_finseq_1(k1_matrix_1(C)))
                      & r2_hidden(B,k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A)))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(E,k4_finseq_1(D))
                              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
                           => r1_xreal_0(E,B) ) ) )
                   => ( r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1)))) ) ) ) ) ) ) )).

fof(t49_goboard1,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] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r1_xreal_0(np__1,k3_finseq_1(B))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
              & r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k1_matrix_1(A))
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(D,k4_finseq_1(B))
                              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,D),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) ) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k1_matrix_1(A))
                      & r1_xreal_0(np__2,k3_finseq_1(B))
                      & r1_xboole_0(k5_topreal1(np__2,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(np__1,C)
                                  & r1_xreal_0(C,k1_matrix_1(A))
                                  & r1_xreal_0(np__1,D)
                                  & r1_xreal_0(D,k1_matrix_1(A))
                                  & r2_hidden(E,k4_finseq_1(B))
                                  & r2_hidden(F,k4_finseq_1(B))
                                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
                                  & ! [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                     => ( ( r2_hidden(G,k4_finseq_1(B))
                                          & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,G),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) )
                                       => r1_xreal_0(G,E) ) )
                                  & ~ r1_xreal_0(F,E)
                                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,F),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
                                  & r1_xreal_0(D,C) ) ) ) ) ) ) ) ) ) )).

fof(t50_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
                      & r2_hidden(B,k2_finseq_1(k1_matrix_1(C)))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1)))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(E,k4_finseq_1(D))
                              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B))) )
                           => r1_xreal_0(A,E) ) ) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r2_hidden(E,k4_finseq_1(D))
                            & r1_xreal_0(E,A) )
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( ( r2_hidden(F,k2_finseq_1(k1_matrix_1(C)))
                                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,F))) )
                               => r1_xreal_0(F,B) ) ) ) ) ) ) ) ) ) )).

fof(t51_goboard1,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] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
              & ~ r1_xreal_0(k1_matrix_1(A),np__1)
              & r1_xreal_0(np__1,k3_finseq_1(B))
              & ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(A,k1_matrix_1(A)),np__1)))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(A,k1_matrix_1(A)),k1_matrix_1(k4_goboard1(A,k1_matrix_1(A))))))
                      & r1_xreal_0(np__1,k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k4_goboard1(A,k1_matrix_1(A)))
                      & r1_tarski(k2_relat_1(C),k2_relat_1(B)) ) ) ) ) ) )).

fof(t52_goboard1,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] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
              & k3_xboole_0(k2_relat_1(B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1))) != k1_xboole_0
              & k3_xboole_0(k2_relat_1(B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A)))) != k1_xboole_0
              & ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_tarski(k2_relat_1(C),k2_relat_1(B))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
                      & r1_xreal_0(np__1,k3_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,A) ) ) ) ) ) )).

fof(t53_goboard1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [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)))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r2_hidden(A,k4_finseq_1(C))
                      & r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))))
                      & r2_hidden(B,k4_finseq_1(D))
                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
                   => ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(A,E)
                              & r1_xreal_0(E,k3_finseq_1(C))
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(F,k4_finseq_1(D))
                                      & r1_xreal_0(B,F)
                                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E))) ) ) ) )
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(E,A)
                              & r1_xreal_0(E,k3_finseq_1(C))
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(F,k4_finseq_1(D))
                                      & ~ r1_xreal_0(F,B)
                                      & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E))) ) ) ) ) ) ) ) ) ) ) )).

fof(s1_goboard1,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,k2_finseq_1(f2_s1_goboard1))
            & ! [B] :
                ( m1_subset_1(B,f1_s1_goboard1)
               => ~ p1_s1_goboard1(A,B) ) ) )
   => ? [A] :
        ( m2_finseq_1(A,f1_s1_goboard1)
        & k3_finseq_1(A) = f2_s1_goboard1
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f2_s1_goboard1))
             => p1_s1_goboard1(B,k4_finseq_4(k5_numbers,f1_s1_goboard1,A,B)) ) ) ) )).

fof(redefinition_v2_goboard1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_matrix_1(B)
        & m1_finseq_1(B,k3_finseq_2(A)) )
     => ( v2_goboard1(B,A)
      <=> v3_relat_1(B) ) ) )).

fof(dt_k1_goboard1,axiom,(
    ! [A,B] :
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k1_goboard1(A,B),k1_numbers) ) )).

fof(redefinition_k1_goboard1,axiom,(
    ! [A,B] :
      ( ( m1_finseq_1(A,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_goboard1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k2_goboard1,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => m2_finseq_1(k2_goboard1(A),k1_numbers) ) )).

fof(dt_k3_goboard1,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => m2_finseq_1(k3_goboard1(A),k1_numbers) ) )).

fof(dt_k4_goboard1,axiom,(
    ! [A,B] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v3_relat_1(k4_goboard1(A,B))
        & v1_matrix_1(k4_goboard1(A,B))
        & v3_goboard1(k4_goboard1(A,B))
        & v4_goboard1(k4_goboard1(A,B))
        & v5_goboard1(k4_goboard1(A,B))
        & v6_goboard1(k4_goboard1(A,B))
        & m2_finseq_1(k4_goboard1(A,B),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) )).
%------------------------------------------------------------------------------