SET007 Axioms: SET007+350.ax


%------------------------------------------------------------------------------
% File     : SET007+350 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Go-Board - Part II
% 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    : goboard2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   1 unit)
%            Number of atoms       :  320 (  50 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives :  326 (  47 ~  ;   5  |; 150  &)
%                                         (   2 <=>; 122 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   1 propositional; 0-3 arity)
%            Number of functors    :   45 (   8 constant; 0-4 arity)
%            Number of variables   :   95 (   0 singleton;  93 !;   2 ?)
%            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(fc1_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k2_goboard1(A))
        & v1_relat_1(k2_goboard1(A))
        & v1_funct_1(k2_goboard1(A))
        & v1_finset_1(k2_goboard1(A))
        & v1_finseq_1(k2_goboard1(A)) ) ) )).

fof(fc2_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k3_goboard1(A))
        & v1_relat_1(k3_goboard1(A))
        & v1_funct_1(k3_goboard1(A))
        & v1_finset_1(k3_goboard1(A))
        & v1_finseq_1(k3_goboard1(A)) ) ) )).

fof(fc3_goboard2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_goboard1(A)
        & m1_finseq_1(A,k1_numbers)
        & ~ v1_xboole_0(B)
        & v1_goboard1(B)
        & m1_finseq_1(B,k1_numbers) )
     => ( v1_relat_1(k1_goboard2(A,B))
        & ~ v3_relat_1(k1_goboard2(A,B))
        & v1_funct_1(k1_goboard2(A,B))
        & v1_finset_1(k1_goboard2(A,B))
        & v1_finseq_1(k1_goboard2(A,B))
        & v1_matrix_1(k1_goboard2(A,B))
        & v3_goboard1(k1_goboard2(A,B))
        & v4_goboard1(k1_goboard2(A,B))
        & v5_goboard1(k1_goboard2(A,B))
        & v6_goboard1(k1_goboard2(A,B)) ) ) )).

fof(fc4_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,k1_numbers) )
     => ( ~ v1_xboole_0(k2_goboard2(A))
        & v1_relat_1(k2_goboard2(A))
        & v1_funct_1(k2_goboard2(A))
        & v1_finset_1(k2_goboard2(A))
        & v1_finseq_1(k2_goboard2(A))
        & v1_goboard1(k2_goboard2(A)) ) ) )).

fof(fc5_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( v1_relat_1(k3_goboard2(A))
        & ~ v3_relat_1(k3_goboard2(A))
        & v1_funct_1(k3_goboard2(A))
        & v1_finset_1(k3_goboard2(A))
        & v1_finseq_1(k3_goboard2(A))
        & v1_matrix_1(k3_goboard2(A))
        & v3_goboard1(k3_goboard2(A))
        & v4_goboard1(k3_goboard2(A))
        & v5_goboard1(k3_goboard2(A))
        & v6_goboard1(k3_goboard2(A)) ) ) )).

fof(t1_goboard2,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( A != k1_xboole_0
       => ( v1_seq_4(A)
          & r2_hidden(k4_seq_4(A),A)
          & v2_seq_4(A)
          & r2_hidden(k5_seq_4(A),A) ) ) ) )).

fof(t2_goboard2,axiom,(
    $true )).

fof(t3_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( ( r1_xreal_0(np__1,A)
                & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
             => ( r2_hidden(A,k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) ) )
            & ( ( r2_hidden(A,k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) )
             => ( r1_xreal_0(np__1,A)
                & r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) ) ) ) ) ) )).

fof(t4_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( ( r1_xreal_0(np__1,A)
                & r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(B)) )
             => ( r2_hidden(A,k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__2),k4_finseq_1(B)) ) )
            & ( ( r2_hidden(A,k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__2),k4_finseq_1(B)) )
             => ( r1_xreal_0(np__1,A)
                & r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(B)) ) ) ) ) ) )).

fof(t5_goboard2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,k3_finseq_1(C)) )
                   => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,B,C),k1_nat_1(D,k3_finseq_1(B))) = k4_finseq_4(k5_numbers,A,C,D) ) ) ) ) ) )).

fof(t6_goboard2,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)
               => ( ( r2_hidden(B,k4_finseq_1(A))
                    & r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A))
                    & r2_hidden(C,k4_finseq_1(A))
                    & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) )
                 => ( r1_xreal_0(C,k1_nat_1(B,np__1))
                    | r1_xboole_0(k4_topreal1(np__2,A,B),k4_topreal1(np__2,A,C)) ) ) ) )
       => v3_topreal1(A) ) ) )).

fof(t7_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( v2_topreal1(A)
              & v3_topreal1(A)
              & v2_funct_1(A)
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_topreal1(np__2,A,B))
              & r2_hidden(B,k4_finseq_1(A))
              & r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) )
           => k1_nat_1(B,np__1) = k3_finseq_1(A) ) ) ) )).

fof(t8_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k3_finseq_1(A) = k1_nat_1(B,np__1)
           => ( B = np__0
              | k5_topreal1(np__2,A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)),k4_topreal1(np__2,A,B)) ) ) ) ) )).

fof(t9_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( k3_finseq_1(A) = k1_nat_1(B,np__1)
              & v2_topreal1(A)
              & v3_topreal1(A) )
           => ( r1_xreal_0(B,np__1)
              | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)),k4_topreal1(np__2,A,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t10_goboard2,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
                      & k1_nat_1(D,k3_finseq_1(A)) = C )
                   => ( r1_xreal_0(C,k3_finseq_1(A))
                      | k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,B,D) ) ) ) ) ) ) )).

fof(t11_goboard2,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)))
         => r1_tarski(k5_topreal1(np__2,A),k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) )).

fof(t12_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v3_topreal1(A)
           => v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t13_goboard2,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)))
         => ( ( v1_topreal1(A)
              & v1_topreal1(B) )
           => ( ( k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))
                & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
              | v1_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t14_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ ( A != k1_xboole_0
          & k2_goboard1(A) = k1_xboole_0 ) ) )).

fof(t15_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ~ ( A != k1_xboole_0
          & k3_goboard1(A) = k1_xboole_0 ) ) )).

fof(t16_goboard2,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)))) )
         => ( v1_topreal1(A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(C,k4_finseq_1(A))
                    & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) )
                 => ! [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)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
                                      & r2_hidden(k4_tarski(F,G),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,D,E)
                                      & 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,F,G)
                                      & D != F
                                      & G != E ) ) ) ) ) ) ) ) ) ) )).

fof(t17_goboard2,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)
                 => ~ ( r2_hidden(C,k4_finseq_1(A))
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(k4_tarski(D,E),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,D,E) ) ) ) ) )
              & v1_topreal1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(C,k4_finseq_1(A))
                      & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A))
                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) ) )
              & ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
                      & k5_topreal1(np__2,A) = k5_topreal1(np__2,C)
                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
                      & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) ) ) ) ) ) )).

fof(t18_goboard2,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(B,C) )
                 => r1_xreal_0(k1_goboard1(A,B),k1_goboard1(A,C)) ) ) ) ) ) )).

fof(t19_goboard2,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))
                    & B != C
                    & k1_goboard1(A,B) = k1_goboard1(A,C) ) ) ) ) ) )).

fof(t20_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v1_goboard1(A)
                  & B = k7_relat_1(A,k2_finseq_1(C)) )
               => v1_goboard1(B) ) ) ) ) )).

fof(t21_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ? [B] :
          ( m2_finseq_1(B,k1_numbers)
          & k2_relat_1(B) = k2_relat_1(A)
          & k3_finseq_1(B) = k4_card_1(k2_relat_1(A))
          & v1_goboard1(B) ) ) )).

fof(t22_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k1_numbers)
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & k2_relat_1(A) = k2_relat_1(B)
              & v1_goboard1(A)
              & v1_goboard1(B) )
           => A = B ) ) ) )).

fof(d1_goboard2,axiom,(
    ! [A] :
      ( ( v1_goboard1(A)
        & m2_finseq_1(A,k1_numbers) )
     => ! [B] :
          ( ( v1_goboard1(B)
            & m2_finseq_1(B,k1_numbers) )
         => ~ ( A != k1_xboole_0
              & B != k1_xboole_0
              & ~ ! [C] :
                    ( ( v1_matrix_1(C)
                      & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
                   => ( C = k1_goboard2(A,B)
                    <=> ( k3_finseq_1(C) = k3_finseq_1(A)
                        & k1_matrix_1(C) = k3_finseq_1(B)
                        & ! [D] :
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                           => ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => ( r2_hidden(k4_tarski(D,E),k2_matrix_1(C))
                                 => k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,D,E) = k23_euclid(k1_goboard1(A,D),k1_goboard1(B,E)) ) ) ) ) ) ) ) ) ) )).

fof(d2_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_goboard1(B)
            & m2_finseq_1(B,k1_numbers) )
         => ( B = k2_goboard2(A)
          <=> ( k2_relat_1(B) = k2_relat_1(A)
              & k3_finseq_1(B) = k4_card_1(k2_relat_1(A)) ) ) ) ) )).

fof(d3_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k3_goboard2(A) = k1_goboard2(k2_goboard2(k2_goboard1(A)),k2_goboard2(k3_goboard1(A))) ) )).

fof(t23_goboard2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_numbers)
     => ~ ( A != k1_xboole_0
          & k2_goboard2(A) = k1_xboole_0 ) ) )).

fof(t24_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( k3_finseq_1(k3_goboard2(A)) = k4_card_1(k2_relat_1(k2_goboard1(A)))
        & k1_matrix_1(k3_goboard2(A)) = k4_card_1(k2_relat_1(k3_goboard1(A))) ) ) )).

fof(t25_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(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))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k3_goboard2(A)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,D) ) ) ) ) ) ) )).

fof(t26_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(A,k4_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => r1_xreal_0(k1_goboard1(k2_goboard1(B),A),k1_goboard1(k2_goboard1(B),C)) ) ) )
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),np__1))) ) ) ) )).

fof(t27_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(A,k4_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => r1_xreal_0(k1_goboard1(k2_goboard1(B),C),k1_goboard1(k2_goboard1(B),A)) ) ) )
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k3_finseq_1(k3_goboard2(B))))) ) ) ) )).

fof(t28_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(A,k4_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => r1_xreal_0(k1_goboard1(k3_goboard1(B),A),k1_goboard1(k3_goboard1(B),C)) ) ) )
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),np__1))) ) ) ) )).

fof(t29_goboard2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(A,k4_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => r1_xreal_0(k1_goboard1(k3_goboard1(B),C),k1_goboard1(k3_goboard1(B),A)) ) ) )
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k1_matrix_1(k3_goboard2(B))))) ) ) ) )).

fof(s1_goboard2,axiom,(
    ? [A] :
      ( m2_finseq_1(A,f1_s1_goboard2)
      & k3_finseq_1(A) = f2_s1_goboard2
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k4_finseq_1(A))
           => k4_finseq_4(k5_numbers,f1_s1_goboard2,A,B) = f3_s1_goboard2(B) ) ) ) )).

fof(dt_k1_goboard2,axiom,(
    ! [A,B] :
      ( ( v1_goboard1(A)
        & m1_finseq_1(A,k1_numbers)
        & v1_goboard1(B)
        & m1_finseq_1(B,k1_numbers) )
     => ( v1_matrix_1(k1_goboard2(A,B))
        & m2_finseq_1(k1_goboard2(A,B),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(dt_k2_goboard2,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k1_numbers)
     => ( v1_goboard1(k2_goboard2(A))
        & m2_finseq_1(k2_goboard2(A),k1_numbers) ) ) )).

fof(dt_k3_goboard2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( v1_matrix_1(k3_goboard2(A))
        & m2_finseq_1(k3_goboard2(A),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) )).
%------------------------------------------------------------------------------