SET007 Axioms: SET007+709.ax


%------------------------------------------------------------------------------
% File     : SET007+709 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : More on the Finite Sequences on the Plane
% 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    : topreal8 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   39 (   0 unit)
%            Number of atoms       :  285 (  41 equality)
%            Maximal formula depth :   23 (   8 average)
%            Number of connectives :  309 (  63 ~  ;   8  |; 129  &)
%                                         (   0 <=>; 109 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   0 propositional; 1-3 arity)
%            Number of functors    :   39 (   6 constant; 0-4 arity)
%            Number of variables   :   96 (   0 singleton;  93 !;   3 ?)
%            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_topreal8,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_realset1(A)
      & v5_seqm_3(A) ) )).

fof(rc2_topreal8,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & ~ v1_realset1(A)
      & ~ v5_seqm_3(A) ) )).

fof(rc3_topreal8,axiom,(
    ? [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v3_topreal1(A) ) )).

fof(t1_topreal8,axiom,(
    ! [A,B,C] :
      ( ( r1_tarski(A,k2_tarski(B,C))
        & r2_hidden(B,A) )
     => ( r2_hidden(C,A)
        | A = k1_tarski(B) ) ) )).

fof(t2_topreal8,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_realset1(A) )
     => ~ r1_xreal_0(k3_finseq_1(A),np__1) ) )).

fof(t3_topreal8,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ! [B] :
          ( ( ~ v5_seqm_3(B)
            & v1_finseq_6(B,A)
            & m2_finseq_1(B,A) )
         => ~ r1_xreal_0(k3_finseq_1(B),np__2) ) ) )).

fof(t4_topreal8,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( r2_hidden(B,k2_relat_1(A))
          | k5_finseq_4(A,B) = np__0 ) ) )).

fof(t5_topreal8,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( ~ v1_xboole_0(C)
            & m2_finseq_1(C,B) )
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ( k5_finseq_4(C,A) = k3_finseq_1(C)
               => k7_finseq_4(k8_finseq_1(B,C,D),A) = D ) ) ) ) )).

fof(t6_topreal8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_funct_1(B)
            & m2_finseq_1(B,A) )
         => k5_finseq_4(B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) = k3_finseq_1(B) ) ) )).

fof(t7_topreal8,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_xreal_0(k3_finseq_1(A),k3_finseq_1(k3_graph_2(A,B))) ) ) )).

fof(t8_topreal8,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( r2_hidden(C,k2_relat_1(A))
             => k5_finseq_4(A,C) = k5_finseq_4(k3_graph_2(A,B),C) ) ) ) )).

fof(t9_topreal8,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_xreal_0(k3_finseq_1(B),k3_finseq_1(k3_graph_2(A,B))) ) ) )).

fof(t10_topreal8,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k2_relat_1(A),k2_relat_1(k3_graph_2(A,B))) ) ) )).

fof(t11_topreal8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( ( ~ v1_realset1(C)
                & m2_finseq_1(C,A) )
             => ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,B,np__1)
               => v1_finseq_6(k4_graph_2(A,B,C),A) ) ) ) ) )).

fof(t12_topreal8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m2_finseq_1(D,A) )
                 => ( ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,D,np__1)
                      & r1_goboard1(A,C,B)
                      & r1_goboard1(A,D,B) )
                   => r1_goboard1(A,k4_graph_2(A,C,D),B) ) ) ) ) ) )).

fof(t13_topreal8,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ( r1_xreal_0(np__1,A)
           => k2_graph_2(B,C,k1_nat_1(A,np__1),k3_finseq_1(C)) = k1_rfinseq(B,C,A) ) ) ) )).

fof(t14_topreal8,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ( r1_xreal_0(A,k3_finseq_1(C))
           => k2_graph_2(B,C,np__1,A) = k16_finseq_1(B,C,A) ) ) ) )).

fof(t15_topreal8,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( ~ v1_xboole_0(C)
            & m2_finseq_1(C,B) )
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ( k5_finseq_4(C,A) = k3_finseq_1(C)
               => k6_finseq_4(k8_finseq_1(B,C,D),A) = k2_graph_2(B,C,np__1,k5_binarith(k3_finseq_1(C),np__1)) ) ) ) ) )).

fof(t16_topreal8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_finseq_1(C,A) )
             => ( k5_finseq_4(B,k4_finseq_4(k5_numbers,A,C,np__1)) = k3_finseq_1(B)
               => k2_finseq_5(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = C ) ) ) ) )).

fof(t17_topreal8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_finseq_1(C,A) )
             => ( k5_finseq_4(B,k4_finseq_4(k5_numbers,A,C,np__1)) = k3_finseq_1(B)
               => k1_finseq_5(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = B ) ) ) ) )).

fof(t18_topreal8,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( ( ~ v1_realset1(C)
                & m2_finseq_1(C,A) )
             => ( ( k4_finseq_4(k5_numbers,A,C,np__1) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(np__1,D)
                          & ~ r1_xreal_0(k3_finseq_1(B),D)
                          & k4_finseq_4(k5_numbers,A,B,D) = k4_finseq_4(k5_numbers,A,C,np__1) ) ) )
               => k1_finseq_6(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = k4_graph_2(A,C,B) ) ) ) ) )).

fof(t19_topreal8,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k4_topreal1(np__2,A,np__1) = k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,np__2)) ) )).

fof(t20_topreal8,axiom,(
    ! [A] :
      ( ( v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(k3_finseq_1(A),B)
           => v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t21_topreal8,axiom,(
    ! [A] :
      ( ( v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(np__1,B)
           => v3_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t22_topreal8,axiom,(
    ! [A] :
      ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(k3_finseq_1(A),B)
              & ~ r1_xreal_0(k3_finseq_1(A),np__4)
              & ~ v2_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t23_topreal8,axiom,(
    ! [A] :
      ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ r1_xreal_0(k3_finseq_1(A),np__4)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( ~ r1_xreal_0(B,np__1)
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(C,k3_finseq_1(A))
                    & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) ) ) ) ) ) )).

fof(t24_topreal8,axiom,(
    ! [A] :
      ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(np__1,B)
           => ( r1_xreal_0(k3_finseq_1(A),np__4)
              | v2_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t25_topreal8,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_topreal1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => v1_topreal1(k2_graph_2(u1_struct_0(k15_euclid(np__2)),C,A,B)) ) ) ) )).

fof(t26_topreal8,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v1_realset1(B)
            & v1_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
           => v1_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t27_topreal8,axiom,(
    ! [A] :
      ( ( v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ r1_xreal_0(k3_finseq_1(A),np__4)
       => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,np__1),k5_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,np__1))) = k2_struct_0(k15_euclid(np__2),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)),A,np__2)) ) ) )).

fof(t28_topreal8,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ~ r1_xreal_0(k3_finseq_1(B),A)
               => k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A) = k4_topreal1(np__2,B,A) ) ) ) ) )).

fof(t29_topreal8,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))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( r1_xreal_0(np__1,A)
               => ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(A,np__1))
                  | k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),k1_nat_1(k3_finseq_1(B),A)) = k4_topreal1(np__2,C,k1_nat_1(A,np__1)) ) ) ) ) ) )).

fof(t30_topreal8,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v1_realset1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
           => k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(A)) = k4_topreal1(np__2,B,np__1) ) ) ) )).

fof(t31_topreal8,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))) )
         => ! [C] :
              ( ( ~ v1_realset1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)
               => ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(A,np__1))
                  | k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),k1_nat_1(k3_finseq_1(B),A)) = k4_topreal1(np__2,C,k1_nat_1(A,np__1)) ) ) ) ) ) )).

fof(t32_topreal8,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_topreal1(A)
        & v3_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(np__1,B)
           => ( r1_xreal_0(k3_finseq_1(A),B)
              | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,B),k5_relset_1(k5_numbers,u1_struct_0(k15_euclid(np__2)),A)) = k2_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))) ) ) ) ) )).

fof(t33_topreal8,axiom,(
    ! [A] :
      ( ( v2_funct_1(A)
        & ~ v1_realset1(A)
        & v2_topreal1(A)
        & v3_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( v2_funct_1(B)
            & ~ v1_realset1(B)
            & v2_topreal1(B)
            & v3_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k2_struct_0(k15_euclid(np__2),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)),B,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)),B,k3_finseq_1(B))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) )
           => v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t34_topreal8,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)))
         => ( ( v2_topreal1(A)
              & v2_topreal1(B)
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1)),k4_topreal1(np__2,B,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
           => v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t35_topreal8,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)))
         => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
           => ( v1_xboole_0(A)
              | v1_realset1(B)
              | k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) ) ) ) ) )).

fof(t36_topreal8,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)))
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(C,k4_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(A))
                                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E) ) ) ) ) )
              & ~ v5_seqm_3(B)
              & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
              & v2_topreal1(B)
              & v1_goboard5(B)
              & v1_topreal1(B)
              & ~ r1_xreal_0(k3_finseq_1(B),np__4)
              & ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,A)
                      & v2_topreal1(C)
                      & v1_goboard5(C)
                      & v1_topreal1(C)
                      & k5_topreal1(np__2,B) = k5_topreal1(np__2,C)
                      & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = 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)),B,k3_finseq_1(B)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))
                      & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) ) )).
%------------------------------------------------------------------------------