SET007 Axioms: SET007+414.ax


%------------------------------------------------------------------------------
% File     : SET007+414 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Special Polygons
% 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    : sppol_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   92 (   5 unit)
%            Number of atoms       :  530 (  65 equality)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives :  481 (  43 ~  ;  13  |; 193  &)
%                                         (   3 <=>; 229 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-3 arity)
%            Number of functors    :   40 (   7 constant; 0-4 arity)
%            Number of variables   :  205 (   0 singleton; 195 !;  10 ?)
%            Maximal term depth    :    7 (   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_sppol_2,axiom,(
    ? [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v4_topreal1(A) ) )).

fof(cc1_sppol_2,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => ( v2_funct_1(A)
          & ~ v1_realset1(A)
          & v1_topreal1(A)
          & v2_topreal1(A)
          & v3_topreal1(A) ) ) ) )).

fof(cc2_sppol_2,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( v2_funct_1(A)
          & ~ v1_realset1(A)
          & v1_topreal1(A)
          & v2_topreal1(A)
          & v3_topreal1(A) )
       => v4_topreal1(A) ) ) )).

fof(cc3_sppol_2,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_topreal1(A)
       => ~ v1_xboole_0(A) ) ) )).

fof(rc2_sppol_2,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_realset1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v3_topreal1(A)
      & v4_topreal1(A) ) )).

fof(fc1_sppol_2,axiom,(
    ! [A,B] :
      ( ( v2_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v2_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc2_sppol_2,axiom,(
    ! [A,B] :
      ( ( v2_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v2_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc3_sppol_2,axiom,(
    ! [A,B] :
      ( ( v2_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v2_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc4_sppol_2,axiom,(
    ! [A,B] :
      ( ( v3_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc5_sppol_2,axiom,(
    ! [A,B] :
      ( ( v3_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v3_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc6_sppol_2,axiom,(
    ! [A,B] :
      ( ( v3_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v3_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc7_sppol_2,axiom,
    ( v1_xboole_0(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_relat_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_funct_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_realset1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_finset_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_finseq_1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_topreal1(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v1_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v2_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v3_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v4_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2))))
    & v5_membered(k6_finseq_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(fc8_sppol_2,axiom,(
    ! [A,B] :
      ( ( v1_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc9_sppol_2,axiom,(
    ! [A,B] :
      ( ( v1_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(fc10_sppol_2,axiom,(
    ! [A,B] :
      ( ( v1_topreal1(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))
        & v1_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) )).

fof(rc3_sppol_2,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
      & ~ v1_xboole_0(A)
      & v5_topreal1(A) ) )).

fof(fc11_sppol_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => ( ~ v1_xboole_0(k1_topreal1(A,B,C))
        & v6_compts_1(k1_topreal1(A,B,C),k15_euclid(A)) ) ) )).

fof(fc12_sppol_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( ~ v1_xboole_0(k1_sppol_2(A,B,C,D))
        & v6_compts_1(k1_sppol_2(A,B,C,D),k15_euclid(np__2)) ) ) )).

fof(rc4_sppol_2,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
      & v1_topreal4(A) ) )).

fof(rc5_sppol_2,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
      & v1_topreal4(A) ) )).

fof(cc4_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal4(A)
       => ~ v1_xboole_0(A) ) ) )).

fof(cc5_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal4(A)
       => ~ v1_realset1(A) ) ) )).

fof(t1_sppol_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( k23_euclid(A,B) = k23_euclid(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t2_sppol_2,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)
             => ( k1_nat_1(B,C) = k3_finseq_1(A)
               => k4_topreal1(np__2,A,B) = k4_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),C) ) ) ) ) )).

fof(t3_sppol_2,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)
             => ( r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,C)))
               => k4_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,C),B) = k4_topreal1(np__2,A,B) ) ) ) ) )).

fof(t4_sppol_2,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)
             => ( ( r1_xreal_0(B,k3_finseq_1(A))
                  & r1_xreal_0(np__1,C) )
               => k4_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,A,k1_nat_1(B,C)) ) ) ) ) )).

fof(t5_sppol_2,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)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k5_real_1(k3_finseq_1(A),C)) )
               => k4_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,C),B) = k4_topreal1(np__2,A,k1_nat_1(C,B)) ) ) ) ) )).

fof(t6_sppol_2,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)
             => ( r1_xreal_0(k1_nat_1(C,np__1),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,A,C) ) ) ) ) )).

fof(t7_sppol_2,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)
             => ( r1_xreal_0(np__1,C)
               => k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(k3_finseq_1(A),C)) = k4_topreal1(np__2,B,C) ) ) ) ) )).

fof(t8_sppol_2,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_xboole_0(A)
              & ~ v1_xboole_0(B)
              & k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(A)) != k3_topreal1(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)) ) ) ) )).

fof(t9_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)))
               => k4_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,A,C) ) ) ) ) )).

fof(t10_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(B,k2_relat_1(A))
               => k4_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(C,np__1)) = k4_topreal1(np__2,A,k1_nat_1(C,k5_finseq_4(A,B))) ) ) ) ) )).

fof(t11_sppol_2,axiom,(
    k5_topreal1(np__2,k6_finseq_1(u1_struct_0(k15_euclid(np__2)))) = k1_xboole_0 )).

fof(t12_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => k5_topreal1(np__2,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),A)) = k1_xboole_0 ) )).

fof(t13_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k5_topreal1(np__2,A))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r2_hidden(B,k4_topreal1(np__2,A,C)) ) ) ) ) ) )).

fof(t14_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( r2_hidden(B,k5_topreal1(np__2,A))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r2_hidden(B,k3_topreal1(np__2,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)))) ) ) ) ) ) )).

fof(t15_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & r2_hidden(B,k3_topreal1(np__2,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)))) )
               => r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t16_sppol_2,axiom,(
    ! [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(k1_nat_1(B,np__1),k3_finseq_1(A)) )
           => r1_tarski(k3_topreal1(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))),k5_topreal1(np__2,A)) ) ) ) )).

fof(t17_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(B,k4_topreal1(np__2,A,C))
               => r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t18_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__2,k3_finseq_1(A))
       => r1_tarski(k2_relat_1(A),k5_topreal1(np__2,A)) ) ) )).

fof(t19_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ v1_xboole_0(A)
           => k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B))) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B)) ) ) ) )).

fof(t20_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ v1_xboole_0(A)
           => k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B),A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k5_topreal1(np__2,A)) ) ) ) )).

fof(t21_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => k5_topreal1(np__2,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) = k3_topreal1(np__2,A,B) ) ) )).

fof(t22_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => k5_topreal1(np__2,A) = k5_topreal1(np__2,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) )).

fof(t23_sppol_2,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_xboole_0(A)
              & ~ v1_xboole_0(B)
              & k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) != k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k3_topreal1(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))),k5_topreal1(np__2,B)) ) ) ) )).

fof(t24_sppol_2,axiom,(
    $true )).

fof(t25_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k2_relat_1(A))
           => k5_topreal1(np__2,A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) )).

fof(t26_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(B,k4_topreal1(np__2,A,C))
               => k5_topreal1(np__2,A) = k5_topreal1(np__2,k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) )).

fof(t27_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(k3_finseq_1(A),np__2)
       => v2_topreal1(A) ) ) )).

fof(t28_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,k2_relat_1(A))
              & v2_topreal1(A) )
           => v2_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t29_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v2_topreal1(A)
       => v2_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) )).

fof(t30_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( v2_topreal1(A)
              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k4_topreal1(np__2,A,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
           => v2_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B),A)) ) ) ) )).

fof(t31_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v2_topreal1(A)
                  & k1_nat_1(C,np__1) = k3_finseq_1(A)
                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B)) = 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(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B))) ) ) ) ) )).

fof(t32_sppol_2,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)
             => ( ( v2_topreal1(A)
                  & v2_topreal1(B)
                  & k1_nat_1(C,np__1) = k3_finseq_1(A)
                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,C),k3_topreal1(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))) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))
                  & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(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,B,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
               => v2_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t33_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v2_topreal1(A)
                  & r2_hidden(B,k4_topreal1(np__2,A,C)) )
               => v2_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) )).

fof(t34_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(k3_finseq_1(A),np__2)
       => v3_topreal1(A) ) ) )).

fof(t35_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,k2_relat_1(A))
              & v3_topreal1(A) )
           => v3_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t36_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v3_topreal1(A)
       => v3_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) )).

fof(t37_sppol_2,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)))
         => ( ( v3_topreal1(A)
              & v3_topreal1(B)
              & r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(A)) )
                   => r1_xboole_0(k4_topreal1(np__2,A,C),k3_topreal1(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))) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__2,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B)) )
                   => r1_xboole_0(k4_topreal1(np__2,B,C),k3_topreal1(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))) ) ) )
           => v3_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t38_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v2_topreal1(A)
                  & v3_topreal1(A)
                  & r2_hidden(B,k4_topreal1(np__2,A,C)) )
               => ( r2_hidden(B,k2_relat_1(A))
                  | v3_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) )).

fof(t39_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => v1_topreal1(k12_finseq_1(u1_struct_0(k15_euclid(np__2)),A)) ) )).

fof(t40_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( k21_euclid(A) = k21_euclid(B)
              | k22_euclid(A) = k22_euclid(B) )
           => v1_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t41_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,k2_relat_1(A))
              & v1_topreal1(A) )
           => v1_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t42_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v1_topreal1(A)
       => v1_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) ) )).

fof(t43_sppol_2,axiom,(
    $true )).

fof(t44_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( v1_topreal1(A)
                  & r2_hidden(B,k4_topreal1(np__2,A,C)) )
               => v1_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) )).

fof(t45_sppol_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r2_hidden(B,k2_relat_1(A))
              & v2_topreal1(A)
              & v3_topreal1(A) )
           => ( np__1 = k5_finseq_4(A,B)
              | k5_finseq_4(A,B) = k3_finseq_1(A)
              | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,B))) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) )).

fof(t46_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( A != B
              & ( k21_euclid(A) = k21_euclid(B)
                | k22_euclid(A) = k22_euclid(B) )
              & ~ v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) )).

fof(t47_sppol_2,axiom,(
    ! [A] :
      ( ( v4_topreal1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => v4_topreal1(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A)) ) )).

fof(t48_sppol_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r2_hidden(A,k4_finseq_1(B))
           => r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k5_topreal1(np__2,B)) ) ) ) )).

fof(t49_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ~ ( A != B
              & ( k21_euclid(A) = k21_euclid(B)
                | k22_euclid(A) = k22_euclid(B) )
              & ~ v5_topreal1(k3_topreal1(np__2,A,B)) ) ) ) )).

fof(t50_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r2_hidden(A,k2_relat_1(B))
           => ( k5_finseq_4(B,A) = np__1
              | v4_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) )).

fof(t51_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( r2_hidden(A,k2_relat_1(B))
           => ( k5_finseq_4(B,A) = k3_finseq_1(B)
              | v4_topreal1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) )).

fof(t52_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v4_topreal1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( r2_hidden(A,k4_topreal1(np__2,C,B))
               => ( r2_hidden(A,k2_relat_1(C))
                  | v4_topreal1(k5_finseq_5(u1_struct_0(k15_euclid(np__2)),C,A,B)) ) ) ) ) ) )).

fof(t53_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_topreal4(A,B,C)
               => r1_topreal4(A,C,B) ) ) ) ) )).

fof(d1_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ( r1_sppol_2(A,B,C)
              <=> ( A != B
                  & ? [D] :
                      ( v4_topreal1(D)
                      & m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                      & ? [E] :
                          ( v4_topreal1(E)
                          & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                          & A = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,np__1)
                          & A = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1)
                          & B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D))
                          & B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E))
                          & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_struct_0(k15_euclid(np__2),A,B)
                          & C = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) ) ) ) ) ) ) ) )).

fof(t54_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_sppol_2(B,C,A)
               => r1_sppol_2(C,B,A) ) ) ) ) )).

fof(t55_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_sppol_2(B,C,A)
                      & r2_hidden(D,A) )
                   => ( D = B
                      | r1_sppol_2(B,D,A) ) ) ) ) ) ) )).

fof(t56_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( r1_sppol_2(B,C,A)
                      & r2_hidden(D,A) )
                   => ( D = C
                      | r1_sppol_2(D,C,A) ) ) ) ) ) ) )).

fof(t57_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_sppol_2(B,C,A)
                          & r2_hidden(D,A)
                          & r2_hidden(E,A) )
                       => ( D = E
                          | r1_sppol_2(D,E,A) ) ) ) ) ) ) ) )).

fof(d2_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal4(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                & r1_sppol_2(B,C,A) ) ) ) ) )).

fof(d3_sppol_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k1_sppol_2(A,B,C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(A,C),k23_euclid(A,D)),k3_topreal1(np__2,k23_euclid(A,D),k23_euclid(B,D))),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(B,D),k23_euclid(B,C)),k3_topreal1(np__2,k23_euclid(B,C),k23_euclid(A,C)))) ) ) ) ) )).

fof(t59_sppol_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( A != B
                      & C != D
                      & ~ v1_topreal4(k1_sppol_2(A,B,C,D)) ) ) ) ) ) )).

fof(t60_sppol_2,axiom,(
    k2_topreal1 = k1_sppol_2(np__0,np__1,np__0,np__1) )).

fof(t61_sppol_2,axiom,(
    v1_topreal4(k2_topreal1) )).

fof(t62_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v5_topreal1(A)
       => v6_compts_1(A,k15_euclid(np__2)) ) ) )).

fof(t63_sppol_2,axiom,(
    ! [A] :
      ( ( v1_topreal4(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => v6_compts_1(A,k15_euclid(np__2)) ) )).

fof(t64_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal4(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => ( B = C
                    | r1_sppol_2(B,C,A) ) ) ) ) ) ) )).

fof(t65_sppol_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal4(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
               => ~ ( B != C
                    & r2_hidden(B,A)
                    & r2_hidden(C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                       => ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                           => ~ ( r1_topreal4(D,B,C)
                                & r1_topreal4(E,B,C)
                                & k5_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) = k2_struct_0(k15_euclid(np__2),B,C)
                                & A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),D,E) ) ) ) ) ) ) ) ) )).

fof(dt_k1_sppol_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_subset_1(k1_sppol_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(t58_sppol_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => k1_sppol_2(A,B,C,D) = a_4_0_sppol_2(A,B,C,D) ) ) ) ) ) )).

fof(fraenkel_a_4_0_sppol_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( r2_hidden(A,a_4_0_sppol_2(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
            & A = F
            & ~ ( ~ ( k21_euclid(F) = B
                    & r1_xreal_0(k22_euclid(F),E)
                    & r1_xreal_0(D,k22_euclid(F)) )
                & ~ ( r1_xreal_0(k21_euclid(F),C)
                    & r1_xreal_0(B,k21_euclid(F))
                    & k22_euclid(F) = E )
                & ~ ( r1_xreal_0(k21_euclid(F),C)
                    & r1_xreal_0(B,k21_euclid(F))
                    & k22_euclid(F) = D )
                & ~ ( k21_euclid(F) = C
                    & r1_xreal_0(k22_euclid(F),E)
                    & r1_xreal_0(D,k22_euclid(F)) ) ) ) ) ) )).
%------------------------------------------------------------------------------