SET007 Axioms: SET007+570.ax


%------------------------------------------------------------------------------
% File     : SET007+570 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Special Polygonal Curves
% 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    : sprect_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   7 unit)
%            Number of atoms       :  668 (  60 equality)
%            Maximal formula depth :   15 (   9 average)
%            Number of connectives :  686 ( 100 ~  ;  15  |; 354  &)
%                                         (   5 <=>; 212 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   42 (   1 propositional; 0-5 arity)
%            Number of functors    :   67 (   7 constant; 0-5 arity)
%            Number of variables   :  184 (   0 singleton; 178 !;   6 ?)
%            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_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k5_topreal1(np__2,A))
        & ~ v1_sppol_1(k5_topreal1(np__2,A))
        & ~ v2_sppol_1(k5_topreal1(np__2,A))
        & v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v1_topreal2(k5_topreal1(np__2,A)) ) ) )).

fof(fc2_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k2_goboard9(A))
        & v2_topreal4(k2_goboard9(A),k15_euclid(np__2)) ) ) )).

fof(fc3_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k3_goboard9(A))
        & v2_topreal4(k3_goboard9(A),k15_euclid(np__2)) ) ) )).

fof(rc1_sprect_3,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)
      & v1_finseq_1(A)
      & ~ v1_realset1(A)
      & v1_sprect_1(A)
      & ~ v5_seqm_3(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
      & v1_goboard5(A)
      & v2_goboard5(A) ) )).

fof(rc2_sprect_3,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)
      & v1_finseq_1(A)
      & v1_sprect_2(A)
      & ~ v1_realset1(A)
      & v1_sprect_1(A)
      & ~ v5_seqm_3(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
      & v1_goboard5(A)
      & v2_goboard5(A) ) )).

fof(cc1_sprect_3,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ( ~ v1_xboole_0(A)
          & v1_sprect_1(A)
          & v1_topreal1(A)
          & v2_topreal1(A)
          & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
          & v1_goboard5(A) )
       => ( ~ v1_xboole_0(A)
          & v1_sprect_2(A)
          & v1_sprect_1(A)
          & ~ v5_seqm_3(A)
          & v1_topreal1(A)
          & v2_topreal1(A)
          & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
          & v1_goboard5(A)
          & v2_goboard5(A) ) ) ) )).

fof(t1_sprect_3,axiom,(
    $true )).

fof(t2_sprect_3,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(A,B)
        & k3_xboole_0(B,C) = k1_tarski(D)
        & r2_hidden(D,A) )
     => k3_xboole_0(A,C) = k1_tarski(D) ) )).

fof(t3_sprect_3,axiom,(
    $true )).

fof(t4_sprect_3,axiom,(
    $true )).

fof(t5_sprect_3,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)
             => ( r1_xreal_0(k5_binarith(A,B),C)
               => r1_xreal_0(A,k1_nat_1(C,B)) ) ) ) ) )).

fof(t6_sprect_3,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)
             => ( r1_xreal_0(A,k1_nat_1(B,C))
               => r1_xreal_0(k5_binarith(A,C),B) ) ) ) ) )).

fof(t7_sprect_3,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)
             => ( ( r1_xreal_0(A,k5_binarith(B,C))
                  & r1_xreal_0(C,B) )
               => r1_xreal_0(k1_nat_1(A,C),B) ) ) ) ) )).

fof(t8_sprect_3,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)
             => ( r1_xreal_0(k1_nat_1(A,B),C)
               => r1_xreal_0(B,k5_binarith(C,A)) ) ) ) ) )).

fof(t9_sprect_3,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)
             => ~ ( r1_xreal_0(A,B)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k5_binarith(C,A),k5_binarith(B,A)) ) ) ) ) )).

fof(t10_sprect_3,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)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(B,C)
                  & r1_xreal_0(k5_binarith(B,C),k5_binarith(A,C)) ) ) ) ) )).

fof(t11_sprect_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,C,B),k3_finseq_1(k8_finseq_1(A,C,B))) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)) ) ) ) )).

fof(t12_sprect_3,axiom,(
    ! [A,B,C,D] : k2_matrix_1(k3_matrix_2(A,B,C,D)) = k2_enumset1(k4_tarski(np__1,np__1),k4_tarski(np__1,np__2),k4_tarski(np__2,np__1),k4_tarski(np__2,np__2)) )).

fof(t13_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( B = k17_euclid(A,k18_euclid(k5_real_1(np__1,D),A,B),k18_euclid(D,A,C))
                   => ( r1_xreal_0(D,np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t14_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( B = k17_euclid(A,k18_euclid(k5_real_1(np__1,D),A,C),k18_euclid(D,A,B))
                   => ( r1_xreal_0(np__1,D)
                      | B = C ) ) ) ) ) ) )).

fof(t15_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( B = k18_euclid(k6_real_1(np__1,np__2),A,k17_euclid(A,B,C))
               => B = C ) ) ) ) )).

fof(t16_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( ( r2_hidden(C,k3_topreal1(A,B,D))
                      & r2_hidden(D,k3_topreal1(A,B,C)) )
                   => C = D ) ) ) ) ) )).

fof(t17_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( A = k9_metric_1(k14_euclid(np__2),B,C)
               => v2_connsp_1(A,k15_euclid(np__2)) ) ) ) ) )).

fof(t18_sprect_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( v3_pre_topc(A,k15_euclid(np__2))
              & r4_connsp_1(k15_euclid(np__2),A,B) )
           => v3_pre_topc(B,k15_euclid(np__2)) ) ) ) )).

fof(t19_sprect_3,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,u1_struct_0(k15_euclid(np__2)))
             => ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
                  & r2_hidden(C,k3_topreal1(np__2,A,B)) )
               => k22_euclid(A) = k22_euclid(C) ) ) ) ) )).

fof(t20_sprect_3,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,u1_struct_0(k15_euclid(np__2)))
             => ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
                  & r2_hidden(C,k3_topreal1(np__2,A,B)) )
               => k21_euclid(A) = k21_euclid(C) ) ) ) ) )).

fof(t21_sprect_3,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,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
                      & v1_sppol_1(k3_topreal1(np__2,C,D)) )
                   => ( r2_subset_1(k3_topreal1(np__2,A,B),k3_topreal1(np__2,C,D))
                      | k22_euclid(A) = k22_euclid(C) ) ) ) ) ) ) )).

fof(t22_sprect_3,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,u1_struct_0(k15_euclid(np__2)))
             => ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
                  & v1_sppol_1(k3_topreal1(np__2,B,C)) )
               => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,B,C)) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) )).

fof(t23_sprect_3,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,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
                      & v2_sppol_1(k3_topreal1(np__2,D,C))
                      & r2_hidden(C,k3_topreal1(np__2,A,B)) )
                   => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,D,C)) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ) )).

fof(t24_sprect_3,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)))) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(A,B)
                      & r1_xreal_0(B,k1_matrix_1(D))
                      & r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(D)) )
                   => r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B))) ) ) ) ) ) )).

fof(t25_sprect_3,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)))) )
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(A,k1_matrix_1(D))
                      & r1_xreal_0(np__1,B)
                      & r1_xreal_0(B,C)
                      & r1_xreal_0(C,k3_finseq_1(D)) )
                   => r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A))) ) ) ) ) ) )).

fof(t26_sprect_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)),k5_topreal1(np__2,k1_sprect_1(A))) ) )).

fof(t27_sprect_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k27_pscomp_1(A),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) )).

fof(t28_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r2_hidden(k32_pscomp_1(A),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) )).

fof(t29_sprect_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => v1_sppol_1(k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) )).

fof(t30_sprect_3,axiom,(
    $true )).

fof(t31_sprect_3,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)))
         => ( ( v4_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)),k5_topreal1(np__2,A)) = k1_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__1) = B
              | ( k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) != k21_euclid(B)
                & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) != k22_euclid(B) )
              | v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B),A)) ) ) ) ) )).

fof(t32_sprect_3,axiom,(
    $true )).

fof(t33_sprect_3,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))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_xreal_0(A,k3_finseq_1(B))
                  & r2_hidden(C,k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__1,A))) )
               => ( r1_xreal_0(A,np__1)
                  | r1_jordan5c(k5_topreal1(np__2,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)),B,k3_finseq_1(B)),C,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) ) )).

fof(t34_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(A,k4_finseq_1(C))
                  & r2_hidden(B,k4_finseq_1(C)) )
               => r1_tarski(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)),k5_topreal1(np__2,C)) ) ) ) ) )).

fof(t35_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(np__1,A)
           => ( r1_xreal_0(B,A)
              | ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ( r1_xreal_0(B,k3_finseq_1(C))
                   => k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,C,A),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))) ) ) ) ) ) ) )).

fof(t36_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(B,k3_finseq_1(C)) )
               => ( r1_xreal_0(B,A)
                  | k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,k5_binarith(B,np__1))),k4_topreal1(np__2,C,k5_binarith(B,np__1))) ) ) ) ) ) )).

fof(t37_sprect_3,axiom,(
    $true )).

fof(t38_sprect_3,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)))
         => ( ( v4_topreal1(A)
              & v4_topreal1(B)
              & r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,B))
              & 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)),k5_topreal1(np__2,A)) = 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)),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
           => ( ( 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)) )
              | v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t39_sprect_3,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))
           => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B),np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) ) ) ) )).

fof(t40_sprect_3,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))) )
         => ! [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_xreal_0(np__1,A)
                      & r2_hidden(C,k4_topreal1(np__2,B,A))
                      & r2_hidden(D,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),C)) )
                   => ( r1_xreal_0(k3_finseq_1(B),A)
                      | r1_jordan5c(k5_topreal1(np__2,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)),B,k3_finseq_1(B)),D,C) ) ) ) ) ) ) )).

fof(t41_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( v3_pre_topc(k2_goboard9(A),k15_euclid(np__2))
        & v3_pre_topc(k3_goboard9(A),k15_euclid(np__2)) ) ) )).

fof(t42_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_subset_1(k3_goboard9(A),k5_topreal1(np__2,A)) ) )).

fof(t43_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_subset_1(k2_goboard9(A),k5_topreal1(np__2,A)) ) )).

fof(t44_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ r1_xreal_0(k8_jordan5d(A),k7_jordan5d(A)) ) )).

fof(t45_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_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(k3_goboard2(A)),B)
          & k32_pscomp_1(k5_topreal1(np__2,A)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A))) ) ) )).

fof(t46_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_sprect_2(B)
            & ~ v5_seqm_3(B)
            & v1_topreal1(B)
            & v2_topreal1(B)
            & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
            & v1_goboard5(B)
            & v2_goboard5(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(A,k4_finseq_1(k3_goboard2(B)))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),A,k1_matrix_1(k3_goboard2(B)))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k32_pscomp_1(k5_topreal1(np__2,B)) )
           => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k1_nat_1(A,np__1),k1_matrix_1(k3_goboard2(B)))
              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k5_binarith(k3_finseq_1(B),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),A,k5_binarith(k1_matrix_1(k3_goboard2(B)),np__1)) ) ) ) ) )).

fof(t47_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & ~ v5_seqm_3(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ~ ( r1_xreal_0(np__1,A)
                  & ~ r1_xreal_0(B,A)
                  & r1_xreal_0(B,k3_finseq_1(C))
                  & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)))
                  & A != np__1
                  & B != k3_finseq_1(C) ) ) ) ) )).

fof(t48_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_2(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
       => r1_tarski(k3_topreal1(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)),k5_topreal1(np__2,k1_sprect_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t49_sprect_3,axiom,(
    ! [A] :
      ( ( v1_sprect_1(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))
              & k21_euclid(B) != k18_pscomp_1(k5_topreal1(np__2,A))
              & k21_euclid(B) != k20_pscomp_1(k5_topreal1(np__2,A))
              & k22_euclid(B) != k21_pscomp_1(k5_topreal1(np__2,A))
              & k22_euclid(B) != k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) )).

fof(t50_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
              & r2_subset_1(k5_topreal1(np__2,A),k5_topreal1(np__2,B)) ) ) ) )).

fof(t51_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => k1_sprect_1(k5_topreal1(np__2,A)) = A ) )).

fof(t53_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => k3_goboard2(A) = k6_matrix_2(u1_struct_0(k15_euclid(np__2)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__4),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__3),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2)) ) )).

fof(t55_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
              & k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),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)),B,k3_finseq_1(B))) = k23_pscomp_1(k5_topreal1(np__2,A)) ) ) ) )).

fof(t56_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
              & k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),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)),B,k3_finseq_1(B))) = k25_pscomp_1(k5_topreal1(np__2,A)) ) ) ) )).

fof(t57_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(B))
                & r1_xreal_0(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
                & r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
                & r1_xreal_0(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A))) )
           => r2_hidden(B,k2_goboard9(A)) ) ) ) )).

fof(t58_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_2(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
       => r1_tarski(k2_goboard9(k1_sprect_1(k5_topreal1(np__2,A))),k2_goboard9(A)) ) ) )).

fof(t59_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
              <=> ( r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B))
                  & r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) ) ) ) ) ) )).

fof(t60_sprect_3,axiom,(
    ! [A] :
      ( ( v1_sprect_1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B))
           => ( ( k21_euclid(B) != k18_pscomp_1(k5_topreal1(np__2,A))
                & k21_euclid(B) != k20_pscomp_1(k5_topreal1(np__2,A))
                & k22_euclid(B) != k21_pscomp_1(k5_topreal1(np__2,A))
                & k22_euclid(B) != k19_pscomp_1(k5_topreal1(np__2,A)) )
              | r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t61_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( r1_xreal_0(np__0,D)
                      & r1_xreal_0(D,np__1)
                      & r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C)) )
                   => r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k17_euclid(np__2,k18_euclid(k5_real_1(np__1,D),np__2,B),k18_euclid(D,np__2,C)))) ) ) ) ) ) )).

fof(t62_sprect_3,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_sprect_2(B,C)
                  & r2_hidden(A,k4_finseq_1(C)) )
               => r1_sprect_2(B,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A))) ) ) ) ) )).

fof(t63_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_sprect_2(A,B)
                  & r2_hidden(C,k5_topreal1(np__2,B)) )
               => r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) ) ) ) ) )).

fof(t64_sprect_3,axiom,(
    ! [A] :
      ( ( v1_sprect_1(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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
               => ( r2_hidden(C,k5_topreal1(np__2,A))
                  | r1_tarski(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,C),k5_topreal1(np__2,A)),k1_struct_0(k15_euclid(np__2),B)) ) ) ) ) ) )).

fof(t65_sprect_3,axiom,(
    ! [A] :
      ( ( v1_sprect_1(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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r2_hidden(B,k5_topreal1(np__2,A))
                  & r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) )
               => ( r2_hidden(C,k5_topreal1(np__2,A))
                  | k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,C),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) ) )).

fof(t66_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & ~ v5_seqm_3(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(A,k3_finseq_1(k3_goboard2(C)))
                  & r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,k1_matrix_1(k3_goboard2(C))) )
               => r1_sprect_2(C,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B))) ) ) ) ) )).

fof(t67_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
               => r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,B,C)))) ) ) ) ) )).

fof(t68_sprect_3,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_sprect_2(A,B)
           => r1_sprect_2(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B)) ) ) ) )).

fof(t69_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_sprect_2(A,B)
                  & r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C))
                  & v4_topreal1(B)
                  & r2_hidden(C,k5_topreal1(np__2,B)) )
               => r1_sprect_2(A,k4_jordan3(B,C)) ) ) ) ) )).

fof(t70_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(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_sprect_2(A,B)
          <=> r1_sprect_2(k1_sprect_1(k5_topreal1(np__2,A)),B) ) ) ) )).

fof(t71_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ! [B] :
          ( ( v4_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ( ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
              & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A)) )
           => r1_sprect_2(A,k3_jordan3(B,k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),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)),B,k3_finseq_1(B))))) ) ) ) )).

fof(t72_sprect_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & ~ v5_seqm_3(C)
                & v1_topreal1(C)
                & v2_topreal1(C)
                & v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
                & v1_goboard5(C)
                & v2_goboard5(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ( ( r1_xreal_0(np__1,A)
                  & r1_xreal_0(np__1,B) )
               => ( r1_xreal_0(k3_finseq_1(k3_goboard2(C)),A)
                  | r1_xreal_0(k1_matrix_1(k3_goboard2(C)),B)
                  | r1_xboole_0(k1_tops_1(k15_euclid(np__2),k3_goboard5(k3_goboard2(C),A,B)),k5_topreal1(np__2,k1_sprect_1(k5_topreal1(np__2,C)))) ) ) ) ) ) )).

fof(t73_sprect_3,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] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_sprect_2(A,B)
                  & r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C))
                  & v4_topreal1(B)
                  & r2_hidden(C,k5_topreal1(np__2,B)) )
               => r1_sprect_2(A,k3_jordan3(B,C)) ) ) ) ) )).

fof(t52_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => k5_topreal1(np__2,A) = a_1_0_sprect_3(A) ) )).

fof(t54_sprect_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_sprect_1(A)
        & v1_topreal1(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))) )
     => ( k2_goboard9(A) = a_1_1_sprect_3(A)
        & k3_goboard9(A) = a_1_2_sprect_3(A) ) ) )).

fof(fraenkel_a_1_0_sprect_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_sprect_1(B)
        & v1_topreal1(B)
        & v2_topreal1(B)
        & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(B)
        & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_1_0_sprect_3(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ ( ~ ( k21_euclid(C) = k18_pscomp_1(k5_topreal1(np__2,B))
                    & r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B)))
                    & r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) )
                & ~ ( r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
                    & r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
                    & k22_euclid(C) = k19_pscomp_1(k5_topreal1(np__2,B)) )
                & ~ ( r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
                    & r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
                    & k22_euclid(C) = k21_pscomp_1(k5_topreal1(np__2,B)) )
                & ~ ( k21_euclid(C) = k20_pscomp_1(k5_topreal1(np__2,B))
                    & r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B)))
                    & r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) ) ) ) ) ) )).

fof(fraenkel_a_1_1_sprect_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_sprect_1(B)
        & v1_topreal1(B)
        & v2_topreal1(B)
        & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(B)
        & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_1_1_sprect_3(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
                & r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
                & r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C))
                & r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B))) ) ) ) ) )).

fof(fraenkel_a_1_2_sprect_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_sprect_1(B)
        & v1_topreal1(B)
        & v2_topreal1(B)
        & v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(B)
        & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_1_2_sprect_3(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ r1_xreal_0(k21_euclid(C),k18_pscomp_1(k5_topreal1(np__2,B)))
            & ~ r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
            & ~ r1_xreal_0(k22_euclid(C),k21_pscomp_1(k5_topreal1(np__2,B)))
            & ~ r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) ) ) ) )).
%------------------------------------------------------------------------------