SET007 Axioms: SET007+533.ax


%------------------------------------------------------------------------------
% File     : SET007+533 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Order on a Special Polygon
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   90 (   7 unit)
%            Number of atoms       :  767 (  81 equality)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :  835 ( 158 ~  ;  22  |; 444  &)
%                                         (   6 <=>; 205 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-3 arity)
%            Number of functors    :   56 (   6 constant; 0-4 arity)
%            Number of variables   :  187 (   0 singleton; 185 !;   2 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_sprect_2,axiom,
    ( ~ v1_xboole_0(k2_topreal1)
    & ~ v1_realset1(k2_topreal1)
    & ~ v1_sppol_1(k2_topreal1)
    & ~ v2_sppol_1(k2_topreal1)
    & v1_topreal4(k2_topreal1)
    & v6_compts_1(k2_topreal1,k15_euclid(np__2)) )).

fof(fc2_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k1_sprect_1(A))
        & v1_relat_1(k1_sprect_1(A))
        & v1_funct_1(k1_sprect_1(A))
        & v1_finset_1(k1_sprect_1(A))
        & v1_finseq_1(k1_sprect_1(A))
        & v1_topreal1(k1_sprect_1(A))
        & v2_topreal1(k1_sprect_1(A))
        & v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(k1_sprect_1(A))
        & v2_goboard5(k1_sprect_1(A))
        & ~ v1_realset1(k1_sprect_1(A))
        & ~ v5_seqm_3(k1_sprect_1(A))
        & v1_sprect_1(k1_sprect_1(A))
        & v1_sprect_2(k1_sprect_1(A)) ) ) )).

fof(rc1_sprect_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)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_topreal1(A)
      & v2_topreal1(A)
      & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
      & v1_goboard5(A)
      & v2_goboard5(A)
      & ~ v1_realset1(A)
      & ~ v5_seqm_3(A)
      & v1_sprect_2(A) ) )).

fof(fc3_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k5_topreal1(np__2,A))
        & v1_topreal2(k5_topreal1(np__2,A))
        & v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) )).

fof(t1_sprect_2,axiom,(
    ! [A,B,C,D] :
      ( ( r1_tarski(k3_xboole_0(A,B),k1_tarski(D))
        & r2_hidden(D,C)
        & r1_xboole_0(C,B) )
     => r1_xboole_0(k2_xboole_0(A,C),B) ) )).

fof(t2_sprect_2,axiom,(
    ! [A,B,C,D] :
      ( ( k3_xboole_0(A,C) = k1_tarski(D)
        & r2_hidden(D,B)
        & r1_tarski(B,C) )
     => k3_xboole_0(A,B) = k1_tarski(D) ) )).

fof(t3_sprect_2,axiom,(
    $true )).

fof(t4_sprect_2,axiom,(
    ! [A,B] :
      ( ! [C,D] :
          ( ( r2_hidden(C,A)
            & r2_hidden(D,B) )
         => r1_xboole_0(C,D) )
     => r1_xboole_0(k3_tarski(A),k3_tarski(B)) ) )).

fof(t5_sprect_2,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] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m2_finseq_1(E,D)
                     => ( ( r1_xreal_0(A,B)
                          & r2_hidden(A,k4_finseq_1(E))
                          & r2_hidden(B,k4_finseq_1(E))
                          & r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
                       => r2_hidden(k5_binarith(k1_nat_1(C,A),np__1),k4_finseq_1(E)) ) ) ) ) ) ) )).

fof(t6_sprect_2,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] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m2_finseq_1(E,D)
                     => ( ( r2_hidden(A,k4_finseq_1(E))
                          & r2_hidden(B,k4_finseq_1(E))
                          & r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
                       => ( r1_xreal_0(A,B)
                          | r2_hidden(k1_nat_1(k5_binarith(A,C),np__1),k4_finseq_1(E)) ) ) ) ) ) ) ) )).

fof(t7_sprect_2,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] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m2_finseq_1(E,D)
                     => ( ( r1_xreal_0(A,B)
                          & r2_hidden(A,k4_finseq_1(E))
                          & r2_hidden(B,k4_finseq_1(E))
                          & r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
                       => k4_finseq_4(k5_numbers,D,k1_jordan3(D,E,A,B),C) = k4_finseq_4(k5_numbers,D,E,k5_binarith(k1_nat_1(C,A),np__1)) ) ) ) ) ) ) )).

fof(t8_sprect_2,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] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m2_finseq_1(E,D)
                     => ( ( r2_hidden(A,k4_finseq_1(E))
                          & r2_hidden(B,k4_finseq_1(E))
                          & r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
                       => ( r1_xreal_0(A,B)
                          | k4_finseq_4(k5_numbers,D,k1_jordan3(D,E,A,B),C) = k4_finseq_4(k5_numbers,D,E,k1_nat_1(k5_binarith(A,C),np__1)) ) ) ) ) ) ) ) )).

fof(t9_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(D)) )
                   => r1_xreal_0(np__1,k3_finseq_1(k1_jordan3(C,D,A,B))) ) ) ) ) ) )).

fof(t10_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(D))
                      & k3_finseq_1(k1_jordan3(C,D,A,B)) = np__1 )
                   => A = B ) ) ) ) ) )).

fof(t11_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ~ ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(D))
                      & v1_xboole_0(k1_jordan3(C,D,A,B)) ) ) ) ) ) )).

fof(t12_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(D)) )
                   => k4_finseq_4(k5_numbers,C,k1_jordan3(C,D,A,B),np__1) = k4_finseq_4(k5_numbers,C,D,A) ) ) ) ) ) )).

fof(t13_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ( ( r2_hidden(A,k4_finseq_1(D))
                      & r2_hidden(B,k4_finseq_1(D)) )
                   => k4_finseq_4(k5_numbers,C,k1_jordan3(C,D,A,B),k3_finseq_1(k1_jordan3(C,D,A,B))) = k4_finseq_4(k5_numbers,C,D,B) ) ) ) ) ) )).

fof(t14_sprect_2,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & 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)))
         => ( ( r2_hidden(B,A)
              & k22_euclid(B) = k19_pscomp_1(A) )
           => r2_hidden(B,k27_pscomp_1(A)) ) ) ) )).

fof(t15_sprect_2,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & 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)))
         => ( ( r2_hidden(B,A)
              & k22_euclid(B) = k21_pscomp_1(A) )
           => r2_hidden(B,k29_pscomp_1(A)) ) ) ) )).

fof(t16_sprect_2,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & 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)))
         => ( ( r2_hidden(B,A)
              & k21_euclid(B) = k18_pscomp_1(A) )
           => r2_hidden(B,k26_pscomp_1(A)) ) ) ) )).

fof(t17_sprect_2,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & 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)))
         => ( ( r2_hidden(B,A)
              & k21_euclid(B) = k20_pscomp_1(A) )
           => r2_hidden(B,k28_pscomp_1(A)) ) ) ) )).

fof(t19_sprect_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => k4_finseq_1(k2_goboard1(A)) = k4_finseq_1(A) ) )).

fof(t20_sprect_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => k4_finseq_1(k3_goboard1(A)) = k4_finseq_1(A) ) )).

fof(t21_sprect_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,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
                  & r1_xreal_0(k21_euclid(A),k21_euclid(B))
                  & r1_xreal_0(k21_euclid(C),k21_euclid(B))
                  & A != B
                  & B != C
                  & ~ ( k21_euclid(A) = k21_euclid(B)
                      & k21_euclid(C) = k21_euclid(B) ) ) ) ) ) )).

fof(t22_sprect_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,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
                  & r1_xreal_0(k22_euclid(A),k22_euclid(B))
                  & r1_xreal_0(k22_euclid(C),k22_euclid(B))
                  & A != B
                  & B != C
                  & ~ ( k22_euclid(A) = k22_euclid(B)
                      & k22_euclid(C) = k22_euclid(B) ) ) ) ) ) )).

fof(t23_sprect_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,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
                  & r1_xreal_0(k21_euclid(B),k21_euclid(A))
                  & r1_xreal_0(k21_euclid(B),k21_euclid(C))
                  & A != B
                  & B != C
                  & ~ ( k21_euclid(A) = k21_euclid(B)
                      & k21_euclid(C) = k21_euclid(B) ) ) ) ) ) )).

fof(t24_sprect_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,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
                  & r1_xreal_0(k22_euclid(B),k22_euclid(A))
                  & r1_xreal_0(k22_euclid(B),k22_euclid(C))
                  & A != B
                  & B != C
                  & ~ ( k22_euclid(A) = k22_euclid(B)
                      & k22_euclid(C) = k22_euclid(B) ) ) ) ) ) )).

fof(d1_sprect_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)))
         => ( r1_sprect_2(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k4_finseq_1(B))
                 => ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)))
                    & r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)),k20_pscomp_1(k5_topreal1(np__2,A)))
                    & r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)))
                    & r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)),k19_pscomp_1(k5_topreal1(np__2,A))) ) ) ) ) ) ) )).

fof(t25_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_sprect_2(A,A) ) )).

fof(t26_sprect_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)))
         => ( r1_sprect_2(A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(C,k4_finseq_1(B))
                        & r2_hidden(D,k4_finseq_1(B)) )
                     => r1_sprect_2(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,C,D)) ) ) ) ) ) ) )).

fof(t27_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A)) )
               => r1_sprect_2(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) )).

fof(t28_sprect_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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( r1_sprect_2(A,B)
                  & r1_sprect_2(A,C) )
               => r1_sprect_2(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C)) ) ) ) ) )).

fof(t29_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t30_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t31_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t32_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(d2_sprect_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)))
         => ( r2_sprect_2(A,B)
          <=> ( r1_sprect_2(A,B)
              & k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) = k18_pscomp_1(k5_topreal1(np__2,A))
              & k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k20_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) )).

fof(d3_sprect_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)))
         => ( r3_sprect_2(A,B)
          <=> ( r1_sprect_2(A,B)
              & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) = k21_pscomp_1(k5_topreal1(np__2,A))
              & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t33_sprect_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( v2_funct_1(B)
            & v1_topreal1(B)
            & m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
         => ! [C] :
              ( ( v2_funct_1(C)
                & v1_topreal1(C)
                & m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
             => ~ ( r1_xreal_0(np__2,k3_finseq_1(B))
                  & r1_xreal_0(np__2,k3_finseq_1(C))
                  & r2_sprect_2(A,B)
                  & r3_sprect_2(A,C)
                  & r1_xboole_0(k5_topreal1(np__2,B),k5_topreal1(np__2,C)) ) ) ) ) )).

fof(d4_sprect_2,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v1_sprect_2(A)
      <=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,k32_pscomp_1(k5_topreal1(np__2,A))),np__2),k27_pscomp_1(k5_topreal1(np__2,A))) ) ) )).

fof(t34_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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))
       => ( v1_sprect_2(A)
        <=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2),k27_pscomp_1(k5_topreal1(np__2,A))) ) ) ) )).

fof(t35_sprect_2,axiom,(
    k19_pscomp_1(k2_topreal1) = np__1 )).

fof(t36_sprect_2,axiom,(
    k18_pscomp_1(k2_topreal1) = np__0 )).

fof(t37_sprect_2,axiom,(
    k20_pscomp_1(k2_topreal1) = np__1 )).

fof(t38_sprect_2,axiom,(
    k21_pscomp_1(k2_topreal1) = np__0 )).

fof(t39_sprect_2,axiom,(
    k27_pscomp_1(k2_topreal1) = k3_topreal1(np__2,k23_euclid(np__0,np__1),k23_euclid(np__1,np__1)) )).

fof(t40_sprect_2,axiom,(
    k32_pscomp_1(k2_topreal1) = k23_euclid(np__0,np__1) )).

fof(t41_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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,C)
                  & ( ( ~ r1_xreal_0(C,np__1)
                      & r1_xreal_0(B,k3_finseq_1(A)) )
                    | ( r1_xreal_0(np__1,C)
                      & ~ r1_xreal_0(k3_finseq_1(A),B) ) )
                  & ~ ( v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                      & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) )).

fof(t42_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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(C,B)
                  & ( ( ~ r1_xreal_0(B,np__1)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                    | ( r1_xreal_0(np__1,B)
                      & ~ r1_xreal_0(k3_finseq_1(A),C) ) )
                  & ~ ( v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                      & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) )).

fof(t43_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k32_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t44_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k33_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t45_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k37_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t46_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k36_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t47_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k30_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t48_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k31_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t49_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k35_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t50_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_realset1(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r2_hidden(k34_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) )).

fof(t51_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_topreal1(E)
                        & v2_topreal1(E)
                        & v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
                        & v1_goboard5(E)
                        & v2_goboard5(E)
                        & ~ v5_seqm_3(E)
                        & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,B)
                          & r1_xreal_0(C,D)
                          & r1_xreal_0(D,k3_finseq_1(E)) )
                       => ( r1_xreal_0(C,B)
                          | ( r1_xreal_0(A,np__1)
                            & r1_xreal_0(k3_finseq_1(E),D) )
                          | r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,A,B)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,C,D))) ) ) ) ) ) ) ) )).

fof(t52_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_topreal1(E)
                        & v2_topreal1(E)
                        & v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
                        & v1_goboard5(E)
                        & v2_goboard5(E)
                        & ~ v5_seqm_3(E)
                        & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,B)
                          & r1_xreal_0(C,D)
                          & r1_xreal_0(D,k3_finseq_1(E)) )
                       => ( r1_xreal_0(C,B)
                          | ( r1_xreal_0(A,np__1)
                            & r1_xreal_0(k3_finseq_1(E),D) )
                          | r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,A,B)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,D,C))) ) ) ) ) ) ) ) )).

fof(t53_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_topreal1(E)
                        & v2_topreal1(E)
                        & v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
                        & v1_goboard5(E)
                        & v2_goboard5(E)
                        & ~ v5_seqm_3(E)
                        & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,B)
                          & r1_xreal_0(C,D)
                          & r1_xreal_0(D,k3_finseq_1(E)) )
                       => ( r1_xreal_0(C,B)
                          | ( r1_xreal_0(A,np__1)
                            & r1_xreal_0(k3_finseq_1(E),D) )
                          | r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,B,A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,D,C))) ) ) ) ) ) ) ) )).

fof(t54_sprect_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_topreal1(E)
                        & v2_topreal1(E)
                        & v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
                        & v1_goboard5(E)
                        & v2_goboard5(E)
                        & ~ v5_seqm_3(E)
                        & m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
                     => ( ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,B)
                          & r1_xreal_0(C,D)
                          & r1_xreal_0(D,k3_finseq_1(E)) )
                       => ( r1_xreal_0(C,B)
                          | ( r1_xreal_0(A,np__1)
                            & r1_xreal_0(k3_finseq_1(E),D) )
                          | r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,B,A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,C,D))) ) ) ) ) ) ) ) )).

fof(t55_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ r1_xreal_0(k21_euclid(k33_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k32_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t56_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k32_pscomp_1(k5_topreal1(np__2,A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) )).

fof(t57_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ r1_xreal_0(k22_euclid(k34_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k35_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t58_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k35_pscomp_1(k5_topreal1(np__2,A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) )).

fof(t59_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ r1_xreal_0(k21_euclid(k36_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k37_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t60_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k37_pscomp_1(k5_topreal1(np__2,A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) )).

fof(t61_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ~ r1_xreal_0(k22_euclid(k31_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k30_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t62_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => k30_pscomp_1(k5_topreal1(np__2,A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) )).

fof(t63_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => r1_subset_1(k3_topreal1(np__2,k23_pscomp_1(k5_topreal1(np__2,A)),k32_pscomp_1(k5_topreal1(np__2,A))),k3_topreal1(np__2,k33_pscomp_1(k5_topreal1(np__2,A)),k24_pscomp_1(k5_topreal1(np__2,A)))) ) )).

fof(t64_sprect_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)))
         => ( ( 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)) )
           => ( B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
              | ( k21_euclid(B) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1))
                & k22_euclid(B) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
              | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),B),A))
                & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),B),A),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) )).

fof(t65_sprect_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)))
         => ( ( 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,k3_finseq_1(A))),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))) )
           => ( B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
              | ( k21_euclid(B) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))
                & k22_euclid(B) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
              | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k13_binarith(u1_struct_0(k15_euclid(np__2)),B)))
                & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k13_binarith(u1_struct_0(k15_euclid(np__2)),B)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) )).

fof(t66_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k33_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k33_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t67_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k34_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t68_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k36_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k36_pscomp_1(k5_topreal1(np__2,A)) = k25_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t69_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k34_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t70_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k32_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k32_pscomp_1(k5_topreal1(np__2,A)) = k23_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t71_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k4_finseq_1(A))
                  & r2_hidden(C,k4_finseq_1(A))
                  & v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
                  & m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k30_pscomp_1(k5_topreal1(np__2,A)) )
               => ( k30_pscomp_1(k5_topreal1(np__2,A)) = k22_pscomp_1(k5_topreal1(np__2,A))
                  | ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
                    & m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) )).

fof(t72_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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_xreal_0(k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k32_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t73_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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_xreal_0(k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A))),np__1) ) ) )).

fof(t74_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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))
          & k33_pscomp_1(k5_topreal1(np__2,A)) != k34_pscomp_1(k5_topreal1(np__2,A))
          & r1_xreal_0(k5_finseq_4(A,k34_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t75_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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_xreal_0(k5_finseq_4(A,k35_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k34_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t76_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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))
          & k35_pscomp_1(k5_topreal1(np__2,A)) != k36_pscomp_1(k5_topreal1(np__2,A))
          & r1_xreal_0(k5_finseq_4(A,k36_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k35_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t77_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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_xreal_0(k5_finseq_4(A,k37_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k36_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t78_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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))
          & k37_pscomp_1(k5_topreal1(np__2,A)) != k30_pscomp_1(k5_topreal1(np__2,A))
          & r1_xreal_0(k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k37_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t79_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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))
          & k32_pscomp_1(k5_topreal1(np__2,A)) != k31_pscomp_1(k5_topreal1(np__2,A))
          & r1_xreal_0(k5_finseq_4(A,k31_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t80_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(A)
        & v1_sprect_2(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_xreal_0(k3_finseq_1(A),k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t81_sprect_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & ~ v5_seqm_3(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_xreal_0(k3_finseq_1(A),k5_finseq_4(A,k31_pscomp_1(k5_topreal1(np__2,A)))) ) ) )).

fof(t18_sprect_2,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(A,B)
                  & r1_xreal_0(B,k3_finseq_1(C)) )
               => k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k3_tarski(a_3_0_sprect_2(A,B,C)) ) ) ) ) )).

fof(fraenkel_a_3_0_sprect_2,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
     => ( r2_hidden(A,a_3_0_sprect_2(B,C,D))
      <=> ? [E] :
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k4_topreal1(np__2,D,E)
            & r1_xreal_0(B,E)
            & ~ r1_xreal_0(C,E) ) ) ) )).
%------------------------------------------------------------------------------