SET007 Axioms: SET007+510.ax


%------------------------------------------------------------------------------
% File     : SET007+510 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subsequences of Standard Special Circular Sequences in cal E^2_T
% 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    : jordan4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   76 (   7 unit)
%            Number of atoms       :  803 (  89 equality)
%            Maximal formula depth :   30 (  11 average)
%            Number of connectives :  841 ( 114 ~  ;  36  |; 390  &)
%                                         (   6 <=>; 295 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-4 arity)
%            Number of functors    :   37 (   5 constant; 0-4 arity)
%            Number of variables   :  238 (   0 singleton; 238 !;   0 ?)
%            Maximal term depth    :    6 (   1 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(t1_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k5_binarith(A,B) = np__0
           => r1_xreal_0(A,B) ) ) ) )).

fof(t2_jordan4,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)
               => k5_binarith(k1_nat_1(B,C),A) = k5_real_1(k1_nat_1(B,C),A) ) ) ) ) )).

fof(t3_jordan4,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)
               => k5_binarith(k1_nat_1(B,C),A) = k1_nat_1(k5_binarith(B,A),C) ) ) ) ) )).

fof(t4_jordan4,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)
             => ( B = k2_nat_1(C,A)
               => ( A = np__0
                  | r1_xreal_0(C,B) ) ) ) ) ) )).

fof(t5_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => k3_nat_1(A,B) = np__0 ) ) ) )).

fof(t6_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(A,np__0)
              & ~ r1_xreal_0(B,A)
              & ~ r1_xreal_0(k1_nat_1(A,A),B)
              & k4_nat_1(B,A) = np__0 ) ) ) )).

fof(t7_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(A,np__0)
              | r1_xreal_0(k1_nat_1(A,A),B)
              | ( k4_nat_1(B,A) = k5_real_1(B,A)
                & k4_nat_1(B,A) = k5_binarith(B,A) ) ) ) ) ) )).

fof(t8_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k4_nat_1(k1_nat_1(A,A),A) = np__0 ) )).

fof(t9_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(A,B)
              & k4_nat_1(A,B) = np__0 )
           => ( r1_xreal_0(A,np__0)
              | A = B ) ) ) ) )).

fof(t10_jordan4,axiom,(
    $true )).

fof(t11_jordan4,axiom,(
    $true )).

fof(t12_jordan4,axiom,(
    $true )).

fof(t13_jordan4,axiom,(
    $true )).

fof(t14_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( ( v1_finseq_6(B,A)
              & r1_xreal_0(np__1,k3_finseq_1(B)) )
           => k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) )).

fof(t15_jordan4,axiom,(
    $true )).

fof(t16_jordan4,axiom,(
    $true )).

fof(t17_jordan4,axiom,(
    $true )).

fof(t18_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(k3_finseq_1(B),C)
               => ( k1_funct_1(k1_rfinseq(A,B,C),k3_finseq_1(k1_rfinseq(A,B,C))) = k1_funct_1(B,k3_finseq_1(B))
                  & k4_finseq_4(k5_numbers,A,k1_rfinseq(A,B,C),k3_finseq_1(k1_rfinseq(A,B,C))) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)) ) ) ) ) ) )).

fof(t19_jordan4,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( v4_topreal1(A)
           => ( r1_xreal_0(k3_finseq_1(A),k1_nat_1(B,np__1))
              | v4_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t20_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,C)
                      & r1_xreal_0(C,k3_finseq_1(B)) )
                   => k3_finseq_1(k1_jordan3(A,B,D,C)) = k1_nat_1(k5_binarith(C,D),np__1) ) ) ) ) ) )).

fof(t21_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,C)
                      & r1_xreal_0(C,k3_finseq_1(B)) )
                   => k3_finseq_1(k1_jordan3(A,B,C,D)) = k1_nat_1(k5_binarith(C,D),np__1) ) ) ) ) ) )).

fof(t22_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,D)
                          & r1_xreal_0(D,k3_finseq_1(B)) )
                       => k1_funct_1(k1_jordan3(A,B,C,D),k3_finseq_1(k1_jordan3(A,B,C,D))) = k1_funct_1(B,D) ) ) ) ) ) ) )).

fof(t23_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,C)
                          & r1_xreal_0(C,k3_finseq_1(B))
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(B)) )
                       => k1_funct_1(k1_jordan3(A,B,C,D),k3_finseq_1(k1_jordan3(A,B,C,D))) = k1_funct_1(B,D) ) ) ) ) ) ) )).

fof(t24_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,C)
                          & r1_xreal_0(C,k3_finseq_1(B))
                          & r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,k1_nat_1(k5_binarith(C,D),np__1)) )
                       => k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k5_binarith(C,E),np__1)) ) ) ) ) ) ) )).

fof(t25_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,E)
                          & r1_xreal_0(E,D)
                          & r1_xreal_0(D,k3_finseq_1(C))
                          & r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,k1_nat_1(k5_binarith(D,E),np__1)) )
                       => ( k1_funct_1(k1_jordan3(B,C,D,E),A) = k1_funct_1(k1_jordan3(B,C,E,D),k3_real_1(k5_real_1(k3_real_1(k5_real_1(D,E),np__1),A),np__1))
                          & k3_real_1(k5_real_1(k3_real_1(k5_real_1(D,E),np__1),A),np__1) = k1_nat_1(k5_binarith(k1_nat_1(k5_binarith(D,E),np__1),A),np__1) ) ) ) ) ) ) ) )).

fof(t26_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,E)
                          & r1_xreal_0(E,k3_finseq_1(C))
                          & r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,k1_nat_1(k5_binarith(E,D),np__1)) )
                       => ( k1_funct_1(k1_jordan3(B,C,D,E),A) = k1_funct_1(k1_jordan3(B,C,E,D),k3_real_1(k5_real_1(k3_real_1(k5_real_1(E,D),np__1),A),np__1))
                          & k3_real_1(k5_real_1(k3_real_1(k5_real_1(E,D),np__1),A),np__1) = k1_nat_1(k5_binarith(k1_nat_1(k5_binarith(E,D),np__1),A),np__1) ) ) ) ) ) ) ) )).

fof(t27_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k3_finseq_1(B)) )
               => ( k1_jordan3(A,B,C,C) = k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,C))
                  & k3_finseq_1(k1_jordan3(A,B,C,C)) = np__1 ) ) ) ) ) )).

fof(t28_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => k1_jordan3(A,B,np__0,np__0) = k16_finseq_1(A,B,np__1) ) ) )).

fof(t29_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(C,k3_finseq_1(B))
               => k1_jordan3(A,B,C,C) = k6_finseq_1(A) ) ) ) ) )).

fof(t30_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k1_jordan3(A,B,C,D) = k4_finseq_5(A,k1_jordan3(A,B,D,C)) ) ) ) ) )).

fof(t31_jordan4,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,B)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & r1_xreal_0(np__1,D) )
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(k1_nat_1(k5_binarith(C,B),np__1),D)
                      | k4_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),D) = k4_topreal1(np__2,A,k5_binarith(k1_nat_1(D,B),np__1)) ) ) ) ) ) ) )).

fof(t32_jordan4,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,B)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & r1_xreal_0(np__1,D) )
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(k1_nat_1(k5_binarith(C,B),np__1),D)
                      | k4_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,B),D) = k4_topreal1(np__2,A,k5_binarith(C,D)) ) ) ) ) ) ) )).

fof(d1_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) != np__0
             => k1_jordan4(A,B) = k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) )
            & ( k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) = np__0
             => k1_jordan4(A,B) = k5_binarith(k3_finseq_1(B),np__1) ) ) ) ) )).

fof(t33_jordan4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k1_jordan4(k5_binarith(k3_finseq_1(A),np__1),A) = k5_binarith(k3_finseq_1(A),np__1) ) )).

fof(t34_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,k5_binarith(k3_finseq_1(B),np__1)) )
           => k1_jordan4(A,B) = A ) ) ) )).

fof(t35_jordan4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k1_jordan4(A,B) = k1_jordan4(k1_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)),B)
            & k1_jordan4(A,B) = k1_jordan4(k1_nat_1(k5_binarith(k3_finseq_1(B),np__1),A),B) ) ) ) )).

fof(d2_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_jordan4(A,B,C,D)
                  <=> ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                      & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
                      & r1_xreal_0(np__1,k3_finseq_1(B))
                      & ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k3_finseq_1(B)) )
                           => k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(C,E),np__1),A)) ) ) ) ) ) ) ) ) )).

fof(d3_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_jordan4(A,B,C,D)
                  <=> ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                      & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
                      & r1_xreal_0(np__1,k3_finseq_1(B))
                      & ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k3_finseq_1(B)) )
                           => k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) )).

fof(d4_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r3_jordan4(A,B,C,D)
                  <=> ( r1_jordan4(A,B,C,D)
                      | r2_jordan4(A,B,C,D) ) ) ) ) ) ) )).

fof(t36_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r3_jordan4(A,B,C,D)
                   => ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
                      & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
                      & r1_xreal_0(np__1,k3_finseq_1(B))
                      & ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
                      & ( ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( ( r1_xreal_0(np__1,E)
                                & r1_xreal_0(E,k3_finseq_1(B)) )
                             => k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(C,E),np__1),A)) ) )
                        | ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( ( r1_xreal_0(np__1,E)
                                & r1_xreal_0(E,k3_finseq_1(B)) )
                             => k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) ) )).

fof(t37_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_jordan4(A,B,C,D)
                      & r1_xreal_0(C,D) )
                   => ( k3_finseq_1(B) = k1_nat_1(k5_binarith(D,C),np__1)
                      & B = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,D) ) ) ) ) ) ) )).

fof(t38_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_jordan4(A,B,C,D)
                   => ( r1_xreal_0(C,D)
                      | ( k3_finseq_1(B) = k5_binarith(k1_nat_1(k3_finseq_1(A),D),C)
                        & B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,k5_binarith(k3_finseq_1(A),np__1)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,D))
                        & B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,k5_binarith(k3_finseq_1(A),np__1)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,D)) ) ) ) ) ) ) ) )).

fof(t39_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_jordan4(A,B,C,D)
                      & r1_xreal_0(D,C) )
                   => ( k3_finseq_1(B) = k1_nat_1(k5_binarith(C,D),np__1)
                      & B = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,D) ) ) ) ) ) ) )).

fof(t40_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_jordan4(A,B,C,D)
                   => ( r1_xreal_0(D,C)
                      | ( k3_finseq_1(B) = k5_binarith(k1_nat_1(k3_finseq_1(A),C),D)
                        & B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),D)) ) ) ) ) ) ) ) )).

fof(t41_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_jordan4(A,B,C,D)
                   => r2_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B),D,C) ) ) ) ) ) )).

fof(t42_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_jordan4(A,B,C,D)
                   => r1_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B),D,C) ) ) ) ) ) )).

fof(t43_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,C) )
               => ( r1_xreal_0(k3_finseq_1(A),C)
                  | r1_jordan4(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),B,C) ) ) ) ) ) )).

fof(t44_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,C) )
               => ( r1_xreal_0(k3_finseq_1(A),C)
                  | r2_jordan4(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,B),C,B) ) ) ) ) ) )).

fof(t45_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(np__1,C)
               => ( r1_xreal_0(B,C)
                  | r1_xreal_0(k3_finseq_1(A),B)
                  | r1_jordan4(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,k5_binarith(k3_finseq_1(A),np__1)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,C)),B,C) ) ) ) ) ) )).

fof(t46_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(np__1,B)
               => ( r1_xreal_0(C,B)
                  | r1_xreal_0(k3_finseq_1(A),C)
                  | r2_jordan4(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),C)),B,C) ) ) ) ) ) )).

fof(t47_jordan4,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,k3_finseq_1(A))
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(C,k3_finseq_1(A)) )
               => r1_tarski(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) )).

fof(t48_jordan4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v2_funct_1(B)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_xreal_0(np__1,C)
                        & r1_xreal_0(C,k3_finseq_1(B))
                        & r1_xreal_0(np__1,D)
                        & r1_xreal_0(D,k3_finseq_1(B)) )
                     => ( ( k1_funct_1(B,C) != k1_funct_1(B,D)
                          & k4_finseq_4(k5_numbers,A,B,C) != k4_finseq_4(k5_numbers,A,B,D) )
                        | C = D ) ) ) ) ) ) ) )).

fof(t49_jordan4,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(k1_nat_1(B,np__1),k3_finseq_1(A))
           => ( r1_xreal_0(B,np__1)
              | v4_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t50_jordan4,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(A),k1_nat_1(B,np__1))
              | v4_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) )).

fof(t51_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
               => ( r1_xreal_0(C,B)
                  | v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) )).

fof(t52_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(C,k3_finseq_1(A))
               => ( r1_xreal_0(B,np__1)
                  | r1_xreal_0(C,B)
                  | v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) )).

fof(t53_jordan4,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)))
                 => ~ ( r2_hidden(A,k3_topreal1(np__2,B,C))
                      & r2_hidden(A,k3_topreal1(np__2,B,D))
                      & B != A
                      & ~ r2_hidden(C,k3_topreal1(np__2,B,D))
                      & ~ r2_hidden(D,k3_topreal1(np__2,B,C)) ) ) ) ) ) )).

fof(t54_jordan4,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))) )
     => k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,np__1),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1))) = k1_tarski(k1_funct_1(A,np__1)) ) )).

fof(t55_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_xreal_0(np__1,B)
                          & D = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)
                          & E = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),C)) )
                       => ( r1_xreal_0(C,B)
                          | r1_xreal_0(k3_finseq_1(A),C)
                          | ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_tarski(k1_funct_1(A,B),k1_funct_1(A,C))
                            & k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k5_topreal1(np__2,A) ) ) ) ) ) ) ) ) )).

fof(t56_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_jordan4(A,B,C,D)
                   => ( r1_xreal_0(D,C)
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t57_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_jordan4(A,B,C,D)
                   => ( r1_xreal_0(C,D)
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t58_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_jordan4(A,B,C,D)
                   => ( C = D
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t59_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_jordan4(A,B,C,D)
                   => ( C = D
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t60_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r3_jordan4(A,B,C,D)
                   => ( C = D
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t61_jordan4,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)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r3_jordan4(A,B,C,D)
                   => ( k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B))
                      | r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) )).

fof(t62_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & B != C
                  & ! [D] :
                      ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ ( r3_jordan4(A,D,B,C)
                              & r3_jordan4(A,E,B,C)
                              & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_tarski(k1_funct_1(A,B),k1_funct_1(A,C))
                              & k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k5_topreal1(np__2,A)
                              & r1_topreal4(k5_topreal1(np__2,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C))
                              & r1_topreal4(k5_topreal1(np__2,E),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C))
                              & ! [F] :
                                  ( m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
                                 => ~ ( r3_jordan4(A,F,B,C)
                                      & F != D
                                      & F != E ) ) ) ) ) ) ) ) ) )).

fof(t63_jordan4,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] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( B = k5_topreal1(np__2,A)
           => v1_topreal2(B) ) ) ) )).

fof(t64_jordan4,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))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r1_jordan4(C,D,A,B)
                          & r1_jordan4(C,E,A,B) )
                       => D = E ) ) ) ) ) ) )).

fof(t65_jordan4,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))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r2_jordan4(C,D,A,B)
                          & r2_jordan4(C,E,A,B) )
                       => D = E ) ) ) ) ) ) )).

fof(t66_jordan4,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))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( A != B
                          & r1_jordan4(C,D,A,B)
                          & r2_jordan4(C,E,A,B)
                          & k1_funct_1(D,np__2) = k1_funct_1(E,np__2) ) ) ) ) ) ) )).

fof(t67_jordan4,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))) )
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ( ( r3_jordan4(C,D,A,B)
                          & r3_jordan4(C,E,A,B)
                          & k1_funct_1(D,np__2) = k1_funct_1(E,np__2) )
                       => ( A = B
                          | D = E ) ) ) ) ) ) ) )).

fof(d5_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
               => ( B = C
                  | ! [D] :
                      ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ( D = k2_jordan4(A,B,C)
                      <=> ( r3_jordan4(A,D,B,C)
                          & ( ~ ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))))
                                & r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)))) )
                           => k1_funct_1(D,np__2) = k1_funct_1(A,k1_nat_1(B,np__1)) )
                          & ( ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))))
                              & r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)))) )
                           => k1_funct_1(D,np__2) = k1_funct_1(A,k1_jordan4(k5_binarith(B,np__1),A)) ) ) ) ) ) ) ) ) ) )).

fof(d6_jordan4,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)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
               => ( B = C
                  | ! [D] :
                      ( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ( D = k3_jordan4(A,B,C)
                      <=> ( r3_jordan4(A,D,B,C)
                          & ( ~ ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)))
                                & r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B))) )
                           => k1_funct_1(D,np__2) = k1_funct_1(A,k1_nat_1(B,np__1)) )
                          & ( ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)))
                              & r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B))) )
                           => k1_funct_1(D,np__2) = k1_funct_1(A,k1_jordan4(k5_binarith(B,np__1),A)) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_jordan4,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => m2_subset_1(k1_jordan4(A,B),k1_numbers,k5_numbers) ) )).

fof(dt_k2_jordan4,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)))
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => m2_finseq_1(k2_jordan4(A,B,C),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k3_jordan4,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)))
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => m2_finseq_1(k3_jordan4(A,B,C),u1_struct_0(k15_euclid(np__2))) ) )).
%------------------------------------------------------------------------------