SET007 Axioms: SET007+726.ax


%------------------------------------------------------------------------------
% File     : SET007+726 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of the Internal Approximation of Jordan's Curve
% 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    : jordan14 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   0 unit)
%            Number of atoms       :  321 (  11 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  311 (  31 ~  ;   2  |; 144  &)
%                                         (   1 <=>; 133 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   0 propositional; 1-3 arity)
%            Number of functors    :   42 (   4 constant; 0-4 arity)
%            Number of variables   :  108 (   0 singleton; 108 !;   0 ?)
%            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_jordan14,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & ~ v5_seqm_3(A)
        & v1_topreal1(A)
        & v2_topreal1(A)
        & v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
        & v1_goboard5(A)
        & v2_goboard5(A)
        & m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ( v3_pre_topc(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2))
        & v2_connsp_1(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2))
        & v2_topreal4(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2)) ) ) )).

fof(fc2_jordan14,axiom,(
    ! [A,B] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k5_numbers) )
     => ( v4_pre_topc(k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan13(A,B))),k15_euclid(np__2))
        & v6_compts_1(k6_pre_topc(k15_euclid(np__2),k3_goboard9(k1_jordan13(A,B))),k15_euclid(np__2)) ) ) )).

fof(t1_jordan14,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))) )
     => ( k1_jordan2c(np__2,k5_topreal1(np__2,A)) = k3_goboard9(A)
        | k1_jordan2c(np__2,k5_topreal1(np__2,A)) = k2_goboard9(A) ) ) )).

fof(t2_jordan14,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))) )
     => ( k2_jordan2c(np__2,k5_topreal1(np__2,A)) = k3_goboard9(A)
        | k2_jordan2c(np__2,k5_topreal1(np__2,A)) = k2_goboard9(A) ) ) )).

fof(t3_jordan14,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(B))
                  & r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
               => v4_pre_topc(k4_gobrd13(B,A,C),k15_euclid(np__2)) ) ) ) ) )).

fof(t4_jordan14,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_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_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),k1_matrix_1(A)) )
                   => ( r2_hidden(B,k1_tops_1(k15_euclid(np__2),k3_goboard5(A,C,D)))
                    <=> ( ~ r1_xreal_0(k21_euclid(B),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)))
                        & ~ r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1),D)),k21_euclid(B))
                        & ~ r1_xreal_0(k22_euclid(B),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,D)))
                        & ~ r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C,k1_nat_1(D,np__1))),k22_euclid(B)) ) ) ) ) ) ) ) )).

fof(t5_jordan14,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))) )
     => v2_connsp_1(k1_jordan2c(np__2,k5_topreal1(np__2,A)),k15_euclid(np__2)) ) )).

fof(d1_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_jordan14(A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k3_jordan1h(A,B),k3_jordan11(A,B)) ) ) )).

fof(t6_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,B),np__1) = k1_jordan14(A,B) ) ) ) )).

fof(t7_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r2_hidden(k1_jordan14(A,B),k1_jordan2c(np__2,A)) ) ) ) )).

fof(t8_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan13(A,B))) )
               => ( r1_xboole_0(k3_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A)
                  & ~ r1_xboole_0(k4_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A) ) ) ) ) ) )).

fof(t9_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_subset_1(A,k5_topreal1(np__2,k1_jordan13(A,B))) ) ) ) )).

fof(t10_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_jordan1h(A,B)
              & r2_subset_1(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) )).

fof(t11_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_subset_1(A,k3_goboard9(k1_jordan13(A,B))) ) ) ) )).

fof(t12_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) )).

fof(t13_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(A,k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) )).

fof(t14_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B))),k1_jordan2c(np__2,A)) ) ) ) )).

fof(t15_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(k2_jordan2c(np__2,A),k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) )).

fof(t16_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(k3_goboard9(k1_jordan13(A,B)),k1_jordan2c(np__2,A)) ) ) ) )).

fof(t17_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(k2_jordan2c(np__2,A),k2_goboard9(k1_jordan13(A,B))) ) ) ) )).

fof(t18_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_xboole_0(k2_jordan2c(np__2,A),k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) )).

fof(t19_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_xboole_0(k2_jordan2c(np__2,A),k3_goboard9(k1_jordan13(A,B))) ) ) ) )).

fof(t20_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_jordan1h(A,C)
                  & r2_jordan2c(np__2,A,B) )
               => r1_xboole_0(B,k5_topreal1(np__2,k1_jordan13(A,C))) ) ) ) ) )).

fof(t21_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_xboole_0(k2_jordan2c(np__2,A),k5_topreal1(np__2,k1_jordan13(A,B))) ) ) ) )).

fof(t22_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_jordan1h(A,B)
           => r1_tarski(k5_topreal1(np__2,k1_jordan13(A,B)),k1_jordan2c(np__2,A)) ) ) ) )).

fof(t23_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_jordan1h(A,E)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
                          & r1_xreal_0(B,np__1) ) ) ) ) ) ) )).

fof(t24_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_jordan1h(A,E)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
                          & r1_xreal_0(k3_finseq_1(k1_jordan8(A,E)),B) ) ) ) ) ) ) )).

fof(t25_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_jordan1h(A,E)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
                          & r1_xreal_0(C,np__1) ) ) ) ) ) ) )).

fof(t26_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ~ ( r1_jordan1h(A,E)
                          & r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(k1_jordan13(A,E)))
                          & r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,E)))
                          & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan13(A,E),D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),B,C)
                          & r1_xreal_0(k1_matrix_1(k1_jordan8(A,E)),C) ) ) ) ) ) ) )).

fof(t27_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_jordan1h(A,B)
              & r1_xreal_0(k1_matrix_1(k1_jordan8(A,B)),k3_jordan11(A,B)) ) ) ) )).

fof(t28_jordan14,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(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(np__1,B) )
               => k3_jordan1h(A,C) = k3_real_1(k4_real_1(k1_card_4(np__2,k5_binarith(C,B)),k5_real_1(k3_jordan1h(A,B),np__2)),np__2) ) ) ) ) )).

fof(t29_jordan14,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k15_euclid(np__2))
        & ~ v1_sppol_1(A)
        & ~ v2_sppol_1(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B) )
               => r1_jordan1h(A,C) ) ) ) ) )).

fof(t30_jordan14,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
                      & v1_topreal1(B)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & r1_xreal_0(D,k1_matrix_1(A)) )
                   => v2_connsp_1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(A,C,D),k5_topreal1(np__2,B)),k15_euclid(np__2)) ) ) ) ) ) )).

fof(t31_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(k3_jordan11(A,B),C)
                  & r1_xreal_0(C,k1_nat_1(k2_nat_1(k1_card_4(np__2,k5_binarith(B,k1_jordan11(A))),k5_binarith(k2_jordan11(A),np__2)),np__2)) )
               => r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(k1_jordan8(A,B),k5_binarith(k3_jordan1h(A,B),np__1),C),k5_topreal1(np__2,k1_jordan13(A,B))),k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan13(A,B)))) ) ) ) ) )).

fof(t32_jordan14,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(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(C,B)
                      & ~ r1_xreal_0(D,np__1)
                      & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(A,C)),k1_nat_1(D,np__1))
                      & r1_xreal_0(k3_finseq_1(k1_jordan8(A,B)),k3_real_1(k3_real_1(k4_real_1(k1_card_4(np__2,k5_binarith(B,C)),k5_real_1(D,np__2)),np__2),np__1)) ) ) ) ) ) )).

fof(t33_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(B,C)
                  & r2_subset_1(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) )).

fof(t34_jordan14,axiom,(
    ! [A] :
      ( ( ~ v3_relat_1(A)
        & v1_matrix_1(A)
        & v3_goboard1(A)
        & v4_goboard1(A)
        & v5_goboard1(A)
        & v6_goboard1(A)
        & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
              & v1_topreal1(B) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_xreal_0(C,k3_finseq_1(A))
                        & r1_xreal_0(D,k1_matrix_1(A)) )
                     => r1_tarski(k1_tops_1(k15_euclid(np__2),k3_goboard5(A,C,D)),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,B))) ) ) ) ) ) ) )).

fof(t35_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(B,C) )
               => r1_tarski(k5_topreal1(np__2,k1_jordan13(A,C)),k6_pre_topc(k15_euclid(np__2),k2_goboard9(k1_jordan13(A,B)))) ) ) ) ) )).

fof(t36_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(B,C) )
               => r1_tarski(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) )).

fof(t37_jordan14,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(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_jordan1h(A,B)
                  & r1_xreal_0(B,C) )
               => r1_tarski(k2_goboard9(k1_jordan13(A,C)),k2_goboard9(k1_jordan13(A,B))) ) ) ) ) )).

fof(dt_k1_jordan14,axiom,(
    ! [A,B] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k1_jordan14(A,B),u1_struct_0(k15_euclid(np__2))) ) )).
%------------------------------------------------------------------------------