SET007 Axioms: SET007+715.ax


%------------------------------------------------------------------------------
% File     : SET007+715 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Remarks on Clockwise Oriented Sequences on Go-boards
% 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    : jordan1i [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   30 (   0 unit)
%            Number of atoms       :  500 (  37 equality)
%            Maximal formula depth :   21 (  14 average)
%            Number of connectives :  570 ( 100 ~  ;   1  |; 353  &)
%                                         (   3 <=>; 113 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   0 propositional; 1-3 arity)
%            Number of functors    :   49 (   6 constant; 0-4 arity)
%            Number of variables   :   98 (   0 singleton;  98 !;   0 ?)
%            Maximal term depth    :    8 (   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(t1_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( v1_jordan2c(B,A)
                  | v1_jordan2c(C,A) )
               => v1_jordan2c(k5_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) )).

fof(t2_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ~ ( ~ v1_jordan2c(B,A)
                  & v1_jordan2c(C,A)
                  & v1_jordan2c(k6_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) )).

fof(t3_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) )).

fof(t4_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) )).

fof(t5_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) )).

fof(t6_jordan1i,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] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k2_relat_1(A))
           => k5_goboard5(A,k5_finseq_4(A,B)) = k5_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B),np__1) ) ) ) )).

fof(t7_jordan1i,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] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,k2_relat_1(A))
           => k4_goboard5(A,k5_finseq_4(A,B)) = k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B),np__1) ) ) ) )).

fof(t8_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => r2_hidden(k30_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) )).

fof(t9_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => r2_hidden(k34_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) )).

fof(t10_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & ~ v1_sppol_1(B)
            & ~ v2_sppol_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => r2_hidden(k36_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) )).

fof(t11_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(B))
           => r2_hidden(B,k2_goboard9(A)) ) ) ) )).

fof(t12_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ r1_xreal_0(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
           => r2_hidden(B,k2_goboard9(A)) ) ) ) )).

fof(t13_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
           => r2_hidden(B,k2_goboard9(A)) ) ) ) )).

fof(t14_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ~ r1_xreal_0(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A)))
           => r2_hidden(B,k2_goboard9(A)) ) ) ) )).

fof(t15_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & r1_xreal_0(k1_matrix_1(B),D) ) ) ) ) ) ) ) )).

fof(t16_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
                            & r1_xreal_0(k3_finseq_1(B),C) ) ) ) ) ) ) ) )).

fof(t17_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
                            & r1_xreal_0(D,np__1) ) ) ) ) ) ) ) )).

fof(t18_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & r1_xreal_0(C,np__1) ) ) ) ) ) ) ) )).

fof(t19_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) )).

fof(t20_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
                            & k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k20_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) )).

fof(t21_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
                            & k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k21_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) )).

fof(t22_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
           => ! [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,E)
                            & r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
                            & r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
                            & r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
                            & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
                            & k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k18_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) )).

fof(t23_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k30_pscomp_1(k5_topreal1(np__2,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
                              & r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(B))
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E)
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,k1_nat_1(E,np__1)) ) ) ) ) ) ) ) )).

fof(t24_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k32_pscomp_1(k5_topreal1(np__2,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
                              & r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(B))
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E)
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(D,np__1),E) ) ) ) ) ) ) ) )).

fof(t25_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(B))
                              & r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,k1_nat_1(E,np__1))
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) ) ) ) )).

fof(t26_jordan1i,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)
        & v1_sprect_2(A)
        & m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
     => ! [B] :
          ( ( ~ v3_relat_1(B)
            & v1_matrix_1(B)
            & v3_goboard1(B)
            & v4_goboard1(B)
            & v5_goboard1(B)
            & v6_goboard1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
                  & r1_xreal_0(np__1,C)
                  & r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                  & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k36_pscomp_1(k5_topreal1(np__2,A))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(B))
                              & r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(D,np__1),E)
                              & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) ) ) ) )).

fof(t27_jordan1i,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))) )
     => ( 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,k30_pscomp_1(k5_topreal1(np__2,A))),np__2),k26_pscomp_1(k5_topreal1(np__2,A))) ) ) )).

fof(t28_jordan1i,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))) )
     => ( 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,k34_pscomp_1(k5_topreal1(np__2,A))),np__2),k28_pscomp_1(k5_topreal1(np__2,A))) ) ) )).

fof(t29_jordan1i,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))) )
     => ( 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,k36_pscomp_1(k5_topreal1(np__2,A))),np__2),k29_pscomp_1(k5_topreal1(np__2,A))) ) ) )).

fof(t30_jordan1i,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v6_compts_1(C,k15_euclid(np__2))
                & ~ v1_sppol_1(C)
                & ~ v2_sppol_1(C)
                & v1_topreal2(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( k21_euclid(D) = k6_real_1(k3_real_1(k18_pscomp_1(C),k20_pscomp_1(C)),np__2)
                      & ~ r1_xreal_0(A,np__0)
                      & r1_xreal_0(np__1,B)
                      & r1_xreal_0(B,k1_matrix_1(k1_jordan8(C,A)))
                      & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B),k8_jordan6(k5_topreal1(np__2,k1_jordan9(C,A))))
                      & k22_euclid(D) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,np__1),k1_jordan1a(k1_jordan8(C,np__1)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(C,A))))))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k1_matrix_1(k1_jordan8(C,A)))
                              & D = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),E) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------