SET007 Axioms: SET007+524.ax
%------------------------------------------------------------------------------
% File : SET007+524 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Ordering of Points on a Curve. Part II
% 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 : jordan5c [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 35 ( 0 unt; 0 def)
% Number of atoms : 430 ( 51 equ)
% Maximal formula atoms : 35 ( 12 avg)
% Number of connectives : 413 ( 18 ~; 11 |; 181 &)
% ( 4 <=>; 199 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 15 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-5 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 165 ( 165 !; 0 ?)
% 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_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ( r2_hidden(E,A)
& r2_hidden(E,B)
& k1_funct_1(F,G) = E
& v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(np__0,H)
& ~ r1_xreal_0(G,H)
& r2_hidden(k1_funct_1(F,H),B) ) ) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( ( v3_tops_2(H,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(H,np__0) = C
& k1_funct_1(H,np__1) = D
& k1_funct_1(H,I) = E
& r1_xreal_0(np__0,I)
& r1_xreal_0(I,np__1) )
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ~ ( r1_xreal_0(np__0,J)
& ~ r1_xreal_0(I,J)
& r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> ( r1_xboole_0(A,B)
| ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( E = k1_jordan5c(A,B,C,D)
<=> ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ( v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& k1_funct_1(F,G) = E
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1) )
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(np__0,H)
& ~ r1_xreal_0(G,H)
& r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,A)
& r1_topreal1(k15_euclid(np__2),D,E,A)
& B = k1_struct_0(k15_euclid(np__2),C) )
=> k1_jordan5c(A,B,D,E) = C ) ) ) ) ) ) ).
fof(t3_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [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(C,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> k1_jordan5c(A,B,C,D) = C ) ) ) ) ) ).
fof(t4_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ( r2_hidden(E,A)
& r2_hidden(E,B)
& k1_funct_1(F,G) = E
& v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(H,np__1)
& ~ r1_xreal_0(H,G)
& r2_hidden(k1_funct_1(F,H),B) ) ) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( ( v3_tops_2(H,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(H,np__0) = C
& k1_funct_1(H,np__1) = D
& k1_funct_1(H,I) = E
& r1_xreal_0(np__0,I)
& r1_xreal_0(I,np__1) )
=> ! [J] :
( m1_subset_1(J,k1_numbers)
=> ~ ( r1_xreal_0(J,np__1)
& ~ r1_xreal_0(J,I)
& r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> ( r1_xboole_0(A,B)
| ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( E = k2_jordan5c(A,B,C,D)
<=> ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B))
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ( v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& k1_funct_1(F,G) = E
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1) )
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( r1_xreal_0(H,np__1)
& ~ r1_xreal_0(H,G)
& r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,A)
& r1_topreal1(k15_euclid(np__2),D,E,A)
& B = k1_struct_0(k15_euclid(np__2),C) )
=> k2_jordan5c(A,B,D,E) = C ) ) ) ) ) ) ).
fof(t6_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [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(D,B)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> k2_jordan5c(A,B,C,D) = D ) ) ) ) ) ).
fof(t7_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_tarski(A,B)
& v4_pre_topc(A,k15_euclid(np__2))
& r1_topreal1(k15_euclid(np__2),C,D,A) )
=> ( k1_jordan5c(A,B,C,D) = C
& k2_jordan5c(A,B,C,D) = D ) ) ) ) ) ) ).
fof(d3_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( r1_jordan5c(A,B,C,D,E)
<=> ( r2_hidden(D,A)
& r2_hidden(E,A)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ( ( v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = B
& k1_funct_1(F,np__1) = C
& k1_funct_1(F,G) = D
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& k1_funct_1(F,H) = E
& r1_xreal_0(np__0,H)
& r1_xreal_0(H,np__1) )
=> r1_xreal_0(G,H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(np__2),A))) )
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(np__2),A))
& k1_funct_1(F,np__0) = B
& k1_funct_1(F,np__1) = C
& k1_funct_1(F,G) = D
& r1_xreal_0(np__0,G)
& r1_xreal_0(G,np__1)
& k1_funct_1(F,H) = E
& r1_xreal_0(np__0,H)
& r1_xreal_0(H,np__1)
& r1_xreal_0(G,H) )
=> r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ).
fof(t9_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [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(D,A)
=> r1_jordan5c(A,B,C,D,D) ) ) ) ) ) ).
fof(t10_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r2_hidden(D,A) )
=> ( r1_jordan5c(A,B,C,B,D)
& r1_jordan5c(A,B,C,D,C) ) ) ) ) ) ) ).
fof(t11_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> r1_jordan5c(A,B,C,B,C) ) ) ) ) ).
fof(t12_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r1_jordan5c(A,B,C,D,E)
& r1_jordan5c(A,B,C,E,D) )
=> D = E ) ) ) ) ) ) ).
fof(t13_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_jordan5c(A,B,C,D,E)
& r1_jordan5c(A,B,C,E,F) )
=> r1_jordan5c(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t14_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_topreal1(k15_euclid(np__2),B,C,A)
& r2_hidden(D,A)
& r2_hidden(E,A)
& D != E
& ~ ( r1_jordan5c(A,B,C,D,E)
& ~ r1_jordan5c(A,B,C,E,D) )
& ~ ( r1_jordan5c(A,B,C,E,D)
& ~ r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t15_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),B),k15_euclid(np__2))
& r2_hidden(C,k5_topreal1(np__2,A))
& r2_hidden(C,B) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),C) ) ) ) ) ).
fof(t16_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),B),k15_euclid(np__2))
& r2_hidden(C,k5_topreal1(np__2,A))
& r2_hidden(C,B) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),C,k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))) ) ) ) ) ).
fof(t17_jordan5c,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)))
=> ( r1_jordan5c(k3_topreal1(np__2,C,D),C,D,A,B)
=> ( C = D
| r2_jordan3(C,D,A,B) ) ) ) ) ) ) ).
fof(t18_jordan5c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_topreal1(k15_euclid(np__2),C,D,A)
& v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,B),k15_euclid(np__2)) )
=> ( r1_xboole_0(A,B)
| ( k1_jordan5c(A,B,C,D) = k2_jordan5c(A,B,D,C)
& k2_jordan5c(A,B,C,D) = k1_jordan5c(A,B,D,C) ) ) ) ) ) ) ) ).
fof(t19_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,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)
=> ( ( v4_pre_topc(B,k15_euclid(np__2))
& v4_topreal1(A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,C)) )
=> ( r1_xboole_0(k5_topreal1(np__2,A),B)
| k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k1_jordan5c(k4_topreal1(np__2,A,C),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,k1_nat_1(C,np__1))) ) ) ) ) ) ).
fof(t20_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,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)
=> ( ( v4_pre_topc(B,k15_euclid(np__2))
& v4_topreal1(A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,C)) )
=> ( r1_xboole_0(k5_topreal1(np__2,A),B)
| k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k2_jordan5c(k4_topreal1(np__2,A,C),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,k1_nat_1(C,np__1))) ) ) ) ) ) ).
fof(t21_jordan5c,axiom,
! [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(k1_nat_1(B,np__1),k3_finseq_1(A))
& v4_topreal1(A)
& r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,B)) )
=> k1_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) ) ) ) ).
fof(t22_jordan5c,axiom,
! [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(k1_nat_1(B,np__1),k3_finseq_1(A))
& v4_topreal1(A)
& r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,B)) )
=> k2_jordan5c(k5_topreal1(np__2,A),k4_topreal1(np__2,A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) ) ) ) ).
fof(t23_jordan5c,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),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,k1_nat_1(B,np__1))) ) ) ) ).
fof(t24_jordan5c,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)
=> ( ( v4_topreal1(A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),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)) ) ) ) ) ).
fof(t25_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v4_topreal1(A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),B) ) ) ) ) ).
fof(t26_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v4_topreal1(A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1))) ) ) ) ) ).
fof(t27_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( v4_topreal1(A)
& v4_pre_topc(B,k15_euclid(np__2))
& r2_hidden(k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,D))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r2_hidden(C,k4_topreal1(np__2,A,E))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(C,B) )
=> ( r1_xboole_0(k5_topreal1(np__2,A),B)
| k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = C
| ( r1_xreal_0(D,E)
& ( D = E
=> r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),k1_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),C) ) ) ) ) ) ) ) ) ) ).
fof(t28_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( v4_topreal1(A)
& v4_pre_topc(B,k15_euclid(np__2))
& r2_hidden(k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k4_topreal1(np__2,A,D))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r2_hidden(C,k4_topreal1(np__2,A,E))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(C,B) )
=> ( r1_xboole_0(k5_topreal1(np__2,A),B)
| k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) = C
| ( r1_xreal_0(E,D)
& ( D = E
=> r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),C,k2_jordan5c(k5_topreal1(np__2,A),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))) ) ) ) ) ) ) ) ) ) ).
fof(t29_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_topreal1(np__2,A,D))
& r2_hidden(C,k4_topreal1(np__2,A,D))
& v4_topreal1(A)
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,C) )
=> r1_jordan5c(k4_topreal1(np__2,A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),B,C) ) ) ) ) ) ).
fof(t30_jordan5c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A))
& v4_topreal1(A) )
=> ( B = C
| ( r1_jordan5c(k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_topreal1(np__2,A,D))
& r2_hidden(C,k4_topreal1(np__2,A,E))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A)) )
=> ( r1_xreal_0(D,E)
& ( D = E
=> r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1)),B,C) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_jordan5c,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k1_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k2_jordan5c,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(D,u1_struct_0(k15_euclid(np__2))) )
=> m1_subset_1(k2_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------