SET007 Axioms: SET007+499.ax
%------------------------------------------------------------------------------
% File : SET007+499 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Reconstructions of Special Sequences
% 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 : jordan3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 98 ( 3 unt; 0 def)
% Number of atoms : 668 ( 129 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 639 ( 69 ~; 32 |; 190 &)
% ( 5 <=>; 343 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 43 ( 43 usr; 5 con; 0-4 aty)
% Number of variables : 267 ( 265 !; 2 ?)
% 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_jordan3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( ~ v1_xboole_0(k3_finseq_5(A))
& v1_relat_1(k3_finseq_5(A))
& v1_funct_1(k3_finseq_5(A))
& v1_finseq_1(k3_finseq_5(A)) ) ) ).
fof(t1_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ( r1_xreal_0(np__1,k5_binarith(A,B))
| r1_xreal_0(np__1,k6_xcmplx_0(A,B)) )
=> k5_binarith(A,B) = k6_xcmplx_0(A,B) ) ) ) ).
fof(t2_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> k5_binarith(A,np__0) = A ) ).
fof(t3_jordan3,axiom,
$true ).
fof(t4_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v4_ordinal2(C)
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(k5_binarith(C,B),k5_binarith(C,A)) ) ) ) ) ).
fof(t5_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v4_ordinal2(C)
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(k5_binarith(A,C),k5_binarith(B,C)) ) ) ) ) ).
fof(t6_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ( r1_xreal_0(np__1,k5_binarith(A,B))
| r1_xreal_0(np__1,k6_xcmplx_0(A,B)) )
=> k2_xcmplx_0(k5_binarith(A,B),B) = A ) ) ) ).
fof(t7_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(k5_binarith(A,np__1),B) ) ) ) ).
fof(t8_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> k5_binarith(A,np__2) = k5_binarith(k5_binarith(A,np__1),np__1) ) ).
fof(t9_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( r1_xreal_0(k2_xcmplx_0(A,np__1),B)
=> ( ~ r1_xreal_0(B,k5_binarith(A,np__1))
& ~ r1_xreal_0(B,k5_binarith(A,np__2))
& r1_xreal_0(A,B) ) ) ) ) ).
fof(t10_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(A,np__2),B)
| r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(A,np__1),np__1),B) )
=> ( ~ r1_xreal_0(B,k2_xcmplx_0(A,np__1))
& ~ r1_xreal_0(B,k5_binarith(k2_xcmplx_0(A,np__1),np__1))
& ~ r1_xreal_0(B,k5_binarith(k2_xcmplx_0(A,np__1),np__2))
& r1_xreal_0(k2_xcmplx_0(A,np__1),B)
& ~ r1_xreal_0(B,k1_nat_1(k5_binarith(A,np__1),np__1))
& ~ r1_xreal_0(B,k5_binarith(k1_nat_1(k5_binarith(A,np__1),np__1),np__1))
& ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(B,k5_binarith(A,np__1))
& ~ r1_xreal_0(B,k5_binarith(A,np__2))
& r1_xreal_0(A,B) ) ) ) ) ).
fof(t11_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ( r1_xreal_0(A,B)
| r1_xreal_0(A,k5_binarith(B,np__1)) )
=> ( ~ r1_xreal_0(k2_xcmplx_0(B,np__1),A)
& r1_xreal_0(A,k2_xcmplx_0(B,np__1))
& ~ r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(B,np__1),np__1),A)
& r1_xreal_0(A,k2_xcmplx_0(k2_xcmplx_0(B,np__1),np__1))
& ~ r1_xreal_0(k2_xcmplx_0(B,np__2),A)
& r1_xreal_0(A,k2_xcmplx_0(B,np__2)) ) ) ) ) ).
fof(t12_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ~ ( r1_xreal_0(B,A)
& ~ r1_xreal_0(k2_xcmplx_0(A,np__1),B) )
=> r1_xreal_0(A,k5_binarith(B,np__1)) ) ) ) ).
fof(t13_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v4_ordinal2(C)
=> ( r1_xreal_0(B,A)
=> r1_xreal_0(k5_binarith(B,C),A) ) ) ) ) ).
fof(t14_jordan3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,k5_binarith(B,A))
& r1_xreal_0(B,k5_binarith(B,A)) ) ) ) ).
fof(t15_jordan3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ ( ~ r1_xreal_0(A,k3_finseq_1(B))
& ( r1_xreal_0(A,k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)))
| r1_xreal_0(A,k3_finseq_1(k7_finseq_1(B,C))) )
& k1_funct_1(k7_finseq_1(B,C),A) != k1_funct_1(C,k5_real_1(A,k3_finseq_1(B))) ) ) ) ) ).
fof(t16_jordan3,axiom,
$true ).
fof(t17_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m2_finseq_1(C,A)
=> ( r1_xreal_0(np__1,k3_finseq_1(C))
=> ( k1_funct_1(k7_finseq_1(C,k9_finseq_1(B)),np__1) = k1_funct_1(C,np__1)
& k1_funct_1(k7_finseq_1(C,k9_finseq_1(B)),np__1) = k4_finseq_4(k5_numbers,A,C,np__1)
& k1_funct_1(k7_finseq_1(k9_finseq_1(B),C),k1_nat_1(k3_finseq_1(C),np__1)) = k1_funct_1(C,k3_finseq_1(C))
& k1_funct_1(k7_finseq_1(k9_finseq_1(B),C),k1_nat_1(k3_finseq_1(C),np__1)) = k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) ) ) ) ) ).
fof(t18_jordan3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( k3_finseq_1(A) = np__1
=> k3_finseq_5(A) = A ) ) ).
fof(t19_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k3_finseq_1(k1_rfinseq(A,B,C)) = k5_binarith(k3_finseq_1(B),C) ) ) ) ).
fof(t20_jordan3,axiom,
$true ).
fof(t21_jordan3,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)
=> k16_finseq_1(A,k1_rfinseq(A,B,C),k5_binarith(D,C)) = k1_rfinseq(A,k16_finseq_1(A,B,D),C) ) ) ) ) ).
fof(d1_jordan3,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(C,D)
=> k1_jordan3(A,B,C,D) = k16_finseq_1(A,k1_rfinseq(A,B,k5_binarith(C,np__1)),k1_nat_1(k5_binarith(D,C),np__1)) )
& ( ~ r1_xreal_0(C,D)
=> k1_jordan3(A,B,C,D) = k4_finseq_5(A,k16_finseq_1(A,k1_rfinseq(A,B,k5_binarith(D,np__1)),k1_nat_1(k5_binarith(C,D),np__1))) ) ) ) ) ) ) ).
fof(t22_jordan3,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,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k4_finseq_5(A,k1_jordan3(A,B,C,D)) = k1_jordan3(A,k4_finseq_5(A,B),k1_nat_1(k5_binarith(k3_finseq_1(B),D),np__1),k1_nat_1(k5_binarith(k3_finseq_1(B),C),np__1)) ) ) ) ) ) ).
fof(t23_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,B),k3_finseq_1(D)) )
=> k1_funct_1(k1_rfinseq(A,D,B),C) = k1_funct_1(D,k1_nat_1(C,B)) ) ) ) ) ) ).
fof(t24_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> k1_funct_1(k4_finseq_5(A,C),B) = k1_funct_1(C,k3_real_1(k5_real_1(k3_finseq_1(C),B),np__1)) ) ) ) ) ).
fof(t25_jordan3,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)
=> k1_jordan3(A,B,np__1,C) = k16_finseq_1(A,B,C) ) ) ) ) ).
fof(t26_jordan3,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,k3_finseq_1(B)) = k1_rfinseq(A,B,k5_binarith(C,np__1)) ) ) ) ) ).
fof(t27_jordan3,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,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),np__1) = k1_funct_1(B,C)
& ( r1_xreal_0(C,D)
=> ( k3_finseq_1(k1_jordan3(A,B,C,D)) = k1_nat_1(k5_binarith(D,C),np__1)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan3(A,B,C,D))) )
=> k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k5_binarith(k1_nat_1(E,C),np__1)) ) ) ) )
& ( ~ r1_xreal_0(C,D)
=> ( k3_finseq_1(k1_jordan3(A,B,C,D)) = k1_nat_1(k5_binarith(C,D),np__1)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(k1_jordan3(A,B,C,D))) )
=> k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k5_binarith(C,E),np__1)) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_jordan3,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_tarski(k2_relat_1(k1_jordan3(A,B,C,D)),k2_relat_1(B)) ) ) ) ) ).
fof(t29_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( r1_xreal_0(np__1,k3_finseq_1(B))
=> k1_jordan3(A,B,np__1,k3_finseq_1(B)) = B ) ) ) ).
fof(t30_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( r1_xreal_0(np__1,k3_finseq_1(B))
=> k1_jordan3(A,B,k3_finseq_1(B),np__1) = k4_finseq_5(A,B) ) ) ) ).
fof(t31_jordan3,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))
& r1_xreal_0(np__1,E) )
=> ( ( ~ r1_xreal_0(E,k1_nat_1(k5_binarith(D,C),np__1))
& ~ r1_xreal_0(E,k3_real_1(k5_real_1(D,C),np__1))
& ~ r1_xreal_0(E,k5_real_1(k1_nat_1(D,np__1),C)) )
| ( k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k5_binarith(k1_nat_1(E,C),np__1))
& k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k5_binarith(E,np__1),C))
& k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k5_real_1(k1_nat_1(E,C),np__1))
& k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k3_real_1(k5_real_1(E,np__1),C)) ) ) ) ) ) ) ) ) ).
fof(t32_jordan3,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)) )
=> k1_funct_1(k1_jordan3(A,B,np__1,C),D) = k1_funct_1(B,D) ) ) ) ) ) ).
fof(t33_jordan3,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,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> r1_xreal_0(k3_finseq_1(k1_jordan3(A,B,C,D)),k3_finseq_1(B)) ) ) ) ) ) ).
fof(t34_jordan3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(A)))
=> ( r1_xreal_0(np__2,k3_finseq_1(B))
=> ( r2_hidden(k1_funct_1(B,np__1),k5_topreal1(A,B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,np__1),k5_topreal1(A,B))
& r2_hidden(k1_funct_1(B,k3_finseq_1(B)),k5_topreal1(A,B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,k3_finseq_1(B)),k5_topreal1(A,B)) ) ) ) ) ).
fof(t35_jordan3,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)))
=> ~ ( ( k21_euclid(A) = k21_euclid(B)
| k22_euclid(A) = k22_euclid(B) )
& r2_hidden(C,k3_topreal1(np__2,A,B))
& r2_hidden(D,k3_topreal1(np__2,A,B))
& k21_euclid(C) != k21_euclid(D)
& k22_euclid(C) != k22_euclid(D) ) ) ) ) ) ).
fof(t36_jordan3,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)))
=> ~ ( ( k21_euclid(A) = k21_euclid(B)
| k22_euclid(A) = k22_euclid(B) )
& r1_tarski(k3_topreal1(np__2,C,D),k3_topreal1(np__2,A,B))
& k21_euclid(C) != k21_euclid(D)
& k22_euclid(C) != k22_euclid(D) ) ) ) ) ) ).
fof(t37_jordan3,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__2,B)
& v4_topreal1(A) )
=> v4_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t38_jordan3,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(B,k3_finseq_1(A))
& r1_xreal_0(np__2,k5_binarith(k3_finseq_1(A),B))
& v4_topreal1(A) )
=> v4_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t39_jordan3,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,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> ( B = C
| v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) ).
fof(t40_jordan3,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)
=> ( r2_hidden(B,k4_topreal1(np__2,A,C))
=> r1_xreal_0(k2_jordan3(A,B),C) ) ) ) ) ).
fof(t41_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ( r1_xreal_0(np__1,k2_jordan3(A,B))
& ~ r1_xreal_0(k3_finseq_1(A),k2_jordan3(A,B)) ) ) ) ) ).
fof(t42_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> r2_hidden(B,k4_topreal1(np__2,A,k2_jordan3(A,B))) ) ) ) ).
fof(t43_jordan3,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)))
=> ( r2_hidden(B,k4_topreal1(np__2,A,np__1))
=> k2_jordan3(A,B) = np__1 ) ) ) ).
fof(t44_jordan3,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)))
=> ( r1_xreal_0(np__2,k3_finseq_1(A))
=> k2_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) = np__1 ) ) ) ).
fof(t45_jordan3,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(C,k3_finseq_1(A))
& B = k1_funct_1(A,C) )
=> ( r1_xreal_0(C,np__1)
| k1_nat_1(k2_jordan3(A,B),np__1) = C ) ) ) ) ) ).
fof(t46_jordan3,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)
=> ~ ( v3_topreal1(A)
& r2_hidden(B,k4_topreal1(np__2,A,C))
& C != k2_jordan3(A,B)
& C != k1_nat_1(k2_jordan3(A,B),np__1) ) ) ) ) ).
fof(t47_jordan3,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)
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_hidden(B,k4_topreal1(np__2,A,C)) )
=> ( B = k1_funct_1(A,C)
| C = k2_jordan3(A,B) ) ) ) ) ) ).
fof(d3_jordan3,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)))
=> ( r1_jordan3(A,B,C)
<=> ( v4_topreal1(A)
& k1_funct_1(A,np__1) = B
& k1_funct_1(A,k3_finseq_1(A)) = C ) ) ) ) ) ).
fof(t48_jordan3,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)))
=> ( r1_jordan3(A,B,C)
=> r1_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),C,B) ) ) ) ) ).
fof(t49_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k5_topreal1(np__2,A))
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),C),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,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(B)) )
=> r1_tarski(k4_topreal1(np__2,B,D),k4_topreal1(np__2,A,k5_binarith(k1_nat_1(k2_jordan3(A,C),D),np__1))) ) ) ) ) ) ).
fof(t50_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(C,k5_topreal1(np__2,A))
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),C),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,C),np__1),k3_finseq_1(A))) )
=> ( C = k1_funct_1(A,k1_nat_1(k2_jordan3(A,C),np__1))
| r1_jordan3(B,C,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) ) ) ) ) ) ).
fof(t51_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k5_topreal1(np__2,A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(B))
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k2_jordan3(A,C)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),C)) )
=> r1_tarski(k4_topreal1(np__2,B,D),k4_topreal1(np__2,A,D)) ) ) ) ) ) ).
fof(t52_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(C,k5_topreal1(np__2,A))
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k2_jordan3(A,C)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),C)) )
=> ( C = k1_funct_1(A,np__1)
| r1_jordan3(B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),C) ) ) ) ) ) ).
fof(d4_jordan3,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)))
=> ( ( B != k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k3_jordan3(A,B) = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1),k3_finseq_1(A))) )
& ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k3_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1),k3_finseq_1(A)) ) ) ) ) ).
fof(d5_jordan3,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)))
=> ( ( B != k1_funct_1(A,np__1)
=> k4_jordan3(A,B) = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k2_jordan3(A,B)),k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B)) )
& ( B = k1_funct_1(A,np__1)
=> k4_jordan3(A,B) = k12_finseq_1(u1_struct_0(k15_euclid(np__2)),B) ) ) ) ) ).
fof(t53_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A))
& B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1)) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| k1_nat_1(k1_nat_1(k2_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),B),k2_jordan3(A,B)),np__1) = k3_finseq_1(A) ) ) ) ) ).
fof(t54_jordan3,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)))
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
| k1_nat_1(k2_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),B),k2_jordan3(A,B)) = k3_finseq_1(A) ) ) ) ) ).
fof(t55_jordan3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,A)
=> k16_finseq_1(A,k8_finseq_1(A,k12_finseq_1(A,D),B),k1_nat_1(C,np__1)) = k8_finseq_1(A,k12_finseq_1(A,D),k16_finseq_1(A,B,C)) ) ) ) ) ).
fof(t56_jordan3,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)
=> ( r2_hidden(C,k4_finseq_1(B))
=> ( r1_xreal_0(D,C)
| k1_jordan3(A,B,C,D) = k7_finseq_1(k9_finseq_1(k1_funct_1(B,C)),k1_jordan3(A,B,k1_nat_1(C,np__1),D)) ) ) ) ) ) ) ).
fof(t57_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> k3_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(np__2)),A),B) = k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B)) ) ) ) ).
fof(t58_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ( k1_funct_1(k3_jordan3(A,B),np__1) = B
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,k3_finseq_1(k3_jordan3(A,B)))
=> ( r1_xreal_0(C,np__1)
| ( ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k1_funct_1(k3_jordan3(A,B),C) = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),C)) )
& ( B != k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k1_funct_1(k3_jordan3(A,B),C) = k1_funct_1(A,k5_real_1(k1_nat_1(k2_jordan3(A,B),C),np__1)) ) ) ) ) ) ) ) ) ) ).
fof(t59_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ( k1_funct_1(k4_jordan3(A,B),k3_finseq_1(k4_jordan3(A,B))) = B
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k2_jordan3(A,B)) )
=> k1_funct_1(k4_jordan3(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) ) ).
fof(t60_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ( ( B != k1_funct_1(A,np__1)
=> k3_finseq_1(k4_jordan3(A,B)) = k1_nat_1(k2_jordan3(A,B),np__1) )
& ( B = k1_funct_1(A,np__1)
=> k3_finseq_1(k4_jordan3(A,B)) = k2_jordan3(A,B) ) ) ) ) ) ).
fof(t61_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ( ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k3_finseq_1(k3_jordan3(A,B)) = k5_real_1(k3_finseq_1(A),k2_jordan3(A,B)) )
& ( B != k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),np__1))
=> k3_finseq_1(k3_jordan3(A,B)) = k3_real_1(k5_real_1(k3_finseq_1(A),k2_jordan3(A,B)),np__1) ) ) ) ) ) ).
fof(d6_jordan3,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_jordan3(A,B,C,D)
<=> ( r2_hidden(C,k3_topreal1(np__2,A,B))
& r2_hidden(D,k3_topreal1(np__2,A,B))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( r1_xreal_0(np__0,E)
& r1_xreal_0(E,np__1)
& C = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,E),np__2,A),k18_euclid(E,np__2,B))
& r1_xreal_0(np__0,F)
& r1_xreal_0(F,np__1)
& D = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,F),np__2,A),k18_euclid(F,np__2,B)) )
=> r1_xreal_0(E,F) ) ) ) ) ) ) ) ) ) ).
fof(d7_jordan3,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)))
=> ( r3_jordan3(A,B,C,D)
<=> ( r2_jordan3(A,B,C,D)
& C != D ) ) ) ) ) ) ).
fof(t62_jordan3,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_jordan3(A,B,C,D)
& r2_jordan3(A,B,D,C) )
=> C = D ) ) ) ) ) ).
fof(t63_jordan3,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(C,k3_topreal1(np__2,A,B))
& r2_hidden(D,k3_topreal1(np__2,A,B)) )
=> ( A = B
| ( ( r2_jordan3(A,B,C,D)
| r3_jordan3(A,B,D,C) )
& ~ ( r2_jordan3(A,B,C,D)
& r3_jordan3(A,B,D,C) ) ) ) ) ) ) ) ) ).
fof(t64_jordan3,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)) )
=> ( r1_xreal_0(k2_jordan3(A,C),k2_jordan3(A,B))
| r2_hidden(C,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) ) ).
fof(t65_jordan3,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_jordan3(C,D,A,B)
=> ( r2_hidden(B,k3_topreal1(np__2,A,D))
& r2_hidden(A,k3_topreal1(np__2,C,B)) ) ) ) ) ) ) ).
fof(t66_jordan3,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))
& k2_jordan3(A,B) = k2_jordan3(A,C)
& r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)),B,C) )
=> ( B = C
| r2_hidden(C,k5_topreal1(np__2,k3_jordan3(A,B))) ) ) ) ) ) ).
fof(d8_jordan3,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))
& ~ r1_xreal_0(k2_jordan3(A,C),k2_jordan3(A,B)) )
| ( k2_jordan3(A,B) = k2_jordan3(A,C)
& r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)),B,C) ) )
=> k5_jordan3(A,B,C) = k4_jordan3(k3_jordan3(A,B),C) )
& ~ ( ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A))
& ~ r1_xreal_0(k2_jordan3(A,C),k2_jordan3(A,B)) )
& ~ ( k2_jordan3(A,B) = k2_jordan3(A,C)
& r2_jordan3(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k2_jordan3(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1)),B,C) )
& k5_jordan3(A,B,C) != k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k4_jordan3(k3_jordan3(A,C),B)) ) ) ) ) ) ).
fof(t67_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,np__1)
| r1_jordan3(k4_jordan3(A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),B) ) ) ) ) ).
fof(t68_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| r1_jordan3(k3_jordan3(A,B),B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) ) ) ) ) ).
fof(t69_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| v4_topreal1(k3_jordan3(A,B)) ) ) ) ) ).
fof(t70_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,np__1)
| v4_topreal1(k4_jordan3(A,B)) ) ) ) ) ).
fof(t71_jordan3,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)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A)) )
=> ( B = C
| r1_jordan3(k5_jordan3(A,B,C),B,C) ) ) ) ) ) ).
fof(t72_jordan3,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)))
=> ( ( v4_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A)) )
=> ( B = C
| v4_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) ).
fof(t73_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__2,k3_finseq_1(B)))) ) ) ) ).
fof(t74_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> r1_jordan3(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__2,k3_finseq_1(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)),B,k3_finseq_1(B))) ) ) ) ).
fof(t75_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k5_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)),k5_topreal1(np__2,A)) ) ) ).
fof(t76_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> r1_tarski(k5_topreal1(np__2,k4_jordan3(A,B)),k5_topreal1(np__2,A)) ) ) ) ).
fof(t77_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> r1_tarski(k5_topreal1(np__2,k3_jordan3(A,B)),k5_topreal1(np__2,A)) ) ) ) ).
fof(t78_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& r2_hidden(C,k5_topreal1(np__2,A))
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> ( C = k1_funct_1(A,k3_finseq_1(A))
| r1_jordan3(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k3_jordan3(A,C),k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__2,k3_finseq_1(B))),C,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) ) ) ) ) ) ).
fof(t79_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& r2_hidden(C,k5_topreal1(np__2,A))
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> ( C = k1_funct_1(A,k3_finseq_1(A))
| v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k3_jordan3(A,C),k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__2,k3_finseq_1(B)))) ) ) ) ) ) ).
fof(t80_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_binarith(k3_finseq_1(A),np__1)),B)) ) ) ) ).
fof(t81_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> r1_jordan3(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_binarith(k3_finseq_1(A),np__1)),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)),B,k3_finseq_1(B))) ) ) ) ).
fof(t82_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& r2_hidden(C,k5_topreal1(np__2,B))
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> ( C = k1_funct_1(B,np__1)
| r1_jordan3(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_binarith(k3_finseq_1(A),np__1)),k4_jordan3(B,C)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),C) ) ) ) ) ) ).
fof(t83_jordan3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1)
& r2_hidden(C,k5_topreal1(np__2,B))
& v4_topreal1(A)
& v4_topreal1(B)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k1_tarski(k1_funct_1(B,np__1)) )
=> ( C = k1_funct_1(B,np__1)
| v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,k5_binarith(k3_finseq_1(A),np__1)),k4_jordan3(B,C))) ) ) ) ) ) ).
fof(dt_k1_jordan3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m2_finseq_1(k1_jordan3(A,B,C,D),A) ) ).
fof(dt_k2_jordan3,axiom,
! [A,B] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m2_subset_1(k2_jordan3(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k3_jordan3,axiom,
! [A,B] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m2_finseq_1(k3_jordan3(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k4_jordan3,axiom,
! [A,B] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> m2_finseq_1(k4_jordan3(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k5_jordan3,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> m2_finseq_1(k5_jordan3(A,B,C),u1_struct_0(k15_euclid(np__2))) ) ).
fof(d2_jordan3,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)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C = k2_jordan3(A,B)
<=> ? [D] :
( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(k5_numbers))
& C = k10_cqc_sim1(D)
& D = a_2_0_jordan3(A,B) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_jordan3,axiom,
! [A,B,C] :
( ( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_2_0_jordan3(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = D
& r2_hidden(C,k4_topreal1(np__2,B,D)) ) ) ) ).
%------------------------------------------------------------------------------