SET007 Axioms: SET007+510.ax
%------------------------------------------------------------------------------
% File : SET007+510 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subsequences of Standard Special Circular Sequences in cal E^2_T
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : jordan4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 76 ( 7 unt; 0 def)
% Number of atoms : 803 ( 89 equ)
% Maximal formula atoms : 27 ( 10 avg)
% Number of connectives : 841 ( 114 ~; 36 |; 390 &)
% ( 6 <=>; 295 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-4 aty)
% Number of functors : 37 ( 37 usr; 5 con; 0-4 aty)
% Number of variables : 238 ( 238 !; 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_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k5_binarith(A,B) = np__0
=> r1_xreal_0(A,B) ) ) ) ).
fof(t2_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> k5_binarith(k1_nat_1(B,C),A) = k5_real_1(k1_nat_1(B,C),A) ) ) ) ) ).
fof(t3_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> k5_binarith(k1_nat_1(B,C),A) = k1_nat_1(k5_binarith(B,A),C) ) ) ) ) ).
fof(t4_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( B = k2_nat_1(C,A)
=> ( A = np__0
| r1_xreal_0(C,B) ) ) ) ) ) ).
fof(t5_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,A)
=> k3_nat_1(A,B) = np__0 ) ) ) ).
fof(t6_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(k1_nat_1(A,A),B)
& k4_nat_1(B,A) = np__0 ) ) ) ).
fof(t7_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k1_nat_1(A,A),B)
| ( k4_nat_1(B,A) = k5_real_1(B,A)
& k4_nat_1(B,A) = k5_binarith(B,A) ) ) ) ) ) ).
fof(t8_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k4_nat_1(k1_nat_1(A,A),A) = np__0 ) ).
fof(t9_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(A,B)
& k4_nat_1(A,B) = np__0 )
=> ( r1_xreal_0(A,np__0)
| A = B ) ) ) ) ).
fof(t10_jordan4,axiom,
$true ).
fof(t11_jordan4,axiom,
$true ).
fof(t12_jordan4,axiom,
$true ).
fof(t13_jordan4,axiom,
$true ).
fof(t14_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( ( v1_finseq_6(B,A)
& r1_xreal_0(np__1,k3_finseq_1(B)) )
=> k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) ).
fof(t15_jordan4,axiom,
$true ).
fof(t16_jordan4,axiom,
$true ).
fof(t17_jordan4,axiom,
$true ).
fof(t18_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> ( k1_funct_1(k1_rfinseq(A,B,C),k3_finseq_1(k1_rfinseq(A,B,C))) = k1_funct_1(B,k3_finseq_1(B))
& k4_finseq_4(k5_numbers,A,k1_rfinseq(A,B,C),k3_finseq_1(k1_rfinseq(A,B,C))) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)) ) ) ) ) ) ).
fof(t19_jordan4,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( v4_topreal1(A)
=> ( r1_xreal_0(k3_finseq_1(A),k1_nat_1(B,np__1))
| v4_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t20_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k3_finseq_1(k1_jordan3(A,B,D,C)) = k1_nat_1(k5_binarith(C,D),np__1) ) ) ) ) ) ).
fof(t21_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k3_finseq_1(k1_jordan3(A,B,C,D)) = k1_nat_1(k5_binarith(C,D),np__1) ) ) ) ) ) ).
fof(t22_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k1_funct_1(k1_jordan3(A,B,C,D),k3_finseq_1(k1_jordan3(A,B,C,D))) = k1_funct_1(B,D) ) ) ) ) ) ) ).
fof(t23_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k1_funct_1(k1_jordan3(A,B,C,D),k3_finseq_1(k1_jordan3(A,B,C,D))) = k1_funct_1(B,D) ) ) ) ) ) ) ).
fof(t24_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_nat_1(k5_binarith(C,D),np__1)) )
=> k1_funct_1(k1_jordan3(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k5_binarith(C,E),np__1)) ) ) ) ) ) ) ).
fof(t25_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,D)
& r1_xreal_0(D,k3_finseq_1(C))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(k5_binarith(D,E),np__1)) )
=> ( k1_funct_1(k1_jordan3(B,C,D,E),A) = k1_funct_1(k1_jordan3(B,C,E,D),k3_real_1(k5_real_1(k3_real_1(k5_real_1(D,E),np__1),A),np__1))
& k3_real_1(k5_real_1(k3_real_1(k5_real_1(D,E),np__1),A),np__1) = k1_nat_1(k5_binarith(k1_nat_1(k5_binarith(D,E),np__1),A),np__1) ) ) ) ) ) ) ) ).
fof(t26_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(C))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(k5_binarith(E,D),np__1)) )
=> ( k1_funct_1(k1_jordan3(B,C,D,E),A) = k1_funct_1(k1_jordan3(B,C,E,D),k3_real_1(k5_real_1(k3_real_1(k5_real_1(E,D),np__1),A),np__1))
& k3_real_1(k5_real_1(k3_real_1(k5_real_1(E,D),np__1),A),np__1) = k1_nat_1(k5_binarith(k1_nat_1(k5_binarith(E,D),np__1),A),np__1) ) ) ) ) ) ) ) ).
fof(t27_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> ( k1_jordan3(A,B,C,C) = k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,C))
& k3_finseq_1(k1_jordan3(A,B,C,C)) = np__1 ) ) ) ) ) ).
fof(t28_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> k1_jordan3(A,B,np__0,np__0) = k16_finseq_1(A,B,np__1) ) ) ).
fof(t29_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,k3_finseq_1(B))
=> k1_jordan3(A,B,C,C) = k6_finseq_1(A) ) ) ) ) ).
fof(t30_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_jordan3(A,B,C,D) = k4_finseq_5(A,k1_jordan3(A,B,D,C)) ) ) ) ) ).
fof(t31_jordan4,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D) )
=> ( r1_xreal_0(C,B)
| r1_xreal_0(k1_nat_1(k5_binarith(C,B),np__1),D)
| k4_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),D) = k4_topreal1(np__2,A,k5_binarith(k1_nat_1(D,B),np__1)) ) ) ) ) ) ) ).
fof(t32_jordan4,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D) )
=> ( r1_xreal_0(C,B)
| r1_xreal_0(k1_nat_1(k5_binarith(C,B),np__1),D)
| k4_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,B),D) = k4_topreal1(np__2,A,k5_binarith(C,D)) ) ) ) ) ) ) ).
fof(d1_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ( k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) != np__0
=> k1_jordan4(A,B) = k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) )
& ( k4_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)) = np__0
=> k1_jordan4(A,B) = k5_binarith(k3_finseq_1(B),np__1) ) ) ) ) ).
fof(t33_jordan4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k1_jordan4(k5_binarith(k3_finseq_1(A),np__1),A) = k5_binarith(k3_finseq_1(A),np__1) ) ).
fof(t34_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_binarith(k3_finseq_1(B),np__1)) )
=> k1_jordan4(A,B) = A ) ) ) ).
fof(t35_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k1_jordan4(A,B) = k1_jordan4(k1_nat_1(A,k5_binarith(k3_finseq_1(B),np__1)),B)
& k1_jordan4(A,B) = k1_jordan4(k1_nat_1(k5_binarith(k3_finseq_1(B),np__1),A),B) ) ) ) ).
fof(d2_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_jordan4(A,B,C,D)
<=> ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
& r1_xreal_0(np__1,k3_finseq_1(B))
& ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(C,E),np__1),A)) ) ) ) ) ) ) ) ) ).
fof(d3_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_jordan4(A,B,C,D)
<=> ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
& r1_xreal_0(np__1,k3_finseq_1(B))
& ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) ).
fof(d4_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_jordan4(A,B,C,D)
<=> ( r1_jordan4(A,B,C,D)
| r2_jordan4(A,B,C,D) ) ) ) ) ) ) ).
fof(t36_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_jordan4(A,B,C,D)
=> ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,D)
& r1_xreal_0(np__1,k3_finseq_1(B))
& ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))
& ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(C,E),np__1),A)) ) )
| ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k1_funct_1(B,E) = k1_funct_1(A,k1_jordan4(k5_binarith(k1_nat_1(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) ) ).
fof(t37_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_jordan4(A,B,C,D)
& r1_xreal_0(C,D) )
=> ( k3_finseq_1(B) = k1_nat_1(k5_binarith(D,C),np__1)
& B = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,D) ) ) ) ) ) ) ).
fof(t38_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_jordan4(A,B,C,D)
=> ( r1_xreal_0(C,D)
| ( k3_finseq_1(B) = k5_binarith(k1_nat_1(k3_finseq_1(A),D),C)
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,k5_binarith(k3_finseq_1(A),np__1)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,D))
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,k5_binarith(k3_finseq_1(A),np__1)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,D)) ) ) ) ) ) ) ) ).
fof(t39_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_jordan4(A,B,C,D)
& r1_xreal_0(D,C) )
=> ( k3_finseq_1(B) = k1_nat_1(k5_binarith(C,D),np__1)
& B = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,D) ) ) ) ) ) ) ).
fof(t40_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_jordan4(A,B,C,D)
=> ( r1_xreal_0(D,C)
| ( k3_finseq_1(B) = k5_binarith(k1_nat_1(k3_finseq_1(A),C),D)
& B = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),D)) ) ) ) ) ) ) ) ).
fof(t41_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_jordan4(A,B,C,D)
=> r2_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B),D,C) ) ) ) ) ) ).
fof(t42_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_jordan4(A,B,C,D)
=> r1_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B),D,C) ) ) ) ) ) ).
fof(t43_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,C) )
=> ( r1_xreal_0(k3_finseq_1(A),C)
| r1_jordan4(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),B,C) ) ) ) ) ) ).
fof(t44_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,C) )
=> ( r1_xreal_0(k3_finseq_1(A),C)
| r2_jordan4(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,C,B),C,B) ) ) ) ) ) ).
fof(t45_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,C)
=> ( r1_xreal_0(B,C)
| r1_xreal_0(k3_finseq_1(A),B)
| r1_jordan4(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,k5_binarith(k3_finseq_1(A),np__1)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,np__1,C)),B,C) ) ) ) ) ) ).
fof(t46_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(C,B)
| r1_xreal_0(k3_finseq_1(A),C)
| r2_jordan4(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),C)),B,C) ) ) ) ) ) ).
fof(t47_jordan4,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> r1_tarski(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t48_jordan4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( v2_funct_1(B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( ( k1_funct_1(B,C) != k1_funct_1(B,D)
& k4_finseq_4(k5_numbers,A,B,C) != k4_finseq_4(k5_numbers,A,B,D) )
| C = D ) ) ) ) ) ) ) ).
fof(t49_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
=> ( r1_xreal_0(B,np__1)
| v4_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t50_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(A),k1_nat_1(B,np__1))
| v4_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t51_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
=> ( r1_xreal_0(C,B)
| v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) ).
fof(t52_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,k3_finseq_1(A))
=> ( r1_xreal_0(B,np__1)
| r1_xreal_0(C,B)
| v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ) ).
fof(t53_jordan4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(A,k3_topreal1(np__2,B,C))
& r2_hidden(A,k3_topreal1(np__2,B,D))
& B != A
& ~ r2_hidden(C,k3_topreal1(np__2,B,D))
& ~ r2_hidden(D,k3_topreal1(np__2,B,C)) ) ) ) ) ) ).
fof(t54_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,np__1),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1))) = k1_tarski(k1_funct_1(A,np__1)) ) ).
fof(t55_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,B)
& D = k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)
& E = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,np__1),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k5_binarith(k3_finseq_1(A),np__1),C)) )
=> ( r1_xreal_0(C,B)
| r1_xreal_0(k3_finseq_1(A),C)
| ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_tarski(k1_funct_1(A,B),k1_funct_1(A,C))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k5_topreal1(np__2,A) ) ) ) ) ) ) ) ) ).
fof(t56_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_jordan4(A,B,C,D)
=> ( r1_xreal_0(D,C)
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t57_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_jordan4(A,B,C,D)
=> ( r1_xreal_0(C,D)
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t58_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_jordan4(A,B,C,D)
=> ( C = D
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t59_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_jordan4(A,B,C,D)
=> ( C = D
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t60_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_jordan4(A,B,C,D)
=> ( C = D
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t61_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_jordan4(A,B,C,D)
=> ( k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B))
| r1_topreal4(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ).
fof(t62_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& B != C
& ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r3_jordan4(A,D,B,C)
& r3_jordan4(A,E,B,C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k2_tarski(k1_funct_1(A,B),k1_funct_1(A,C))
& k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,D),k5_topreal1(np__2,E)) = k5_topreal1(np__2,A)
& r1_topreal4(k5_topreal1(np__2,D),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C))
& r1_topreal4(k5_topreal1(np__2,E),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C))
& ! [F] :
( m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r3_jordan4(A,F,B,C)
& F != D
& F != E ) ) ) ) ) ) ) ) ) ).
fof(t63_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( B = k5_topreal1(np__2,A)
=> v1_topreal2(B) ) ) ) ).
fof(t64_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_jordan4(C,D,A,B)
& r1_jordan4(C,E,A,B) )
=> D = E ) ) ) ) ) ) ).
fof(t65_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_jordan4(C,D,A,B)
& r2_jordan4(C,E,A,B) )
=> D = E ) ) ) ) ) ) ).
fof(t66_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ~ ( A != B
& r1_jordan4(C,D,A,B)
& r2_jordan4(C,E,A,B)
& k1_funct_1(D,np__2) = k1_funct_1(E,np__2) ) ) ) ) ) ) ).
fof(t67_jordan4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r3_jordan4(C,D,A,B)
& r3_jordan4(C,E,A,B)
& k1_funct_1(D,np__2) = k1_funct_1(E,np__2) )
=> ( A = B
| D = E ) ) ) ) ) ) ) ).
fof(d5_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
=> ( B = C
| ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( D = k2_jordan4(A,B,C)
<=> ( r3_jordan4(A,D,B,C)
& ( ~ ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))))
& r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)))) )
=> k1_funct_1(D,np__2) = k1_funct_1(A,k1_nat_1(B,np__1)) )
& ( ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))))
& r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)))) )
=> k1_funct_1(D,np__2) = k1_funct_1(A,k1_jordan4(k5_binarith(B,np__1),A)) ) ) ) ) ) ) ) ) ) ).
fof(d6_jordan4,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A)) )
=> ( B = C
| ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( D = k3_jordan4(A,B,C)
<=> ( r3_jordan4(A,D,B,C)
& ( ~ ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)))
& r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B))) )
=> k1_funct_1(D,np__2) = k1_funct_1(A,k1_nat_1(B,np__1)) )
& ( ( r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)))
& r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1))),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B))) )
=> k1_funct_1(D,np__2) = k1_funct_1(A,k1_jordan4(k5_binarith(B,np__1),A)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_jordan4,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> m2_subset_1(k1_jordan4(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k2_jordan4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m2_finseq_1(k2_jordan4(A,B,C),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k3_jordan4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m2_finseq_1(k3_jordan4(A,B,C),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------