SET007 Axioms: SET007+888.ax
%------------------------------------------------------------------------------
% File : SET007+888 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subsequences of Finite Sequences
% Version : [Urb08] axioms.
% English : Subsequences of Almost, Weakly and Poorly One-to-one Finite
% Sequences
% 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 : jordan23 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 67 ( 0 unt; 0 def)
% Number of atoms : 566 ( 59 equ)
% Maximal formula atoms : 34 ( 8 avg)
% Number of connectives : 551 ( 52 ~; 23 |; 295 &)
% ( 8 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 9 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 34 ( 33 usr; 0 prp; 1-3 aty)
% Number of functors : 37 ( 37 usr; 5 con; 0-4 aty)
% Number of variables : 147 ( 140 !; 7 ?)
% 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_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(k5_finseq_1(A))
& v1_relat_1(k5_finseq_1(A))
& v1_funct_1(k5_finseq_1(A))
& v2_funct_1(k5_finseq_1(A))
& v1_finset_1(k5_finseq_1(A))
& v1_finseq_1(k5_finseq_1(A))
& v5_seqm_3(k5_finseq_1(A))
& v1_realset1(k5_finseq_1(A)) ) ).
fof(cc1_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_jordan23(A) ) ) ).
fof(cc2_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_jordan23(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v3_jordan23(A) ) ) ).
fof(fc2_jordan23,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v5_seqm_3(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_realset1(k1_xboole_0)
& v1_jordan23(k1_xboole_0)
& v2_jordan23(k1_xboole_0)
& v3_jordan23(k1_xboole_0) ) ).
fof(fc3_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(k5_finseq_1(A))
& v1_relat_1(k5_finseq_1(A))
& v1_funct_1(k5_finseq_1(A))
& v2_funct_1(k5_finseq_1(A))
& v1_finset_1(k5_finseq_1(A))
& v1_finseq_1(k5_finseq_1(A))
& v5_seqm_3(k5_finseq_1(A))
& v1_realset1(k5_finseq_1(A))
& v1_jordan23(k5_finseq_1(A))
& v2_jordan23(k5_finseq_1(A))
& v3_jordan23(k5_finseq_1(A)) ) ).
fof(fc4_jordan23,axiom,
! [A,B] :
( v1_relat_1(k10_finseq_1(A,B))
& v1_funct_1(k10_finseq_1(A,B))
& v1_finset_1(k10_finseq_1(A,B))
& v1_finseq_1(k10_finseq_1(A,B))
& ~ v1_realset1(k10_finseq_1(A,B))
& v3_jordan23(k10_finseq_1(A,B)) ) ).
fof(rc1_jordan23,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v2_jordan23(A) ) ).
fof(rc2_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_finseq_1(B,A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_finseq_6(B,A)
& v2_jordan23(B) ) ) ).
fof(rc3_jordan23,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finseq_1(A)
& v1_jordan23(A)
& v3_jordan23(A) ) ).
fof(fc5_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_jordan23(A) )
=> ( v1_relat_1(k3_finseq_5(A))
& v1_funct_1(k3_finseq_5(A))
& v1_finseq_1(k3_finseq_5(A))
& v1_jordan23(k3_finseq_5(A))
& v3_jordan23(k3_finseq_5(A)) ) ) ).
fof(fc6_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v2_jordan23(A) )
=> ( v1_relat_1(k3_finseq_5(A))
& v1_funct_1(k3_finseq_5(A))
& v1_finseq_1(k3_finseq_5(A))
& v2_jordan23(k3_finseq_5(A)) ) ) ).
fof(fc7_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v3_jordan23(A) )
=> ( v1_relat_1(k3_finseq_5(A))
& v1_funct_1(k3_finseq_5(A))
& v1_finseq_1(k3_finseq_5(A))
& v3_jordan23(k3_finseq_5(A)) ) ) ).
fof(rc4_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_finseq_1(B,A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B)
& v1_finseq_1(B)
& v1_finseq_6(B,A)
& v1_jordan23(B)
& v3_jordan23(B) ) ) ).
fof(fc8_jordan23,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_jordan23(B)
& m1_finseq_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_relat_1(k1_finseq_6(A,B,C))
& v1_funct_1(k1_finseq_6(A,B,C))
& v1_finseq_1(k1_finseq_6(A,B,C))
& v1_jordan23(k1_finseq_6(A,B,C))
& v3_jordan23(k1_finseq_6(A,B,C)) ) ) ).
fof(fc9_jordan23,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finseq_6(B,A)
& v2_jordan23(B)
& m1_finseq_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_relat_1(k1_finseq_6(A,B,C))
& v1_funct_1(k1_finseq_6(A,B,C))
& v1_finseq_1(k1_finseq_6(A,B,C))
& v2_jordan23(k1_finseq_6(A,B,C)) ) ) ).
fof(fc10_jordan23,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finseq_6(B,A)
& v3_jordan23(B)
& m1_finseq_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_relat_1(k1_finseq_6(A,B,C))
& v1_funct_1(k1_finseq_6(A,B,C))
& v1_finseq_1(k1_finseq_6(A,B,C))
& v3_jordan23(k1_finseq_6(A,B,C)) ) ) ).
fof(fc11_jordan23,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan9(A,B))
& v1_relat_1(k1_jordan9(A,B))
& v1_funct_1(k1_jordan9(A,B))
& v1_finseq_1(k1_jordan9(A,B))
& ~ v5_seqm_3(k1_jordan9(A,B))
& v1_topreal1(k1_jordan9(A,B))
& v2_topreal1(k1_jordan9(A,B))
& v1_finseq_6(k1_jordan9(A,B),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_jordan9(A,B))
& v2_goboard5(k1_jordan9(A,B))
& v1_sprect_2(k1_jordan9(A,B))
& ~ v1_realset1(k1_jordan9(A,B))
& v1_jordan23(k1_jordan9(A,B))
& v3_jordan23(k1_jordan9(A,B)) ) ) ).
fof(fc12_jordan23,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan9(A,B))
& v1_relat_1(k1_jordan9(A,B))
& v1_funct_1(k1_jordan9(A,B))
& v1_finseq_1(k1_jordan9(A,B))
& ~ v5_seqm_3(k1_jordan9(A,B))
& v1_topreal1(k1_jordan9(A,B))
& v2_topreal1(k1_jordan9(A,B))
& v1_finseq_6(k1_jordan9(A,B),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_jordan9(A,B))
& v2_goboard5(k1_jordan9(A,B))
& v1_sprect_2(k1_jordan9(A,B))
& ~ v1_realset1(k1_jordan9(A,B))
& v1_jordan23(k1_jordan9(A,B))
& v2_jordan23(k1_jordan9(A,B))
& v3_jordan23(k1_jordan9(A,B)) ) ) ).
fof(cc3_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v2_jordan23(A) ) ) ).
fof(t1_jordan23,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,k3_finseq_1(k3_jordan3(A,B))) ) ) ) ).
fof(t2_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(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__1,k3_finseq_1(k4_jordan3(A,B))) ) ) ).
fof(t3_jordan23,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)))
=> k5_jordan3(A,B,C) != k1_xboole_0 ) ) ) ).
fof(d1_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_jordan23(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& k1_funct_1(A,B) = k1_funct_1(A,C) )
=> ( ( B = np__1
& C = k3_finseq_1(A) )
| ( B = k3_finseq_1(A)
& C = np__1 )
| B = C ) ) ) ) ) ) ).
fof(d2_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v2_jordan23(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(A),B)
& k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,np__1)) ) ) ) ) ).
fof(d3_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( ( k3_finseq_1(A) != np__2
=> ( v3_jordan23(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(A),B)
& k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,np__1)) ) ) ) )
& ( k3_finseq_1(A) = np__2
=> v3_jordan23(A) ) ) ) ).
fof(t4_jordan23,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ( v1_jordan23(B)
<=> ! [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))
& r2_hidden(D,k4_finseq_1(B))
& k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,D) )
=> ( ( C = np__1
& D = k3_finseq_1(B) )
| ( C = k3_finseq_1(B)
& D = np__1 )
| C = D ) ) ) ) ) ) ).
fof(t5_jordan23,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ( v2_jordan23(B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(B),C)
& k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,k1_nat_1(C,np__1)) ) ) ) ) ).
fof(t6_jordan23,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ( v3_jordan23(B)
<=> ( k3_finseq_1(B) != np__2
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(B),C)
& k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,k1_nat_1(C,np__1)) ) ) ) ) ) ).
fof(t7_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( k3_finseq_1(A) != np__2
=> ( v2_jordan23(A)
<=> v3_jordan23(A) ) ) ) ).
fof(t8_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_jordan23(A)
=> v1_jordan23(k3_finseq_5(A)) ) ) ).
fof(t9_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v2_jordan23(A)
=> v2_jordan23(k3_finseq_5(A)) ) ) ).
fof(t10_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v3_jordan23(A)
=> v3_jordan23(k3_finseq_5(A)) ) ) ).
fof(t11_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( v1_jordan23(B)
=> ! [C] :
( m1_subset_1(C,A)
=> v1_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) ).
fof(t12_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( ( v2_jordan23(B)
& v1_finseq_6(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> v2_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) ).
fof(t13_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( ( v3_jordan23(B)
& v1_finseq_6(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> v3_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) ).
fof(t14_jordan23,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( v1_jordan23(B)
<=> ( v2_funct_1(k1_rfinseq(A,B,np__1))
& v2_funct_1(k16_finseq_1(A,B,k5_binarith(k3_finseq_1(B),np__1))) ) ) ) ) ).
fof(t15_jordan23,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))
& v2_jordan23(A) )
=> k5_jordan3(A,B,B) = k13_binarith(u1_struct_0(k15_euclid(np__2)),B) ) ) ) ).
fof(t16_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v2_funct_1(A)
=> v2_jordan23(A) ) ) ).
fof(t17_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_jordan23(A)
=> ! [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)) )
=> k5_jordan3(A,B,C) = k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,C,B)) ) ) ) ) ) ).
fof(t18_jordan23,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_jordan23(A)
& v2_topreal1(A)
& v3_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(t19_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_jordan23(A)
=> ! [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)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,B,C),np__1) = B ) ) ) ) ) ).
fof(t20_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_jordan23(A)
=> ! [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)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k5_jordan3(A,B,C),k3_finseq_1(k5_jordan3(A,B,C))) = C ) ) ) ) ) ).
fof(t21_jordan23,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(t22_jordan23,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))
& v2_jordan23(A) )
=> r1_tarski(k5_topreal1(np__2,k5_jordan3(A,B,C)),k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t23_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> r1_tarski(k4_finseq_1(A),k4_finseq_1(k3_graph_2(A,B))) ) ) ).
fof(t24_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> r1_tarski(k4_finseq_1(B),k4_finseq_1(k3_graph_2(A,B))) ) ) ).
fof(t25_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v5_seqm_3(k3_graph_2(A,B))
=> v5_seqm_3(A) ) ) ) ).
fof(t26_jordan23,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ( v5_seqm_3(k3_graph_2(A,B))
& k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,np__1) )
=> ( A = k1_xboole_0
| v5_seqm_3(B) ) ) ) ) ).
fof(t27_jordan23,axiom,
! [A] :
( ( v1_topreal1(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)
=> v1_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ).
fof(t28_jordan23,axiom,
! [A] :
( ( v2_topreal1(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)
=> v2_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ).
fof(t29_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> v1_topreal1(k3_jordan3(A,B)) ) ) ) ) ).
fof(t30_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> v1_topreal1(k4_jordan3(A,B)) ) ) ) ) ).
fof(t31_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_topreal1(A)
& v2_jordan23(A) )
=> ! [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)) )
=> v1_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) ).
fof(t32_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> v2_topreal1(k3_jordan3(A,B)) ) ) ) ) ).
fof(t33_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> v2_topreal1(k4_jordan3(A,B)) ) ) ) ) ).
fof(t34_jordan23,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_topreal1(A)
& v2_jordan23(A) )
=> ! [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)) )
=> v2_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) ).
fof(t35_jordan23,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)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_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)),k13_binarith(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(t36_jordan23,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)))
=> ( ( v3_jordan23(A)
& 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)) )
=> ( 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(t37_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(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_jordan23(A)
& r1_xreal_0(np__2,k3_finseq_1(A)) )
=> k3_jordan3(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) = A ) ) ) ).
fof(t38_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v3_jordan23(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k3_finseq_1(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(t39_jordan23,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)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_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(t40_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| B = k1_funct_1(A,np__1)
| 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(t41_jordan23,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)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,np__1)
| v4_topreal1(k4_jordan3(A,B)) ) ) ) ) ).
fof(t42_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A)) )
=> ( B = k1_funct_1(A,k3_finseq_1(A))
| B = k1_funct_1(A,np__1)
| v4_topreal1(k3_jordan3(A,B)) ) ) ) ) ).
fof(t43_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(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)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A)) )
=> ( k3_finseq_1(A) = np__2
| B = C
| B = k1_funct_1(A,np__1)
| C = k1_funct_1(A,np__1)
| r1_jordan3(k5_jordan3(A,B,C),B,C) ) ) ) ) ) ).
fof(t44_jordan23,axiom,
! [A] :
( ( ~ v1_xboole_0(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)))
=> ( ( v1_jordan23(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(C,k5_topreal1(np__2,A)) )
=> ( k3_finseq_1(A) = np__2
| B = C
| B = k1_funct_1(A,np__1)
| C = k1_funct_1(A,np__1)
| v4_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) ).
fof(t45_jordan23,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [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,k1_jordan2c(np__2,k5_topreal1(np__2,k1_jordan9(B,A))))
& ! [E] :
( ( v4_topreal1(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( E = k5_jordan3(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))),k5_binarith(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))))),np__1)),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))
& ? [F] :
( v4_topreal1(F)
& m2_finseq_1(F,u1_struct_0(k15_euclid(np__2)))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),F,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(np__2)),E,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))))
& k5_topreal1(np__2,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))))) = k5_topreal1(np__2,F)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,np__1) = k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),F,k3_finseq_1(F)) = k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))
& r1_xreal_0(np__2,k3_finseq_1(F))
& ? [G] :
( v4_topreal1(G)
& m2_finseq_1(G,u1_struct_0(k15_euclid(np__2)))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),G,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(np__2)),E,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k1_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(np__2,k1_jordan9(B,A)))))))
& k5_topreal1(np__2,E) = k5_topreal1(np__2,G)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),G,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),G,k3_finseq_1(G))
& r1_xreal_0(k3_finseq_1(E),k3_finseq_1(G))
& ? [H] :
( ~ v1_xboole_0(H)
& ~ v5_seqm_3(H)
& v1_topreal1(H)
& v2_topreal1(H)
& v1_finseq_6(H,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(H)
& v2_goboard5(H)
& m2_finseq_1(H,u1_struct_0(k15_euclid(np__2)))
& H = k4_graph_2(u1_struct_0(k15_euclid(np__2)),G,F) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------