SET007 Axioms: SET007+834.ax
%------------------------------------------------------------------------------
% File : SET007+834 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Continuous Functions on Normed Linear Spaces
% 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 : nfcont_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 0 unt; 0 def)
% Number of atoms : 1628 ( 47 equ)
% Maximal formula atoms : 30 ( 19 avg)
% Number of connectives : 1718 ( 172 ~; 2 |;1162 &)
% ( 23 <=>; 359 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 14 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-4 aty)
% Number of functors : 48 ( 48 usr; 5 con; 0-4 aty)
% Number of variables : 355 ( 346 !; 9 ?)
% 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(d1_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( C = k1_nfcont_1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,D) = k5_rlvect_1(A,k2_normsp_1(A,B,D)) ) ) ) ) ) ).
fof(t1_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k4_normsp_1(A,B,C) = k3_normsp_1(A,B,k1_nfcont_1(A,C)) ) ) ) ).
fof(t2_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> k1_nfcont_1(A,B) = k6_normsp_1(A,B,k1_real_1(np__1)) ) ) ).
fof(d2_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(A),k1_numbers) )
=> ( D = k2_nfcont_1(A,B,C)
<=> ( k4_relset_1(u1_struct_0(A),k1_numbers,D) = k4_relset_1(u1_struct_0(A),u1_struct_0(B),C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,k4_relset_1(u1_struct_0(A),k1_numbers,D))
=> k2_seq_1(u1_struct_0(A),k1_numbers,D,E) = k1_normsp_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) ).
fof(t4_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_nfcont_1(C,A,B)
=> r2_hidden(B,C) ) ) ) ).
fof(d4_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_nfcont_1(B,A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ~ ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ~ ( m1_bhsp_3(D,A,C)
& v4_normsp_1(D,A)
& r2_hidden(k8_normsp_1(A,D),B) ) ) ) ) ) ) ) ).
fof(d5_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_nfcont_1(B,A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),B)
& v4_normsp_1(C,A) )
=> r2_hidden(k8_normsp_1(A,C),B) ) ) ) ) ) ).
fof(d6_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_nfcont_1(B,A)
<=> v2_nfcont_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(d7_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
=> k3_nfcont_1(A,B,C,D) = k5_relat_1(D,C) ) ) ) ) ) ).
fof(d8_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),k4_relset_1(u1_struct_0(A),k1_numbers,B))
=> k4_nfcont_1(A,B,C) = k5_relat_1(C,B) ) ) ) ) ).
fof(d9_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_nfcont_1(A,B,C,D)
<=> ( r2_hidden(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),E),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& v4_normsp_1(E,A)
& k8_normsp_1(A,E) = D )
=> ( v4_normsp_1(k3_nfcont_1(A,B,C,E),B)
& k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D) = k8_normsp_1(B,k3_nfcont_1(A,B,C,E)) ) ) ) ) ) ) ) ) ) ).
fof(d10_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_nfcont_1(A,B,C)
<=> ( r2_hidden(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),k1_numbers,B))
& v4_normsp_1(D,A)
& k8_normsp_1(A,D) = C )
=> ( v4_seq_2(k4_nfcont_1(A,B,D))
& k4_finseq_4(u1_struct_0(A),k1_numbers,B,C) = k2_seq_2(k4_nfcont_1(A,B,D)) ) ) ) ) ) ) ) ) ).
fof(t5_nfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(B))
& m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),D),k4_relset_1(u1_struct_0(B),u1_struct_0(C),E))
=> r2_hidden(k2_normsp_1(B,D,A),k4_relset_1(u1_struct_0(B),u1_struct_0(C),E)) ) ) ) ) ) ) ).
fof(t6_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( r2_hidden(C,k5_relset_1(k5_numbers,u1_struct_0(A),B))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& C = k2_normsp_1(A,B,D) ) ) ) ) ).
fof(t7_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( m1_bhsp_3(C,A,B)
=> r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),k5_relset_1(k5_numbers,u1_struct_0(A),B)) ) ) ) ) ).
fof(t8_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(B))
& m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),D),k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k3_nfcont_1(B,A,C,D),E) = k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,k2_normsp_1(B,D,E)) ) ) ) ) ) ) ).
fof(t9_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),k4_relset_1(u1_struct_0(A),k1_numbers,B))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k4_nfcont_1(A,B,C),D) = k4_finseq_4(u1_struct_0(A),k1_numbers,B,k2_normsp_1(A,C,D)) ) ) ) ) ) ).
fof(t10_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,k1_numbers)
& v1_seqm_3(E)
& v7_seqm_3(E)
& m2_relset_1(E,k5_numbers,k1_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
=> k5_lopban_3(B,E,k3_nfcont_1(A,B,C,D)) = k3_nfcont_1(A,B,C,k5_lopban_3(A,E,D)) ) ) ) ) ) ) ).
fof(t11_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& v1_seqm_3(D)
& v7_seqm_3(D)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),k4_relset_1(u1_struct_0(A),k1_numbers,B))
=> k3_seqm_3(D,k4_nfcont_1(A,B,C)) = k4_nfcont_1(A,B,k5_lopban_3(A,D,C)) ) ) ) ) ) ).
fof(t12_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& m1_bhsp_3(E,A,D) )
=> m1_bhsp_3(k3_nfcont_1(A,B,C,E),B,k3_nfcont_1(A,B,C,D)) ) ) ) ) ) ) ).
fof(t13_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),C),k4_relset_1(u1_struct_0(A),k1_numbers,B))
& m1_bhsp_3(D,A,C) )
=> m1_seqm_3(k4_nfcont_1(A,B,D),k4_nfcont_1(A,B,C)) ) ) ) ) ) ).
fof(t14_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_nfcont_1(B,A,C,D)
<=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,np__0)
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( r2_hidden(G,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ~ r1_xreal_0(F,k1_normsp_1(B,k6_rlvect_1(B,G,D)))
& r1_xreal_0(E,k1_normsp_1(A,k6_rlvect_1(A,k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,G),k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> ( r2_nfcont_1(A,C,B)
<=> ( r2_hidden(B,k4_relset_1(u1_struct_0(A),k1_numbers,C))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_hidden(F,k4_relset_1(u1_struct_0(A),k1_numbers,C))
& ~ r1_xreal_0(E,k1_normsp_1(A,k6_rlvect_1(A,F,B)))
& r1_xreal_0(D,k18_complex1(k5_real_1(k4_finseq_4(u1_struct_0(A),k1_numbers,C,F),k4_finseq_4(u1_struct_0(A),k1_numbers,C,B)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_nfcont_1(B,A,C,D)
<=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [E] :
( m1_nfcont_1(E,A,k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D))
=> ? [F] :
( m1_nfcont_1(F,B,D)
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( r2_hidden(G,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& r2_hidden(G,F) )
=> r2_hidden(k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,G),E) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_nfcont_1(B,A,C,D)
<=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [E] :
( m1_nfcont_1(E,A,k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D))
=> ? [F] :
( m1_nfcont_1(F,B,D)
& r1_tarski(k10_relset_1(u1_struct_0(B),u1_struct_0(A),C,F),E) ) ) ) ) ) ) ) ) ).
fof(t18_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
=> ( ! [E] :
( m1_nfcont_1(E,B,D)
=> k5_subset_1(u1_struct_0(B),k4_relset_1(u1_struct_0(B),u1_struct_0(A),C),E) != k1_struct_0(B,D) )
| r1_nfcont_1(B,A,C,D) ) ) ) ) ) ) ).
fof(t19_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),E),k5_subset_1(u1_struct_0(A),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C),k4_relset_1(u1_struct_0(A),u1_struct_0(B),D)))
=> ( k3_nfcont_1(A,B,k1_vfunct_1(u1_struct_0(A),B,C,D),E) = k3_normsp_1(B,k3_nfcont_1(A,B,C,E),k3_nfcont_1(A,B,D,E))
& k3_nfcont_1(A,B,k2_vfunct_1(u1_struct_0(A),B,C,D),E) = k4_normsp_1(B,k3_nfcont_1(A,B,C,E),k3_nfcont_1(A,B,D,E)) ) ) ) ) ) ) ) ).
fof(t20_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
=> k3_nfcont_1(A,B,k4_vfunct_1(u1_struct_0(A),B,C,E),D) = k6_normsp_1(B,k3_nfcont_1(A,B,C,D),E) ) ) ) ) ) ) ).
fof(t21_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),D),k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
=> ( k7_normsp_1(B,k3_nfcont_1(A,B,C,D)) = k4_nfcont_1(A,k2_nfcont_1(A,B,C),D)
& k1_nfcont_1(B,k3_nfcont_1(A,B,C,D)) = k3_nfcont_1(A,B,k6_vfunct_1(u1_struct_0(A),B,C),D) ) ) ) ) ) ) ).
fof(t22_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( ( r1_nfcont_1(B,A,C,E)
& r1_nfcont_1(B,A,D,E) )
=> ( r1_nfcont_1(B,A,k1_vfunct_1(u1_struct_0(B),A,C,D),E)
& r1_nfcont_1(B,A,k2_vfunct_1(u1_struct_0(B),A,C,D),E) ) ) ) ) ) ) ) ).
fof(t23_nfcont_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r1_nfcont_1(C,B,D,E)
=> r1_nfcont_1(C,B,k4_vfunct_1(u1_struct_0(C),B,D,A),E) ) ) ) ) ) ) ).
fof(t24_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_nfcont_1(B,A,C,D)
=> ( r2_nfcont_1(B,k2_nfcont_1(B,A,C),D)
& r1_nfcont_1(B,A,k6_vfunct_1(u1_struct_0(B),A,C),D) ) ) ) ) ) ) ).
fof(d11_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( r3_nfcont_1(A,B,C,D)
<=> ( r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,D)
=> r1_nfcont_1(A,B,k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,D),E) ) ) ) ) ) ) ) ).
fof(d12_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( r4_nfcont_1(A,B,C)
<=> ( r1_tarski(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> r2_nfcont_1(A,k2_partfun1(u1_struct_0(A),k1_numbers,B,C),D) ) ) ) ) ) ) ).
fof(t25_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C,D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( r3_nfcont_1(B,A,D,C)
<=> ( r1_tarski(C,k4_relset_1(u1_struct_0(B),u1_struct_0(A),D))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(B))
& m2_relset_1(E,k5_numbers,u1_struct_0(B)) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),E),C)
& v4_normsp_1(E,B)
& r2_hidden(k8_normsp_1(B,E),C) )
=> ( v4_normsp_1(k3_nfcont_1(B,A,D,E),A)
& k4_finseq_4(u1_struct_0(B),u1_struct_0(A),D,k8_normsp_1(B,E)) = k8_normsp_1(A,k3_nfcont_1(B,A,D,E)) ) ) ) ) ) ) ) ) ).
fof(t26_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ( r3_nfcont_1(C,B,D,A)
<=> ( r1_tarski(A,k4_relset_1(u1_struct_0(C),u1_struct_0(B),D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( r2_hidden(E,A)
& ~ r1_xreal_0(F,np__0)
& ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(G,np__0)
& ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ~ ( r2_hidden(H,A)
& ~ r1_xreal_0(G,k1_normsp_1(C,k6_rlvect_1(C,H,E)))
& r1_xreal_0(F,k1_normsp_1(B,k6_rlvect_1(B,k4_finseq_4(u1_struct_0(C),u1_struct_0(B),D,H),k4_finseq_4(u1_struct_0(C),u1_struct_0(B),D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( r4_nfcont_1(B,C,A)
<=> ( r1_tarski(A,k4_relset_1(u1_struct_0(B),k1_numbers,C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(D,A)
& ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,np__0)
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( r2_hidden(G,A)
& ~ r1_xreal_0(F,k1_normsp_1(B,k6_rlvect_1(B,G,D)))
& r1_xreal_0(E,k18_complex1(k5_real_1(k4_finseq_4(u1_struct_0(B),k1_numbers,C,G),k4_finseq_4(u1_struct_0(B),k1_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r3_nfcont_1(B,C,D,A)
<=> r3_nfcont_1(B,C,k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,A),A) ) ) ) ) ).
fof(t29_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( r4_nfcont_1(B,C,A)
<=> r4_nfcont_1(B,k2_partfun1(u1_struct_0(B),k1_numbers,C,A),A) ) ) ) ).
fof(t30_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( r3_nfcont_1(C,D,E,A)
& r1_tarski(B,A) )
=> r3_nfcont_1(C,D,E,B) ) ) ) ) ).
fof(t31_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
=> r3_nfcont_1(B,A,C,k1_struct_0(B,D)) ) ) ) ) ) ).
fof(t32_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C,D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( r3_nfcont_1(B,A,D,C)
& r3_nfcont_1(B,A,E,C) )
=> ( r3_nfcont_1(B,A,k1_vfunct_1(u1_struct_0(B),A,D,E),C)
& r3_nfcont_1(B,A,k2_vfunct_1(u1_struct_0(B),A,D,E),C) ) ) ) ) ) ) ).
fof(t33_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C,D,E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( r3_nfcont_1(B,A,E,C)
& r3_nfcont_1(B,A,F,D) )
=> ( r3_nfcont_1(B,A,k1_vfunct_1(u1_struct_0(B),A,E,F),k3_xboole_0(C,D))
& r3_nfcont_1(B,A,k2_vfunct_1(u1_struct_0(B),A,E,F),k3_xboole_0(C,D)) ) ) ) ) ) ) ).
fof(t34_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D,E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( r3_nfcont_1(B,A,E,D)
=> r3_nfcont_1(B,A,k4_vfunct_1(u1_struct_0(B),A,E,C),D) ) ) ) ) ) ).
fof(t35_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r3_nfcont_1(B,C,D,A)
=> ( r4_nfcont_1(B,k2_nfcont_1(B,C,D),A)
& r3_nfcont_1(B,C,k6_vfunct_1(u1_struct_0(B),C,D),A) ) ) ) ) ) ).
fof(t36_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v1_partfun1(C,u1_struct_0(B),u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,k4_rlvect_1(B,D,E)) = k4_rlvect_1(A,k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D),k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,E)) ) ) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ~ r1_nfcont_1(B,A,C,D) )
| r3_nfcont_1(B,A,C,u1_struct_0(B)) ) ) ) ) ) ).
fof(t37_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v1_nfcont_1(k4_relset_1(u1_struct_0(B),u1_struct_0(A),C),B)
& r3_nfcont_1(B,A,C,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C)) )
=> v1_nfcont_1(k5_relset_1(u1_struct_0(B),u1_struct_0(A),C),A) ) ) ) ) ).
fof(t38_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( ( v1_nfcont_1(k4_relset_1(u1_struct_0(A),k1_numbers,B),A)
& r4_nfcont_1(A,B,k4_relset_1(u1_struct_0(A),k1_numbers,B)) )
=> v1_rcomp_1(k5_relset_1(u1_struct_0(A),k1_numbers,B)) ) ) ) ).
fof(t39_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& v1_nfcont_1(D,B)
& r3_nfcont_1(B,A,C,D) )
=> v1_nfcont_1(k10_relset_1(u1_struct_0(B),u1_struct_0(A),C,D),A) ) ) ) ) ) ).
fof(t40_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ~ ( k4_relset_1(u1_struct_0(A),k1_numbers,B) != k1_xboole_0
& v1_nfcont_1(k4_relset_1(u1_struct_0(A),k1_numbers,B),A)
& r4_nfcont_1(A,B,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& r2_hidden(D,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& k4_finseq_4(u1_struct_0(A),k1_numbers,B,C) = k4_seq_4(k5_relset_1(u1_struct_0(A),k1_numbers,B))
& k4_finseq_4(u1_struct_0(A),k1_numbers,B,D) = k5_seq_4(k5_relset_1(u1_struct_0(A),k1_numbers,B)) ) ) ) ) ) ) ).
fof(t41_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ~ ( k4_relset_1(u1_struct_0(B),u1_struct_0(A),C) != k1_xboole_0
& v1_nfcont_1(k4_relset_1(u1_struct_0(B),u1_struct_0(A),C),B)
& r3_nfcont_1(B,A,C,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ~ ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& r2_hidden(E,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& k4_finseq_4(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),D) = k4_seq_4(k5_relset_1(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C)))
& k4_finseq_4(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),E) = k5_seq_4(k5_relset_1(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C))) ) ) ) ) ) ) ) ).
fof(t42_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> k2_partfun1(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,C,D),A) = k2_nfcont_1(B,C,k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,A)) ) ) ) ).
fof(t43_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( D != k1_xboole_0
& r1_tarski(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& v1_nfcont_1(D,B)
& r3_nfcont_1(B,A,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( r2_hidden(E,D)
& r2_hidden(F,D)
& k4_finseq_4(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),E) = k4_seq_4(k10_relset_1(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),D))
& k4_finseq_4(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),F) = k5_seq_4(k10_relset_1(u1_struct_0(B),k1_numbers,k2_nfcont_1(B,A,C),D)) ) ) ) ) ) ) ) ) ).
fof(t44_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != k1_xboole_0
& r1_tarski(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
& v1_nfcont_1(C,A)
& r4_nfcont_1(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& k4_finseq_4(u1_struct_0(A),k1_numbers,B,D) = k4_seq_4(k10_relset_1(u1_struct_0(A),k1_numbers,B,C))
& k4_finseq_4(u1_struct_0(A),k1_numbers,B,E) = k5_seq_4(k10_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) ).
fof(d13_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C,D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( r5_nfcont_1(A,B,C,D)
<=> ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),D))
& ? [E] :
( m1_subset_1(E,k1_numbers)
& ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_hidden(F,C)
& r2_hidden(G,C) )
=> r1_xreal_0(k1_normsp_1(B,k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),D,F),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),D,G))),k4_real_1(E,k1_normsp_1(A,k6_rlvect_1(A,F,G)))) ) ) ) ) ) ) ) ) ) ).
fof(d14_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> ( r6_nfcont_1(A,B,C)
<=> ( r1_tarski(B,k4_relset_1(u1_struct_0(A),k1_numbers,C))
& ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_hidden(F,B) )
=> r1_xreal_0(k18_complex1(k5_real_1(k4_finseq_4(u1_struct_0(A),k1_numbers,C,E),k4_finseq_4(u1_struct_0(A),k1_numbers,C,F))),k4_real_1(D,k1_normsp_1(A,k6_rlvect_1(A,E,F)))) ) ) ) ) ) ) ) ) ).
fof(t45_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( r5_nfcont_1(C,D,A,E)
& r1_tarski(B,A) )
=> r5_nfcont_1(C,D,B,E) ) ) ) ) ).
fof(t46_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( r5_nfcont_1(C,D,A,E)
& r5_nfcont_1(C,D,B,F) )
=> r5_nfcont_1(C,D,k3_xboole_0(A,B),k1_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) ).
fof(t47_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( r5_nfcont_1(C,D,A,E)
& r5_nfcont_1(C,D,B,F) )
=> r5_nfcont_1(C,D,k3_xboole_0(A,B),k2_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) ).
fof(t48_nfcont_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ( r5_nfcont_1(C,D,A,E)
=> r5_nfcont_1(C,D,A,k4_vfunct_1(u1_struct_0(C),D,E,B)) ) ) ) ) ) ).
fof(t49_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r5_nfcont_1(B,C,A,D)
=> ( r5_nfcont_1(B,C,A,k6_vfunct_1(u1_struct_0(B),C,D))
& r6_nfcont_1(B,A,k2_nfcont_1(B,C,D)) ) ) ) ) ) ).
fof(t50_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
& r1_partfun2(u1_struct_0(B),u1_struct_0(C),D,A) )
=> r5_nfcont_1(B,C,A,D) ) ) ) ) ).
fof(t51_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r5_nfcont_1(A,A,B,k1_partfun2(u1_struct_0(A),B)) ) ) ).
fof(t52_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r5_nfcont_1(B,C,A,D)
=> r3_nfcont_1(B,C,D,A) ) ) ) ) ).
fof(t53_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( r6_nfcont_1(B,A,C)
=> r4_nfcont_1(B,C,A) ) ) ) ).
fof(t54_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& k5_relset_1(u1_struct_0(B),u1_struct_0(A),C) = k1_struct_0(A,D) )
=> r3_nfcont_1(B,A,C,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C)) ) ) ) ) ).
fof(t55_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
& r1_partfun2(u1_struct_0(B),u1_struct_0(C),D,A) )
=> r3_nfcont_1(B,C,D,A) ) ) ) ) ).
fof(t56_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(A),B,C) = C ) )
=> r3_nfcont_1(A,A,B,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B)) ) ) ) ).
fof(t57_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( B = k1_partfun2(u1_struct_0(A),k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
=> r3_nfcont_1(A,A,B,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B)) ) ) ) ).
fof(t58_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( r1_tarski(B,k4_relset_1(u1_struct_0(A),u1_struct_0(A),C))
& k2_partfun1(u1_struct_0(A),u1_struct_0(A),C,B) = k1_partfun2(u1_struct_0(A),B) )
=> r3_nfcont_1(A,A,C,B) ) ) ) ) ).
fof(t59_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(B),C))
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r2_hidden(F,A)
=> k4_finseq_4(u1_struct_0(B),u1_struct_0(B),C,F) = k4_rlvect_1(B,k3_rlvect_1(B,F,D),E) ) ) )
=> r3_nfcont_1(B,B,C,A) ) ) ) ) ) ).
fof(t60_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k4_relset_1(u1_struct_0(A),k1_numbers,B))
=> k4_finseq_4(u1_struct_0(A),k1_numbers,B,C) = k1_normsp_1(A,C) ) )
=> r4_nfcont_1(A,B,k4_relset_1(u1_struct_0(A),k1_numbers,B)) ) ) ) ).
fof(t61_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( ( r1_tarski(A,k4_relset_1(u1_struct_0(B),k1_numbers,C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(D,A)
=> k4_finseq_4(u1_struct_0(B),k1_numbers,C,D) = k1_normsp_1(B,D) ) ) )
=> r4_nfcont_1(B,C,A) ) ) ) ).
fof(dt_m1_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ! [C] :
( m1_nfcont_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ? [C] : m1_nfcont_1(C,A,B) ) ).
fof(dt_k1_nfcont_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k1_nfcont_1(A,B))
& v1_funct_2(k1_nfcont_1(A,B),k5_numbers,u1_struct_0(A))
& m2_relset_1(k1_nfcont_1(A,B),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k2_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_nfcont_1(A,B,C))
& m2_relset_1(k2_nfcont_1(A,B,C),u1_struct_0(A),k1_numbers) ) ) ).
fof(dt_k3_nfcont_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m1_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k3_nfcont_1(A,B,C,D))
& v1_funct_2(k3_nfcont_1(A,B,C,D),k5_numbers,u1_struct_0(B))
& m2_relset_1(k3_nfcont_1(A,B,C,D),k5_numbers,u1_struct_0(B)) ) ) ).
fof(dt_k4_nfcont_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& m1_relset_1(B,u1_struct_0(A),k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k4_nfcont_1(A,B,C))
& v1_funct_2(k4_nfcont_1(A,B,C),k5_numbers,k1_numbers)
& m2_relset_1(k4_nfcont_1(A,B,C),k5_numbers,k1_numbers) ) ) ).
fof(d3_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_nfcont_1(C,A,B)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,np__0)
& r1_tarski(a_3_0_nfcont_1(A,B,D),C) ) ) ) ) ) ).
fof(t3_nfcont_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,np__0)
=> m1_nfcont_1(a_3_0_nfcont_1(A,B,C),A,B) ) ) ) ) ).
fof(fraenkel_a_3_0_nfcont_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_0_nfcont_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ r1_xreal_0(D,k1_normsp_1(B,k6_rlvect_1(B,E,C))) ) ) ) ).
%------------------------------------------------------------------------------