SET007 Axioms: SET007+842.ax
%------------------------------------------------------------------------------
% File : SET007+842 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Differentiable 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 : ndiff_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 71 ( 0 unt; 0 def)
% Number of atoms : 1485 ( 56 equ)
% Maximal formula atoms : 36 ( 20 avg)
% Number of connectives : 1611 ( 197 ~; 3 |;1068 &)
% ( 18 <=>; 325 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 14 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-4 aty)
% Number of functors : 50 ( 50 usr; 4 con; 0-4 aty)
% Number of variables : 306 ( 295 !; 11 ?)
% 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(rc1_ndiff_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)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ? [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_ndiff_1(B,A) ) ) ).
fof(rc2_ndiff_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)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ? [B] :
( m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v5_seqm_3(B) ) ) ).
fof(rc3_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v3_ndiff_1(C,A,B) ) ) ).
fof(fc1_ndiff_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)
& ~ v3_realset2(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v2_ndiff_1(B,A)
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> ( v1_relat_1(k3_lopban_3(A,B,C))
& v1_funct_1(k3_lopban_3(A,B,C))
& v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& v2_ndiff_1(k3_lopban_3(A,B,C),A) ) ) ).
fof(fc2_ndiff_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)
& ~ v3_realset2(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& v5_seqm_3(B)
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> ( v1_relat_1(k3_lopban_3(A,B,C))
& v1_funct_1(k3_lopban_3(A,B,C))
& v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
& v5_seqm_3(k3_lopban_3(A,B,C)) ) ) ).
fof(t1_ndiff_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)
=> ! [D] :
( m1_nfcont_1(D,A,B)
=> ? [E] :
( m1_nfcont_1(E,A,B)
& r1_tarski(E,C)
& r1_tarski(E,D) ) ) ) ) ) ).
fof(t2_ndiff_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)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_nfcont_1(D,A,C)
=> ~ r1_tarski(D,B) ) ) ) ) ) ) ).
fof(t4_ndiff_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] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_nfcont_1(D,A,C)
=> ~ r1_tarski(D,B) ) ) )
=> v3_nfcont_1(B,A) ) ) ) ).
fof(t5_ndiff_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] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_nfcont_1(D,A,C)
=> ~ r1_tarski(D,B) ) ) )
<=> v3_nfcont_1(B,A) ) ) ) ).
fof(d1_ndiff_1,axiom,
! [A] :
( l2_struct_0(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)) )
=> ( v1_ndiff_1(B,A)
<=> r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),B),k4_xboole_0(u1_struct_0(A),k1_tarski(k1_rlvect_1(A)))) ) ) ) ).
fof(t6_ndiff_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)) )
=> ( v1_ndiff_1(B,A)
<=> ! [C] :
~ ( r2_hidden(C,k5_numbers)
& k1_funct_1(B,C) = k1_rlvect_1(A) ) ) ) ) ).
fof(t7_ndiff_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)) )
=> ( v1_ndiff_1(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) != k1_rlvect_1(A) ) ) ) ) ).
fof(d2_ndiff_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,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [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)) )
=> ( D = k1_ndiff_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k3_rlvect_1(A,k2_normsp_1(A,B,E),k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) ) ) ) ) ).
fof(d3_ndiff_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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [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)) )
=> ( D = k2_ndiff_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k3_rlvect_1(A,B,k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) ) ) ) ) ).
fof(t8_ndiff_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,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> k1_ndiff_1(A,B,k9_seq_1(C,D)) = k3_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D)) ) ) ) ) ).
fof(t9_ndiff_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,k1_numbers)
& m2_relset_1(B,k5_numbers,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)) )
=> k1_ndiff_1(A,k3_normsp_1(A,C,D),B) = k3_normsp_1(A,k1_ndiff_1(A,C,B),k1_ndiff_1(A,D,B)) ) ) ) ) ).
fof(t10_ndiff_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> k6_normsp_1(B,k1_ndiff_1(B,C,D),A) = k1_ndiff_1(B,k6_normsp_1(B,C,A),D) ) ) ) ) ).
fof(t11_ndiff_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,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> k1_ndiff_1(A,B,k10_seq_1(C,D)) = k4_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D)) ) ) ) ) ).
fof(t12_ndiff_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,k1_numbers)
& m2_relset_1(B,k5_numbers,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)) )
=> k1_ndiff_1(A,k4_normsp_1(A,C,D),B) = k4_normsp_1(A,k1_ndiff_1(A,C,B),k1_ndiff_1(A,D,B)) ) ) ) ) ).
fof(t13_ndiff_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,k1_numbers)
& m2_relset_1(B,k5_numbers,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)) )
=> ( ( v4_seq_2(B)
& v4_normsp_1(C,A) )
=> v4_normsp_1(k1_ndiff_1(A,C,B),A) ) ) ) ) ).
fof(t14_ndiff_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,k1_numbers)
& m2_relset_1(B,k5_numbers,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)) )
=> ( ( v4_seq_2(B)
& v4_normsp_1(C,A) )
=> k8_normsp_1(A,k1_ndiff_1(A,C,B)) = k3_rlvect_1(A,k8_normsp_1(A,C),k2_seq_2(B)) ) ) ) ) ).
fof(t15_ndiff_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [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)) )
=> k3_lopban_3(B,k3_normsp_1(B,C,D),A) = k3_normsp_1(B,k3_lopban_3(B,C,A),k3_lopban_3(B,D,A)) ) ) ) ) ).
fof(t16_ndiff_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [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)) )
=> k3_lopban_3(B,k4_normsp_1(B,C,D),A) = k4_normsp_1(B,k3_lopban_3(B,C,A),k3_lopban_3(B,D,A)) ) ) ) ) ).
fof(t17_ndiff_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ( v1_ndiff_1(C,B)
=> v1_ndiff_1(k3_lopban_3(B,C,A),B) ) ) ) ) ).
fof(t18_ndiff_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> m1_bhsp_3(k3_lopban_3(B,C,A),B,C) ) ) ) ).
fof(t19_ndiff_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)) )
=> ( ( v5_seqm_3(B)
& m1_bhsp_3(C,A,B) )
=> v5_seqm_3(C) ) ) ) ) ).
fof(t20_ndiff_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)) )
=> ( ( v5_seqm_3(B)
& m1_bhsp_3(C,A,B) )
=> B = C ) ) ) ) ).
fof(d4_ndiff_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)) )
=> ( v2_ndiff_1(B,A)
<=> ( v1_ndiff_1(B,A)
& v4_normsp_1(B,A)
& k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t21_ndiff_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)) )
=> ( v5_seqm_3(B)
=> ( v4_normsp_1(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_normsp_1(A,B) = k2_normsp_1(A,B,C) ) ) ) ) ) ).
fof(t22_ndiff_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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,E) = k3_rlvect_1(A,C,k6_real_1(np__1,k3_real_1(E,D))) )
=> ( r1_xreal_0(D,np__0)
| v4_normsp_1(B,A) ) ) ) ) ) ) ).
fof(t23_ndiff_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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,E) = k3_rlvect_1(A,C,k6_real_1(np__1,k3_real_1(E,D))) )
=> ( r1_xreal_0(D,np__0)
| k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) ) ) ).
fof(t24_ndiff_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,k1_numbers)
& v1_fdiff_1(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C != k1_rlvect_1(A)
=> v2_ndiff_1(k2_ndiff_1(A,C,B),A) ) ) ) ) ).
fof(t25_ndiff_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] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
<=> r2_hidden(C,u1_struct_0(A)) ) )
<=> B = u1_struct_0(A) ) ) ) ).
fof(d5_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_ndiff_1(C,A,B)
<=> ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& v2_ndiff_1(D,A)
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( v4_normsp_1(k1_ndiff_1(B,k3_nfcont_1(A,B,C,D),k18_seq_1(k7_normsp_1(A,D))),B)
& k8_normsp_1(B,k1_ndiff_1(B,k3_nfcont_1(A,B,C,D),k18_seq_1(k7_normsp_1(A,D)))) = k1_rlvect_1(B) ) ) ) ) ) ) ) ).
fof(t26_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
=> ( v3_ndiff_1(C,A,B)
<=> ! [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))
=> ~ ( F != k1_rlvect_1(A)
& ~ r1_xreal_0(E,k1_normsp_1(A,F))
& r1_xreal_0(D,k4_real_1(k2_real_1(k1_normsp_1(A,F)),k1_normsp_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,F)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v3_ndiff_1(C,A,B)
& 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))
& v2_ndiff_1(D,A)
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( v4_normsp_1(k3_nfcont_1(A,B,C,D),B)
& k8_normsp_1(B,k3_nfcont_1(A,B,C,D)) = k1_rlvect_1(B) ) ) ) ) ) ).
fof(t28_ndiff_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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),k3_lopban_3(B,C,A)),k5_relset_1(k5_numbers,u1_struct_0(B),C)) ) ) ) ).
fof(t29_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [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),k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
=> k3_lopban_3(C,k3_nfcont_1(B,C,D,E),A) = k3_nfcont_1(B,C,D,k3_lopban_3(B,E,A)) ) ) ) ) ) ) ).
fof(t30_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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)) )
=> ( ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( 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(t31_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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)
=> ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
=> 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(t32_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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] :
( ( 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),k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& v4_normsp_1(E,B)
& k8_normsp_1(B,E) = D
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k2_normsp_1(B,E,F) != D ) )
=> ( v4_normsp_1(k3_nfcont_1(B,A,C,E),A)
& k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D) = k8_normsp_1(A,k3_nfcont_1(B,A,C,E)) ) ) ) ) ) ) ) ) ) ).
fof(t33_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v3_ndiff_1(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k1_vfunct_1(u1_struct_0(B),A,C,D))
& v3_ndiff_1(k1_vfunct_1(u1_struct_0(B),A,C,D),B,A)
& m2_relset_1(k1_vfunct_1(u1_struct_0(B),A,C,D),u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(k2_vfunct_1(u1_struct_0(B),A,C,D))
& v3_ndiff_1(k2_vfunct_1(u1_struct_0(B),A,C,D),B,A)
& m2_relset_1(k2_vfunct_1(u1_struct_0(B),A,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ).
fof(t34_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k4_vfunct_1(u1_struct_0(B),A,D,C))
& v3_ndiff_1(k4_vfunct_1(u1_struct_0(B),A,D,C),B,A)
& m2_relset_1(k4_vfunct_1(u1_struct_0(B),A,D,C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ).
fof(d6_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(A,B,C,D)
<=> ? [E] :
( m1_nfcont_1(E,A,D)
& r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ? [F] :
( m1_subset_1(F,u1_struct_0(k16_lopban_1(A,B)))
& ? [G] :
( v1_funct_1(G)
& v3_ndiff_1(G,A,B)
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(B))
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r2_hidden(H,E)
=> k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,H),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)) = k4_rlvect_1(B,k17_lopban_1(A,B,F,k6_rlvect_1(A,H,D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),G,k6_rlvect_1(A,H,D))) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B)))
=> ( E = k3_ndiff_1(A,B,C,D)
<=> ? [F] :
( m1_nfcont_1(F,A,D)
& r1_tarski(F,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ? [G] :
( v1_funct_1(G)
& v3_ndiff_1(G,A,B)
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(B))
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r2_hidden(H,F)
=> k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,H),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)) = k4_rlvect_1(B,k17_lopban_1(A,B,E,k6_rlvect_1(A,H,D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),G,k6_rlvect_1(A,H,D))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_ndiff_1(A,B,C,D)
<=> ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,A)
=> r1_ndiff_1(B,C,k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,A),E) ) ) ) ) ) ) ) ).
fof(t35_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_ndiff_1(A,B,C,D)
=> m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ).
fof(t36_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_nfcont_1(D,A)
=> ( r2_ndiff_1(D,A,B,C)
<=> ( 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_ndiff_1(A,B,C,E) ) ) ) ) ) ) ) ) ) ).
fof(t37_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_ndiff_1(D,A,B,C)
=> v3_nfcont_1(D,A) ) ) ) ) ) ).
fof(d9_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( r2_ndiff_1(D,A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B))) )
=> ( E = k4_ndiff_1(A,B,C,D)
<=> ( k4_relset_1(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),E) = D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,D)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),E,F) = k3_ndiff_1(A,B,C,F) ) ) ) ) ) ) ) ) ) ).
fof(t38_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_nfcont_1(D,A)
& r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k5_relset_1(u1_struct_0(A),u1_struct_0(B),C) != k1_struct_0(B,E) )
| ( r2_ndiff_1(D,A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,D)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,C,D),E) = k1_rlvect_1(k16_lopban_1(A,B)) ) ) ) ) ) ) ) ) ) ).
fof(t39_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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))
=> ! [E] :
( m1_nfcont_1(E,A,D)
=> ( ( r1_ndiff_1(A,B,C,D)
& r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,u1_struct_0(A))
& v2_ndiff_1(F,A)
& m2_relset_1(F,k5_numbers,u1_struct_0(A)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k5_numbers,u1_struct_0(A))
& v5_seqm_3(G)
& m2_relset_1(G,k5_numbers,u1_struct_0(A)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(A),G) = k1_struct_0(A,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),k3_normsp_1(A,F,G)),E) )
=> ( v4_normsp_1(k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,F,G)),k3_nfcont_1(A,B,C,G)),B)
& k8_normsp_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,F,G)),k3_nfcont_1(A,B,C,G))) = k1_rlvect_1(B) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(B,A,C,E)
& r1_ndiff_1(B,A,D,E) )
=> ( r1_ndiff_1(B,A,k1_vfunct_1(u1_struct_0(B),A,C,D),E)
& k3_ndiff_1(B,A,k1_vfunct_1(u1_struct_0(B),A,C,D),E) = k4_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,C,E),k3_ndiff_1(B,A,D,E)) ) ) ) ) ) ) ) ).
fof(t41_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(B,A,C,E)
& r1_ndiff_1(B,A,D,E) )
=> ( r1_ndiff_1(B,A,k2_vfunct_1(u1_struct_0(B),A,C,D),E)
& k3_ndiff_1(B,A,k2_vfunct_1(u1_struct_0(B),A,C,D),E) = k6_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,C,E),k3_ndiff_1(B,A,D,E)) ) ) ) ) ) ) ) ).
fof(t42_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [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_ndiff_1(B,A,D,E)
=> ( r1_ndiff_1(B,A,k4_vfunct_1(u1_struct_0(B),A,D,C),E)
& k3_ndiff_1(B,A,k4_vfunct_1(u1_struct_0(B),A,D,C),E) = k3_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,D,E),C) ) ) ) ) ) ) ) ).
fof(t43_ndiff_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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_nfcont_1(C,A)
& r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
& k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) = k1_partfun2(u1_struct_0(A),C) )
=> ( r2_ndiff_1(C,A,A,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,A)),k4_ndiff_1(A,A,B,C),D) = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) ) ).
fof(t44_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_nfcont_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k1_vfunct_1(u1_struct_0(A),B,D,E)))
& r2_ndiff_1(C,A,B,D)
& r2_ndiff_1(C,A,B,E) )
=> ( r2_ndiff_1(C,A,B,k1_vfunct_1(u1_struct_0(A),B,D,E))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,C)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k1_vfunct_1(u1_struct_0(A),B,D,E),C),F) = k4_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,D,F),k3_ndiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_nfcont_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k2_vfunct_1(u1_struct_0(A),B,D,E)))
& r2_ndiff_1(C,A,B,D)
& r2_ndiff_1(C,A,B,E) )
=> ( r2_ndiff_1(C,A,B,k2_vfunct_1(u1_struct_0(A),B,D,E))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,C)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k2_vfunct_1(u1_struct_0(A),B,D,E),C),F) = k6_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,D,F),k3_ndiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_nfcont_1(C,A)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k4_vfunct_1(u1_struct_0(A),B,E,D)))
& r2_ndiff_1(C,A,B,E) )
=> ( r2_ndiff_1(C,A,B,k4_vfunct_1(u1_struct_0(A),B,E,D))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,C)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k4_vfunct_1(u1_struct_0(A),B,E,D),C),F) = k3_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,E,F),D) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_nfcont_1(D,A)
& r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& r1_partfun2(u1_struct_0(A),u1_struct_0(B),C,D) )
=> ( r2_ndiff_1(D,A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,D)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,C,D),E) = k1_rlvect_1(k16_lopban_1(A,B)) ) ) ) ) ) ) ) ) ).
fof(t48_ndiff_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)
& ~ v3_realset2(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,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_nfcont_1(E,A)
& r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,E)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(A),B,F) = k4_rlvect_1(A,k3_rlvect_1(A,F,C),D) ) ) )
=> ( r2_ndiff_1(E,A,A,B)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(F,E)
=> k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,A)),k4_ndiff_1(A,A,B,E),F) = k5_lopban_2(A,k7_lopban_2(A),C) ) ) ) ) ) ) ) ) ) ).
fof(t49_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(B,A,C,D)
=> r1_nfcont_1(B,A,C,D) ) ) ) ) ) ).
fof(t50_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_ndiff_1(A,B,C,D)
=> r3_nfcont_1(B,C,D,A) ) ) ) ) ).
fof(t51_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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,k1_zfmisc_1(u1_struct_0(C)))
=> ( ( v3_nfcont_1(E,C)
& r2_ndiff_1(A,C,B,D)
& r1_tarski(E,A) )
=> r2_ndiff_1(E,C,B,D) ) ) ) ) ) ).
fof(t52_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(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_ndiff_1(B,A,C,D)
& ! [E] :
( m1_nfcont_1(E,B,D)
=> ~ ( r1_tarski(E,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ? [F] :
( v1_funct_1(F)
& v3_ndiff_1(F,B,A)
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(A))
& k4_finseq_4(u1_struct_0(B),u1_struct_0(A),F,k1_rlvect_1(B)) = k1_rlvect_1(A)
& r1_nfcont_1(B,A,F,k1_rlvect_1(B))
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( r2_hidden(G,E)
=> 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)) = k4_rlvect_1(A,k17_lopban_1(B,A,k3_ndiff_1(B,A,C,D),k6_rlvect_1(B,G,D)),k4_finseq_4(u1_struct_0(B),u1_struct_0(A),F,k6_rlvect_1(B,G,D))) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_ndiff_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)
& 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(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m1_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k1_ndiff_1(A,B,C))
& v1_funct_2(k1_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k1_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k2_ndiff_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)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m1_relset_1(C,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k2_ndiff_1(A,B,C))
& v1_funct_2(k2_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k2_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k3_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k3_ndiff_1(A,B,C,D),u1_struct_0(k16_lopban_1(A,B))) ) ).
fof(dt_k4_ndiff_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)
& ~ v3_realset2(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)
& ~ v3_realset2(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k4_ndiff_1(A,B,C,D))
& m2_relset_1(k4_ndiff_1(A,B,C,D),u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B))) ) ) ).
fof(t3_ndiff_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)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& r1_tarski(a_3_0_ndiff_1(A,C,D),B) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_ndiff_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_ndiff_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))) ) ) ) ).
%------------------------------------------------------------------------------