SET007 Axioms: SET007+827.ax
%------------------------------------------------------------------------------
% File : SET007+827 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Cauchy Sequence of Complex Unitary Space
% 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 : clvect_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 72 ( 0 unt; 0 def)
% Number of atoms : 1068 ( 50 equ)
% Maximal formula atoms : 21 ( 14 avg)
% Number of connectives : 1081 ( 85 ~; 2 |; 745 &)
% ( 8 <=>; 241 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 0 prp; 1-3 aty)
% Number of functors : 50 ( 50 usr; 7 con; 0-4 aty)
% Number of variables : 241 ( 228 !; 13 ?)
% 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_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(A,B)
<=> ( k2_normsp_1(A,C,np__0) = k2_normsp_1(A,B,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,k1_nat_1(D,np__1)) = k4_rlvect_1(A,k2_normsp_1(A,C,D),k2_normsp_1(A,B,k1_nat_1(D,np__1))) ) ) ) ) ) ) ).
fof(t1_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k18_csspace(A,k1_clvect_3(A,B),k1_clvect_3(A,C)) = k1_clvect_3(A,k18_csspace(A,B,C)) ) ) ) ).
fof(t2_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k7_clvect_1(A,k1_clvect_3(A,B),k1_clvect_3(A,C)) = k1_clvect_3(A,k7_clvect_1(A,B,C)) ) ) ) ).
fof(t3_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
=> k1_clvect_3(A,k9_clvect_1(A,B,C)) = k9_clvect_1(A,k1_clvect_3(A,B),C) ) ) ) ).
fof(t4_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(A,k16_csspace(A,B)) = k16_csspace(A,k1_clvect_3(A,B)) ) ) ).
fof(t5_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> k18_csspace(A,k9_clvect_1(A,k1_clvect_3(A,B),D),k9_clvect_1(A,k1_clvect_3(A,C),E)) = k1_clvect_3(A,k18_csspace(A,k9_clvect_1(A,B,D),k9_clvect_1(A,C,E))) ) ) ) ) ) ).
fof(d2_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(B,A)
<=> v1_clvect_2(k1_clvect_3(A,B),A) ) ) ) ).
fof(d3_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k2_clvect_3(A,B) = k1_clvect_2(A,k1_clvect_3(A,B)) ) ) ).
fof(t6_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ( ( v1_clvect_3(B,A)
& v1_clvect_3(C,A) )
=> ( v1_clvect_3(k18_csspace(A,B,C),A)
& k2_clvect_3(A,k18_csspace(A,B,C)) = k4_rlvect_1(A,k2_clvect_3(A,B),k2_clvect_3(A,C)) ) ) ) ) ) ).
fof(t7_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ( ( v1_clvect_3(B,A)
& v1_clvect_3(C,A) )
=> ( v1_clvect_3(k7_clvect_1(A,B,C),A)
& k2_clvect_3(A,k7_clvect_1(A,B,C)) = k6_rlvect_1(A,k2_clvect_3(A,B),k2_clvect_3(A,C)) ) ) ) ) ) ).
fof(t8_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
=> ( v1_clvect_3(B,A)
=> ( v1_clvect_3(k9_clvect_1(A,B,C),A)
& k2_clvect_3(A,k9_clvect_1(A,B,C)) = k1_clvect_1(A,k2_clvect_3(A,B),C) ) ) ) ) ) ).
fof(t9_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(B,A)
=> ( v1_clvect_2(B,A)
& k1_clvect_2(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t10_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_2(A)
=> ( v1_clvect_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(D,F)
& r1_xreal_0(C,k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,k1_clvect_3(A,B),E),k2_normsp_1(A,k1_clvect_3(A,B),F)))) ) ) ) ) ) ) ) ) ) ).
fof(t11_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(B,A)
=> v3_clvect_2(k1_clvect_3(A,B),A) ) ) ) ).
fof(t12_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,D) = k2_normsp_1(A,C,np__0) )
=> k1_clvect_3(A,k8_clvect_2(A,C,np__1)) = k7_clvect_1(A,k8_clvect_2(A,k1_clvect_3(A,C),np__1),B) ) ) ) ) ).
fof(t13_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> v1_clvect_3(k8_clvect_2(A,B,C),A) ) ) ) ) ).
fof(t14_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& v1_clvect_3(k8_clvect_2(A,B,C),A) )
=> v1_clvect_3(B,A) ) ) ) ).
fof(d4_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k3_clvect_3(A,B,C) = k2_normsp_1(A,k1_clvect_3(A,B),C) ) ) ) ).
fof(t15_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k3_clvect_3(A,B,np__0) = k2_normsp_1(A,B,np__0) ) ) ).
fof(t16_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k3_clvect_3(A,B,np__1) = k4_rlvect_1(A,k3_clvect_3(A,B,np__0),k2_normsp_1(A,B,np__1)) ) ) ).
fof(t17_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k3_clvect_3(A,B,np__1) = k4_rlvect_1(A,k2_normsp_1(A,B,np__0),k2_normsp_1(A,B,np__1)) ) ) ).
fof(t18_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k3_clvect_3(A,B,k1_nat_1(C,np__1)) = k4_rlvect_1(A,k3_clvect_3(A,B,C),k2_normsp_1(A,B,k1_nat_1(C,np__1))) ) ) ) ).
fof(t19_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,k1_nat_1(C,np__1)) = k6_rlvect_1(A,k3_clvect_3(A,B,k1_nat_1(C,np__1)),k3_clvect_3(A,B,C)) ) ) ) ).
fof(t20_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k2_normsp_1(A,B,np__1) = k6_rlvect_1(A,k3_clvect_3(A,B,np__1),k3_clvect_3(A,B,np__0)) ) ) ).
fof(d5_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k4_clvect_3(A,B,C,D) = k6_rlvect_1(A,k3_clvect_3(A,B,C),k3_clvect_3(A,B,D)) ) ) ) ) ).
fof(t21_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> k4_clvect_3(A,B,np__1,np__0) = k2_normsp_1(A,B,np__1) ) ) ).
fof(t22_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k4_clvect_3(A,B,k1_nat_1(C,np__1),C) = k2_normsp_1(A,B,k1_nat_1(C,np__1)) ) ) ) ).
fof(t23_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_2(A)
=> ( v1_clvect_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(D,F)
& r1_xreal_0(C,k13_csspace(A,k6_rlvect_1(A,k3_clvect_3(A,B,E),k3_clvect_3(A,B,F)))) ) ) ) ) ) ) ) ) ) ).
fof(t24_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_2(A)
=> ( v1_clvect_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(D,F)
& r1_xreal_0(C,k13_csspace(A,k4_clvect_3(A,B,E,F))) ) ) ) ) ) ) ) ) ) ).
fof(d6_clvect_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k5_clvect_3(A,B) = k1_comseq_1(k7_comseq_3(A),B) ) ) ).
fof(d7_clvect_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k6_clvect_3(A,B,C) = k11_complex1(k5_clvect_3(A,B),k5_clvect_3(A,C)) ) ) ) ).
fof(d8_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(B,A)
<=> v1_series_1(k2_clvect_2(A,B)) ) ) ) ).
fof(t25_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ( ( v2_clvect_3(B,A)
& v2_clvect_3(C,A) )
=> v2_clvect_3(k18_csspace(A,B,C),A) ) ) ) ) ).
fof(t26_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
=> ( v2_clvect_3(B,A)
=> v2_clvect_3(k9_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t27_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k2_clvect_2(A,B),D),k2_seq_1(k5_numbers,k1_numbers,C,D)) )
& v1_series_1(C) )
=> v2_clvect_3(B,A) ) ) ) ) ).
fof(t28_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k2_normsp_1(A,B,D) != k1_rlvect_1(A)
& k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_real_1(k13_csspace(A,k2_normsp_1(A,B,k1_nat_1(D,np__1))),k13_csspace(A,k2_normsp_1(A,B,D))) ) )
& v4_seq_2(C) )
=> ( r1_xreal_0(np__1,k2_seq_2(C))
| v2_clvect_3(B,A) ) ) ) ) ) ).
fof(t29_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
=> r1_xreal_0(C,k13_csspace(A,k2_normsp_1(A,B,E))) ) ) )
& v1_clvect_2(B,A)
& k1_clvect_2(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t30_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) != k1_rlvect_1(A) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(np__1,k6_real_1(k13_csspace(A,k2_normsp_1(A,B,k1_nat_1(D,np__1))),k13_csspace(A,k2_normsp_1(A,B,D)))) ) ) )
& v1_clvect_3(B,A) ) ) ) ).
fof(t31_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,D) != k1_rlvect_1(A) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_real_1(k13_csspace(A,k2_normsp_1(A,B,k1_nat_1(D,np__1))),k13_csspace(A,k2_normsp_1(A,B,D))) )
& v4_seq_2(C)
& ~ r1_xreal_0(k2_seq_2(C),np__1)
& v1_clvect_3(B,A) ) ) ) ) ).
fof(t32_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k13_csspace(A,k2_normsp_1(A,B,D))) )
& v4_seq_2(C) )
=> ( r1_xreal_0(np__1,k2_seq_2(C))
| v2_clvect_3(B,A) ) ) ) ) ) ).
fof(t33_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k2_clvect_2(A,B),D)) )
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
=> r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) )
& v1_clvect_3(B,A) ) ) ) ) ).
fof(t34_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k2_clvect_2(A,B),D)) )
& v4_seq_2(C)
& ~ r1_xreal_0(k2_seq_2(C),np__1)
& v1_clvect_3(B,A) ) ) ) ) ).
fof(t35_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> v3_seqm_3(k1_series_1(k2_clvect_2(A,B))) ) ) ).
fof(t36_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k2_clvect_2(A,B)),C)) ) ) ) ).
fof(t37_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k2_normsp_1(A,k1_clvect_3(A,B),C)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k2_clvect_2(A,B)),C)) ) ) ) ).
fof(t38_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k3_clvect_3(A,B,C)),k5_bhsp_4(k2_clvect_2(A,B),C)) ) ) ) ).
fof(t39_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,k1_clvect_3(A,B),D),k2_normsp_1(A,k1_clvect_3(A,B),C))),k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k2_clvect_2(A,B)),D),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k2_clvect_2(A,B)),C)))) ) ) ) ) ).
fof(t40_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k6_rlvect_1(A,k3_clvect_3(A,B,D),k3_clvect_3(A,B,C))),k18_complex1(k5_real_1(k5_bhsp_4(k2_clvect_2(A,B),D),k5_bhsp_4(k2_clvect_2(A,B),C)))) ) ) ) ) ).
fof(t41_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k4_clvect_3(A,B,D,C)),k18_complex1(k6_bhsp_4(k2_clvect_2(A,B),D,C))) ) ) ) ) ).
fof(t42_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_2(A)
& v2_clvect_3(B,A) )
=> v1_clvect_3(B,A) ) ) ) ).
fof(d9_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_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 = k7_clvect_3(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k1_clvect_1(A,k2_normsp_1(A,B,E),k1_comseq_1(C,E)) ) ) ) ) ) ) ).
fof(t43_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> k7_clvect_3(A,k18_csspace(A,B,C),D) = k18_csspace(A,k7_clvect_3(A,B,D),k7_clvect_3(A,C,D)) ) ) ) ) ).
fof(t44_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> k7_clvect_3(A,B,k2_comseq_1(k5_numbers,C,D)) = k18_csspace(A,k7_clvect_3(A,B,C),k7_clvect_3(A,B,D)) ) ) ) ) ).
fof(t45_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> k7_clvect_3(A,B,k3_comseq_1(k5_numbers,C,D)) = k7_clvect_3(A,k7_clvect_3(A,B,D),C) ) ) ) ) ).
fof(t46_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k7_clvect_3(A,B,k4_comseq_1(k5_numbers,C,D)) = k9_clvect_1(A,k7_clvect_3(A,B,C),D) ) ) ) ) ).
fof(t47_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> k7_clvect_3(A,k16_csspace(A,B),C) = k7_clvect_3(A,B,k5_comseq_1(k5_numbers,C)) ) ) ) ).
fof(t48_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( v2_comseq_2(C)
& v1_clvect_2(B,A) )
=> v1_clvect_2(k7_clvect_3(A,B,C),A) ) ) ) ) ).
fof(t49_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_2(C)
& v3_clvect_2(B,A) )
=> v3_clvect_2(k7_clvect_3(A,B,C),A) ) ) ) ) ).
fof(t50_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( v2_comseq_2(C)
& v1_clvect_2(B,A) )
=> ( v1_clvect_2(k7_clvect_3(A,B,C),A)
& k1_clvect_2(A,k7_clvect_3(A,B,C)) = k1_clvect_1(A,k1_clvect_2(A,B),k2_comseq_2(C)) ) ) ) ) ) ).
fof(d10_clvect_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v3_clvect_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& r1_xreal_0(C,E)
& r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(A,D),k1_comseq_1(A,E)))) ) ) ) ) ) ) ) ).
fof(t51_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( v5_clvect_2(A)
& v2_clvect_2(B,A)
& v3_clvect_3(C) )
=> v2_clvect_2(k7_clvect_3(A,B,C),A) ) ) ) ) ).
fof(t52_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k1_clvect_3(A,k7_clvect_3(A,k1_clvect_3(A,B),k6_comseq_1(k5_numbers,C,k6_comseq_3(C,np__1)))),D) = k6_rlvect_1(A,k2_normsp_1(A,k1_clvect_3(A,k7_clvect_3(A,B,C)),k1_nat_1(D,np__1)),k2_normsp_1(A,k7_clvect_3(A,k1_clvect_3(A,B),C),k1_nat_1(D,np__1))) ) ) ) ) ).
fof(t53_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k1_clvect_3(A,k7_clvect_3(A,B,C)),k1_nat_1(D,np__1)) = k6_rlvect_1(A,k2_normsp_1(A,k7_clvect_3(A,k1_clvect_3(A,B),C),k1_nat_1(D,np__1)),k2_normsp_1(A,k1_clvect_3(A,k7_clvect_3(A,k1_clvect_3(A,B),k6_comseq_1(k5_numbers,k6_comseq_3(C,np__1),C))),D)) ) ) ) ) ).
fof(t54_clvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_clvect_3(A,k7_clvect_3(A,B,C),k1_nat_1(D,np__1)) = k6_rlvect_1(A,k2_normsp_1(A,k7_clvect_3(A,k1_clvect_3(A,B),C),k1_nat_1(D,np__1)),k3_clvect_3(A,k7_clvect_3(A,k1_clvect_3(A,B),k6_comseq_1(k5_numbers,k6_comseq_3(C,np__1),C)),D)) ) ) ) ) ).
fof(s1_clvect_3,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,u1_struct_0(f1_s1_clvect_3))
& m2_relset_1(A,k5_numbers,u1_struct_0(f1_s1_clvect_3))
& k2_normsp_1(f1_s1_clvect_3,A,np__0) = f2_s1_clvect_3
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s1_clvect_3))
=> ( C = k2_normsp_1(f1_s1_clvect_3,A,B)
=> k2_normsp_1(f1_s1_clvect_3,A,k1_nat_1(B,np__1)) = f3_s1_clvect_3(B,C) ) ) ) ) ).
fof(dt_k1_clvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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_clvect_3(A,B))
& v1_funct_2(k1_clvect_3(A,B),k5_numbers,u1_struct_0(A))
& m2_relset_1(k1_clvect_3(A,B),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k2_clvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)) )
=> m1_subset_1(k2_clvect_3(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_clvect_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k3_clvect_3(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k4_clvect_3,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)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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))
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m1_subset_1(k4_clvect_3(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k5_clvect_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers)
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k5_clvect_3(A,B),k2_numbers) ) ).
fof(dt_k6_clvect_3,axiom,
! [A,B,C] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k6_clvect_3(A,B,C),k2_numbers) ) ).
fof(dt_k7_clvect_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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,k2_numbers)
& m1_relset_1(C,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k7_clvect_3(A,B,C))
& v1_funct_2(k7_clvect_3(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k7_clvect_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
%------------------------------------------------------------------------------