SET007 Axioms: SET007+829.ax
%------------------------------------------------------------------------------
% File : SET007+829 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Banach Algebra of Bounded Complex Linear Operators
% 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 : clopban2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 1 unt; 0 def)
% Number of atoms : 945 ( 76 equ)
% Maximal formula atoms : 45 ( 13 avg)
% Number of connectives : 961 ( 84 ~; 0 |; 746 &)
% ( 6 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 39 ( 38 usr; 0 prp; 1-3 aty)
% Number of functors : 47 ( 47 usr; 5 con; 0-7 aty)
% Number of variables : 160 ( 150 !; 10 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k7_clopban2(A))
& v3_vectsp_1(k7_clopban2(A)) ) ) ).
fof(fc2_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k7_clopban2(A))
& v2_group_1(k7_clopban2(A))
& v3_vectsp_1(k7_clopban2(A)) ) ) ).
fof(fc3_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k7_clopban2(A))
& v3_rlvect_1(k7_clopban2(A))
& v4_rlvect_1(k7_clopban2(A))
& v5_rlvect_1(k7_clopban2(A))
& v6_rlvect_1(k7_clopban2(A))
& v2_group_1(k7_clopban2(A))
& v4_group_1(k7_clopban2(A))
& v3_vectsp_1(k7_clopban2(A))
& v6_vectsp_1(k7_clopban2(A))
& v7_vectsp_1(k7_clopban2(A))
& v8_vectsp_1(k7_clopban2(A)) ) ) ).
fof(fc4_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k8_clopban2(A))
& v1_cfuncdom(k8_clopban2(A)) ) ) ).
fof(fc5_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k8_clopban2(A))
& v2_group_1(k8_clopban2(A))
& v1_cfuncdom(k8_clopban2(A)) ) ) ).
fof(fc6_clopban2,axiom,
( ~ v3_struct_0(k3_csspace3)
& v3_rlvect_1(k3_csspace3)
& v4_rlvect_1(k3_csspace3)
& v5_rlvect_1(k3_csspace3)
& v6_rlvect_1(k3_csspace3)
& v2_clvect_1(k3_csspace3)
& v5_clvect_1(k3_csspace3)
& v4_clopban1(k3_csspace3) ) ).
fof(fc7_clopban2,axiom,
( ~ v3_struct_0(k3_csspace3)
& v3_rlvect_1(k3_csspace3)
& v4_rlvect_1(k3_csspace3)
& v5_rlvect_1(k3_csspace3)
& v6_rlvect_1(k3_csspace3)
& v2_clvect_1(k3_csspace3)
& v5_clvect_1(k3_csspace3)
& v4_clopban1(k3_csspace3)
& ~ v3_realset2(k3_csspace3) ) ).
fof(rc1_clopban2,axiom,
? [A] :
( l2_clvect_1(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)
& v5_clvect_1(A)
& v4_clopban1(A)
& ~ v3_realset2(A) ) ).
fof(rc2_clopban2,axiom,
? [A] :
( l1_clopban2(A)
& v1_clopban2(A) ) ).
fof(rc3_clopban2,axiom,
? [A] :
( l1_clopban2(A)
& ~ v3_struct_0(A) ) ).
fof(fc8_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k9_clopban2(A))
& v1_clopban2(k9_clopban2(A)) ) ) ).
fof(fc9_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k9_clopban2(A))
& v2_group_1(k9_clopban2(A))
& v1_clopban2(k9_clopban2(A)) ) ) ).
fof(rc4_clopban2,axiom,
? [A] :
( l1_clopban2(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)
& v5_clvect_1(A)
& v4_group_1(A)
& v2_cfuncdom(A)
& v1_clopban2(A) ) ).
fof(fc10_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k9_clopban2(A))
& v3_rlvect_1(k9_clopban2(A))
& v4_rlvect_1(k9_clopban2(A))
& v5_rlvect_1(k9_clopban2(A))
& v6_rlvect_1(k9_clopban2(A))
& v2_clvect_1(k9_clopban2(A))
& v5_clvect_1(k9_clopban2(A))
& v2_group_1(k9_clopban2(A))
& v4_group_1(k9_clopban2(A))
& v2_cfuncdom(k9_clopban2(A))
& v1_clopban2(k9_clopban2(A)) ) ) ).
fof(cc1_clopban2,axiom,
! [A] :
( l1_clopban2(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)
& v5_clvect_1(A)
& v4_group_1(A)
& v2_cfuncdom(A)
& v5_clopban2(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)
& v5_clvect_1(A)
& v4_clopban1(A)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_cfuncdom(A)
& v2_clopban2(A)
& v3_clopban2(A)
& v4_clopban2(A) ) ) ) ).
fof(cc2_clopban2,axiom,
! [A] :
( l1_clopban2(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)
& v5_clvect_1(A)
& v4_clopban1(A)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_cfuncdom(A)
& v2_clopban2(A)
& v3_clopban2(A)
& v4_clopban2(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)
& v5_clvect_1(A)
& v4_group_1(A)
& v2_cfuncdom(A)
& v5_clopban2(A) ) ) ) ).
fof(fc11_clopban2,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)
& v5_clvect_1(A)
& v4_clopban1(A)
& ~ v3_realset2(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k9_clopban2(A))
& v3_rlvect_1(k9_clopban2(A))
& v4_rlvect_1(k9_clopban2(A))
& v5_rlvect_1(k9_clopban2(A))
& v6_rlvect_1(k9_clopban2(A))
& v2_clvect_1(k9_clopban2(A))
& v5_clvect_1(k9_clopban2(A))
& v4_clopban1(k9_clopban2(A))
& v2_group_1(k9_clopban2(A))
& v4_group_1(k9_clopban2(A))
& v5_vectsp_1(k9_clopban2(A))
& v8_vectsp_1(k9_clopban2(A))
& v2_cfuncdom(k9_clopban2(A))
& v1_clopban2(k9_clopban2(A))
& v2_clopban2(k9_clopban2(A))
& v3_clopban2(k9_clopban2(A))
& v4_clopban2(k9_clopban2(A))
& v5_clopban2(k9_clopban2(A)) ) ) ).
fof(rc5_clopban2,axiom,
? [A] :
( l1_clopban2(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)
& v5_clvect_1(A)
& v4_clopban1(A)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_cfuncdom(A)
& v2_clopban2(A)
& v3_clopban2(A)
& v4_clopban2(A)
& v5_clopban2(A) ) ).
fof(t1_clopban2,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)
& l1_clvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& l1_clvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& l1_clvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_clopban1(D,A,B)
& v2_clopban1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_clopban1(E,B,C)
& v2_clopban1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
& v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& v1_clopban1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v2_clopban1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t2_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v5_clvect_1(C)
& l2_clvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_clopban1(D,A,B)
& v2_clopban1(D,A,B)
& v3_clopban1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_clopban1(E,B,C)
& v2_clopban1(E,B,C)
& v3_clopban1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
& v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& v1_clopban1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v2_clopban1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v3_clopban1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_xreal_0(k5_clvect_1(C,k8_funct_2(u1_struct_0(A),u1_struct_0(C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),F)),k4_real_1(k4_real_1(k2_seq_1(k8_clopban1(B,C),k1_numbers,k13_clopban1(B,C),E),k2_seq_1(k8_clopban1(A,B),k1_numbers,k13_clopban1(A,B),D)),k5_clvect_1(A,F)))
& r1_xreal_0(k2_seq_1(k8_clopban1(A,C),k1_numbers,k13_clopban1(A,C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)),k4_real_1(k2_seq_1(k8_clopban1(B,C),k1_numbers,k13_clopban1(B,C),E),k2_seq_1(k8_clopban1(A,B),k1_numbers,k13_clopban1(A,B),D))) ) ) ) ) ) ) ) ) ).
fof(d1_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> k2_clopban2(A,B,C) = k2_binop_1(k8_clopban1(A,A),k8_clopban1(A,A),k8_clopban1(A,A),k8_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),B,C) ) ) ) ).
fof(d2_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> k3_clopban2(A,B,C) = k1_clopban2(A,k11_clopban1(A,A,B),k11_clopban1(A,A,C)) ) ) ) ).
fof(d3_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k4_clopban2(A,B,C) = k2_binop_1(k2_numbers,k8_clopban1(A,A),k8_clopban1(A,A),k9_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),C,B) ) ) ) ).
fof(d4_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A))
& m2_relset_1(B,k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A)) )
=> ( B = k5_clopban2(A)
<=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_struct_0(D,k6_clopban1(A,A),k8_clopban1(A,A))
=> k2_binop_1(k8_clopban1(A,A),k8_clopban1(A,A),k8_clopban1(A,A),B,C,D) = k3_clopban2(A,D,C) ) ) ) ) ) ).
fof(t3_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( v1_funct_1(k6_partfun1(u1_struct_0(A)))
& v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(k6_partfun1(u1_struct_0(A)),A,A)
& v2_clopban1(k6_partfun1(u1_struct_0(A)),A,A)
& v3_clopban1(k6_partfun1(u1_struct_0(A)),A,A)
& m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(d5_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k6_clopban2(A) = k6_partfun1(u1_struct_0(A)) ) ).
fof(t4_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(B,A,A)
& v2_clopban1(B,A,A)
& v3_clopban1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(C,A,A)
& v2_clopban1(C,A,A)
& v3_clopban1(C,A,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(D,A,A)
& v2_clopban1(D,A,A)
& v3_clopban1(D,A,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( D = k1_clopban2(A,C,B)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E)) ) ) ) ) ) ) ).
fof(t5_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(B,A,A)
& v2_clopban1(B,A,A)
& v3_clopban1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(C,A,A)
& v2_clopban1(C,A,A)
& v3_clopban1(C,A,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(D,A,A)
& v2_clopban1(D,A,A)
& v3_clopban1(D,A,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> k1_clopban2(A,k1_clopban2(A,D,C),B) = k1_clopban2(A,D,k1_clopban2(A,C,B)) ) ) ) ) ).
fof(t6_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(B,A,A)
& v2_clopban1(B,A,A)
& v3_clopban1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B) = B
& k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_partfun1(u1_struct_0(A))) = B ) ) ) ).
fof(t7_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_struct_0(D,k6_clopban1(A,A),k8_clopban1(A,A))
=> k3_clopban2(A,k3_clopban2(A,D,C),B) = k3_clopban2(A,D,k3_clopban2(A,C,B)) ) ) ) ) ).
fof(t8_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ( k3_clopban2(A,k6_clopban2(A),B) = B
& k3_clopban2(A,B,k6_clopban2(A)) = B ) ) ) ).
fof(t9_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_struct_0(D,k6_clopban1(A,A),k8_clopban1(A,A))
=> k3_clopban2(A,k2_clopban2(A,C,D),B) = k2_clopban2(A,k3_clopban2(A,C,B),k3_clopban2(A,D,B)) ) ) ) ) ).
fof(t10_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_struct_0(D,k6_clopban1(A,A),k8_clopban1(A,A))
=> k3_clopban2(A,B,k2_clopban2(A,C,D)) = k2_clopban2(A,k3_clopban2(A,B,C),k3_clopban2(A,B,D)) ) ) ) ) ).
fof(t11_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> k4_clopban2(A,k3_clopban2(A,C,B),k9_complex1(D,E)) = k3_clopban2(A,k4_clopban2(A,C,E),k4_clopban2(A,B,D)) ) ) ) ) ) ).
fof(t12_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_struct_0(B,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [C] :
( m1_struct_0(C,k6_clopban1(A,A),k8_clopban1(A,A))
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_clopban2(A,k3_clopban2(A,C,B),D) = k3_clopban2(A,C,k4_clopban2(A,B,D)) ) ) ) ) ).
fof(d6_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k7_clopban2(A) = g3_vectsp_1(k8_clopban1(A,A),k8_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k5_clopban2(A),k6_clopban2(A),k10_csspace(k6_clopban1(A,A),k8_clopban1(A,A))) ) ).
fof(t13_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_clopban2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_clopban2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k7_clopban2(A)))
=> ( k2_rlvect_1(k7_clopban2(A),B,C) = k2_rlvect_1(k7_clopban2(A),C,B)
& k2_rlvect_1(k7_clopban2(A),k2_rlvect_1(k7_clopban2(A),B,C),D) = k2_rlvect_1(k7_clopban2(A),B,k2_rlvect_1(k7_clopban2(A),C,D))
& k2_rlvect_1(k7_clopban2(A),B,k1_rlvect_1(k7_clopban2(A))) = B
& ? [E] :
( m1_subset_1(E,u1_struct_0(k7_clopban2(A)))
& k2_rlvect_1(k7_clopban2(A),B,E) = k1_rlvect_1(k7_clopban2(A)) )
& k1_group_1(k7_clopban2(A),k1_group_1(k7_clopban2(A),B,C),D) = k1_group_1(k7_clopban2(A),B,k1_group_1(k7_clopban2(A),C,D))
& k1_group_1(k7_clopban2(A),B,k2_group_1(k7_clopban2(A))) = B
& k1_group_1(k7_clopban2(A),k2_group_1(k7_clopban2(A)),B) = B
& k1_group_1(k7_clopban2(A),B,k2_rlvect_1(k7_clopban2(A),C,D)) = k2_rlvect_1(k7_clopban2(A),k1_group_1(k7_clopban2(A),B,C),k1_group_1(k7_clopban2(A),B,D))
& k1_group_1(k7_clopban2(A),k2_rlvect_1(k7_clopban2(A),C,D),B) = k2_rlvect_1(k7_clopban2(A),k1_group_1(k7_clopban2(A),C,B),k1_group_1(k7_clopban2(A),D,B)) ) ) ) ) ) ).
fof(t14_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k7_clopban2(A))
& v3_rlvect_1(k7_clopban2(A))
& v4_rlvect_1(k7_clopban2(A))
& v5_rlvect_1(k7_clopban2(A))
& v6_rlvect_1(k7_clopban2(A))
& v4_group_1(k7_clopban2(A))
& v6_vectsp_1(k7_clopban2(A))
& v7_vectsp_1(k7_clopban2(A))
& v8_vectsp_1(k7_clopban2(A))
& l3_vectsp_1(k7_clopban2(A)) ) ) ).
fof(d7_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k8_clopban2(A) = g1_cfuncdom(k8_clopban1(A,A),k5_clopban2(A),k8_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k9_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k6_clopban2(A),k10_csspace(k6_clopban1(A,A),k8_clopban1(A,A))) ) ).
fof(t15_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_clopban2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_clopban2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k8_clopban2(A)))
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ( k2_rlvect_1(k8_clopban2(A),B,C) = k2_rlvect_1(k8_clopban2(A),C,B)
& k2_rlvect_1(k8_clopban2(A),k2_rlvect_1(k8_clopban2(A),B,C),D) = k2_rlvect_1(k8_clopban2(A),B,k2_rlvect_1(k8_clopban2(A),C,D))
& k2_rlvect_1(k8_clopban2(A),B,k1_rlvect_1(k8_clopban2(A))) = B
& ? [G] :
( m1_subset_1(G,u1_struct_0(k8_clopban2(A)))
& k2_rlvect_1(k8_clopban2(A),B,G) = k1_rlvect_1(k8_clopban2(A)) )
& k1_group_1(k8_clopban2(A),k1_group_1(k8_clopban2(A),B,C),D) = k1_group_1(k8_clopban2(A),B,k1_group_1(k8_clopban2(A),C,D))
& k1_group_1(k8_clopban2(A),B,k2_group_1(k8_clopban2(A))) = B
& k1_group_1(k8_clopban2(A),k2_group_1(k8_clopban2(A)),B) = B
& k1_group_1(k8_clopban2(A),B,k2_rlvect_1(k8_clopban2(A),C,D)) = k2_rlvect_1(k8_clopban2(A),k1_group_1(k8_clopban2(A),B,C),k1_group_1(k8_clopban2(A),B,D))
& k1_group_1(k8_clopban2(A),k2_rlvect_1(k8_clopban2(A),C,D),B) = k2_rlvect_1(k8_clopban2(A),k1_group_1(k8_clopban2(A),C,B),k1_group_1(k8_clopban2(A),D,B))
& k1_clvect_1(k8_clopban2(A),k1_group_1(k8_clopban2(A),B,C),E) = k1_group_1(k8_clopban2(A),k1_clvect_1(k8_clopban2(A),B,E),C)
& k1_clvect_1(k8_clopban2(A),k2_rlvect_1(k8_clopban2(A),B,C),E) = k2_rlvect_1(k8_clopban2(A),k1_clvect_1(k8_clopban2(A),B,E),k1_clvect_1(k8_clopban2(A),C,E))
& k1_clvect_1(k8_clopban2(A),B,k8_complex1(E,F)) = k2_rlvect_1(k8_clopban2(A),k1_clvect_1(k8_clopban2(A),B,E),k1_clvect_1(k8_clopban2(A),B,F))
& k1_clvect_1(k8_clopban2(A),B,k9_complex1(E,F)) = k1_clvect_1(k8_clopban2(A),k1_clvect_1(k8_clopban2(A),B,F),E)
& k1_clvect_1(k8_clopban2(A),k1_group_1(k8_clopban2(A),B,C),k9_complex1(E,F)) = k1_group_1(k8_clopban2(A),k1_clvect_1(k8_clopban2(A),B,E),k1_clvect_1(k8_clopban2(A),C,F)) ) ) ) ) ) ) ) ).
fof(t16_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( ~ v3_struct_0(k8_clopban2(A))
& v3_rlvect_1(k8_clopban2(A))
& v4_rlvect_1(k8_clopban2(A))
& v5_rlvect_1(k8_clopban2(A))
& v6_rlvect_1(k8_clopban2(A))
& v4_group_1(k8_clopban2(A))
& v2_cfuncdom(k8_clopban2(A))
& l1_cfuncdom(k8_clopban2(A)) ) ) ).
fof(t17_clopban2,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)
& v5_clvect_1(A)
& ~ v3_realset2(A)
& l2_clvect_1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& k5_clvect_1(A,B) = np__1 ) ) ).
fof(t18_clopban2,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)
& v5_clvect_1(A)
& ~ v3_realset2(A)
& l2_clvect_1(A) )
=> k2_seq_1(k8_clopban1(A,A),k1_numbers,k13_clopban1(A,A),k6_partfun1(u1_struct_0(A))) = np__1 ) ).
fof(d8_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k9_clopban2(A) = g1_clopban2(k8_clopban1(A,A),k5_clopban2(A),k8_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k9_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k6_clopban2(A),k10_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),k13_clopban1(A,A)) ) ).
fof(t19_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_clopban2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_clopban2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_clopban2(A)))
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ( k2_rlvect_1(k9_clopban2(A),B,C) = k2_rlvect_1(k9_clopban2(A),C,B)
& k2_rlvect_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),B,C),D) = k2_rlvect_1(k9_clopban2(A),B,k2_rlvect_1(k9_clopban2(A),C,D))
& k2_rlvect_1(k9_clopban2(A),B,k1_rlvect_1(k9_clopban2(A))) = B
& ? [G] :
( m1_subset_1(G,u1_struct_0(k9_clopban2(A)))
& k2_rlvect_1(k9_clopban2(A),B,G) = k1_rlvect_1(k9_clopban2(A)) )
& k1_group_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),D) = k1_group_1(k9_clopban2(A),B,k1_group_1(k9_clopban2(A),C,D))
& k1_group_1(k9_clopban2(A),B,k2_group_1(k9_clopban2(A))) = B
& k1_group_1(k9_clopban2(A),k2_group_1(k9_clopban2(A)),B) = B
& k1_group_1(k9_clopban2(A),B,k2_rlvect_1(k9_clopban2(A),C,D)) = k2_rlvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),k1_group_1(k9_clopban2(A),B,D))
& k1_group_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),C,D),B) = k2_rlvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),C,B),k1_group_1(k9_clopban2(A),D,B))
& k1_clvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),E) = k1_group_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),C)
& k1_clvect_1(k9_clopban2(A),k1_group_1(k9_clopban2(A),B,C),k9_complex1(E,F)) = k1_group_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),C,F))
& k1_clvect_1(k9_clopban2(A),k2_rlvect_1(k9_clopban2(A),B,C),E) = k2_rlvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),C,E))
& k1_clvect_1(k9_clopban2(A),B,k8_complex1(E,F)) = k2_rlvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,E),k1_clvect_1(k9_clopban2(A),B,F))
& k1_clvect_1(k9_clopban2(A),B,k9_complex1(E,F)) = k1_clvect_1(k9_clopban2(A),k1_clvect_1(k9_clopban2(A),B,F),E)
& k1_clvect_1(k9_clopban2(A),B,k6_complex1) = B ) ) ) ) ) ) ) ).
fof(t20_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( v5_clvect_1(k9_clopban2(A))
& v3_rlvect_1(k9_clopban2(A))
& v4_rlvect_1(k9_clopban2(A))
& v5_rlvect_1(k9_clopban2(A))
& v6_rlvect_1(k9_clopban2(A))
& v4_group_1(k9_clopban2(A))
& v2_cfuncdom(k9_clopban2(A))
& v2_clvect_1(k9_clopban2(A)) ) ) ).
fof(d9_clopban2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clopban2(A) )
=> ( v2_clopban2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k5_clvect_1(A,k1_group_1(A,B,C)),k4_real_1(k5_clvect_1(A,B),k5_clvect_1(A,C))) ) ) ) ) ).
fof(d10_clopban2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clopban2(A) )
=> ( v3_clopban2(A)
<=> k5_clvect_1(A,k2_group_1(A)) = np__1 ) ) ).
fof(d11_clopban2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_clopban2(A) )
=> ( v4_clopban2(A)
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_clvect_1(A,k1_group_1(A,C,D),B) = k1_group_1(A,C,k1_clvect_1(A,D,B)) ) ) ) ) ) ).
fof(d12_clopban2,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)
& v5_clvect_1(A)
& v4_group_1(A)
& v2_cfuncdom(A)
& l1_clopban2(A) )
=> ( v5_clopban2(A)
<=> ( v2_clopban2(A)
& v3_clopban2(A)
& v4_clopban2(A)
& v8_vectsp_1(A)
& v5_vectsp_1(A)
& v4_clopban1(A) ) ) ) ).
fof(t21_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k2_group_1(k7_clopban2(A)) = k6_clopban2(A) ) ).
fof(t22_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k2_group_1(k8_clopban2(A)) = k6_clopban2(A) ) ).
fof(t23_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> k2_group_1(k9_clopban2(A)) = k6_clopban2(A) ) ).
fof(dt_l1_clopban2,axiom,
! [A] :
( l1_clopban2(A)
=> ( l1_cfuncdom(A)
& l2_clvect_1(A) ) ) ).
fof(existence_l1_clopban2,axiom,
? [A] : l1_clopban2(A) ).
fof(abstractness_v1_clopban2,axiom,
! [A] :
( l1_clopban2(A)
=> ( v1_clopban2(A)
=> A = g1_clopban2(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u1_clvect_1(A),u1_vectsp_1(A),u2_struct_0(A),u2_clvect_1(A)) ) ) ).
fof(dt_k1_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(B,A,A)
& v2_clopban1(B,A,A)
& v3_clopban1(B,A,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(C,A,A)
& v2_clopban1(C,A,A)
& v3_clopban1(C,A,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_funct_1(k1_clopban2(A,B,C))
& v1_funct_2(k1_clopban2(A,B,C),u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(k1_clopban2(A,B,C),A,A)
& v2_clopban1(k1_clopban2(A,B,C),A,A)
& v3_clopban1(k1_clopban2(A,B,C),A,A)
& m2_relset_1(k1_clopban2(A,B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k1_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(B,A,A)
& v2_clopban1(B,A,A)
& v3_clopban1(B,A,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_clopban1(C,A,A)
& v2_clopban1(C,A,A)
& v3_clopban1(C,A,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> k1_clopban2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k2_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A)
& m1_subset_1(B,k8_clopban1(A,A))
& m1_subset_1(C,k8_clopban1(A,A)) )
=> m1_struct_0(k2_clopban2(A,B,C),k6_clopban1(A,A),k8_clopban1(A,A)) ) ).
fof(dt_k3_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A)
& m1_subset_1(B,k8_clopban1(A,A))
& m1_subset_1(C,k8_clopban1(A,A)) )
=> m1_struct_0(k3_clopban2(A,B,C),k6_clopban1(A,A),k8_clopban1(A,A)) ) ).
fof(dt_k4_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A)
& m1_subset_1(B,k8_clopban1(A,A))
& m1_subset_1(C,k2_numbers) )
=> m1_struct_0(k4_clopban2(A,B,C),k6_clopban1(A,A),k8_clopban1(A,A)) ) ).
fof(dt_k5_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> ( v1_funct_1(k5_clopban2(A))
& v1_funct_2(k5_clopban2(A),k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A))
& m2_relset_1(k5_clopban2(A),k2_zfmisc_1(k8_clopban1(A,A),k8_clopban1(A,A)),k8_clopban1(A,A)) ) ) ).
fof(dt_k6_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> m1_struct_0(k6_clopban2(A),k6_clopban1(A,A),k8_clopban1(A,A)) ) ).
fof(dt_k7_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> l3_vectsp_1(k7_clopban2(A)) ) ).
fof(dt_k8_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> l1_cfuncdom(k8_clopban2(A)) ) ).
fof(dt_k9_clopban2,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)
& v5_clvect_1(A)
& l2_clvect_1(A) )
=> l1_clopban2(k9_clopban2(A)) ) ).
fof(dt_g1_clopban2,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& v1_funct_1(G)
& v1_funct_2(G,A,k1_numbers)
& m1_relset_1(G,A,k1_numbers) )
=> ( v1_clopban2(g1_clopban2(A,B,C,D,E,F,G))
& l1_clopban2(g1_clopban2(A,B,C,D,E,F,G)) ) ) ).
fof(free_g1_clopban2,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& v1_funct_1(G)
& v1_funct_2(G,A,k1_numbers)
& m1_relset_1(G,A,k1_numbers) )
=> ! [H,I,J,K,L,M,N] :
( g1_clopban2(A,B,C,D,E,F,G) = g1_clopban2(H,I,J,K,L,M,N)
=> ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
%------------------------------------------------------------------------------