SET007 Axioms: SET007+747.ax
%------------------------------------------------------------------------------
% File : SET007+747 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Quotient Vector Spaces and Functionals
% 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 : vectsp10 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 88 ( 1 unt; 0 def)
% Number of atoms : 1735 ( 96 equ)
% Maximal formula atoms : 37 ( 19 avg)
% Number of connectives : 1885 ( 238 ~; 9 |;1287 &)
% ( 12 <=>; 339 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 15 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-4 aty)
% Number of functors : 41 ( 41 usr; 0 con; 1-6 aty)
% Number of variables : 360 ( 342 !; 18 ?)
% 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_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc2_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v3_rlvect_1(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc3_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v4_rlvect_1(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc4_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v5_rlvect_1(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc5_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v6_rlvect_1(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc6_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A)
& v12_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(fc7_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_vectsp10(A))
& v11_vectsp_1(k1_vectsp10(A),A)
& ~ v3_realset2(k1_vectsp10(A)) ) ) ).
fof(rc1_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l4_vectsp_1(B,A)
& ~ v3_struct_0(B)
& ~ v3_realset2(B) ) ) ).
fof(rc2_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l4_vectsp_1(B,A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v11_vectsp_1(B,A) ) ) ).
fof(rc3_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l4_vectsp_1(B,A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v11_vectsp_1(B,A)
& v12_vectsp_1(B,A) ) ) ).
fof(rc4_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l4_vectsp_1(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v11_vectsp_1(B,A)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B) ) ) ).
fof(rc5_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v3_hahnban1(C,A,B) ) ) ).
fof(cc1_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B) ) ) ) ) ).
fof(cc2_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B) ) ) ) ) ).
fof(fc8_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k7_hahnban1(A,B))
& v1_funct_1(k7_hahnban1(A,B))
& v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
& v5_seqm_3(k7_hahnban1(A,B))
& v3_hahnban1(k7_hahnban1(A,B),A,B) ) ) ).
fof(rc6_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v5_seqm_3(C) ) ) ).
fof(rc7_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v5_seqm_3(C)
& v1_hahnban1(C,A,B)
& v3_hahnban1(C,A,B) ) ) ).
fof(cc3_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(C) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v1_realset1(C) ) ) ) ) ).
fof(rc8_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(C)
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& v3_hahnban1(C,A,B)
& ~ v1_realset1(C) ) ) ).
fof(cc4_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_realset1(C) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v5_seqm_3(C) ) ) ) ) ).
fof(fc9_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v4_rlvect_1(k8_hahnban1(A,B))
& v5_rlvect_1(k8_hahnban1(A,B))
& v6_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A)
& v12_vectsp_1(k8_hahnban1(A,B),A)
& ~ v3_realset2(k8_hahnban1(A,B)) ) ) ).
fof(fc10_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ~ v1_xboole_0(k8_vectsp10(A,B,C)) ) ).
fof(cc5_vectsp10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B)
& ~ v2_vectsp10(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(C)
& ~ v1_realset1(C) ) ) ) ) ).
fof(fc11_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(C)
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k11_vectsp10(A,B,C))
& v1_funct_1(k11_vectsp10(A,B,C))
& v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
& ~ v5_seqm_3(k11_vectsp10(A,B,C))
& v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& v3_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& ~ v1_realset1(k11_vectsp10(A,B,C)) ) ) ).
fof(fc12_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k11_vectsp10(A,B,C))
& v1_funct_1(k11_vectsp10(A,B,C))
& v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
& v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& v3_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& ~ v2_vectsp10(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C))) ) ) ).
fof(d1_vectsp10,axiom,
! [A] :
( l3_vectsp_1(A)
=> k1_vectsp10(A) = g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) ).
fof(t1_vectsp10,axiom,
$true ).
fof(t2_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( k6_vectsp_1(A,C,k1_rlvect_1(A),D) = k1_rlvect_1(C)
& k6_vectsp_1(A,C,B,k1_rlvect_1(C)) = k1_rlvect_1(C) ) ) ) ) ) ).
fof(t3_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,E) )
=> E = k1_rlvect_1(B) ) ) ) ) ) ) ).
fof(t4_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C,D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_rlvect_1(k1_vectsp_7(A,B,k7_rlvect_2(B,D)),C)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& C = k6_vectsp_1(A,B,E,D) ) ) ) ) ) ).
fof(t5_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k6_vectsp_1(A,B,D,C) = k6_vectsp_1(A,B,E,C)
=> ( C = k1_rlvect_1(B)
| D = E ) ) ) ) ) ) ) ).
fof(t6_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( r1_rlvect_1(C,F)
& r1_rlvect_1(D,G)
& E = k4_rlvect_1(B,F,G) )
=> k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) ) ) ) ) ) ) ) ) ) ).
fof(t7_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
=> E = k4_rlvect_1(B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t8_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
=> ( r1_rlvect_1(C,F)
& r1_rlvect_1(D,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G)
=> k4_vectsp_5(A,B,E,D,C) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),G,F) ) ) ) ) ) ) ) ) ) ).
fof(t10_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_rlvect_1(C,E)
=> k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,k1_rlvect_1(B)) ) ) ) ) ) ) ) ).
fof(t11_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( r1_vectsp_5(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_rlvect_1(D,E)
=> k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),k1_rlvect_1(B),E) ) ) ) ) ) ) ) ).
fof(t12_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_rlvect_1(D,E)
=> m1_subset_1(E,u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t13_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ! [F] :
( m1_vectsp_4(F,A,E)
=> ! [G] :
( m1_vectsp_4(G,A,E)
=> ( ( F = C
& G = D )
=> k1_vectsp_5(A,E,F,G) = k1_vectsp_5(A,B,C,D) ) ) ) ) ) ) ) ) ).
fof(t14_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( D = E
=> k1_vectsp_7(A,C,k7_rlvect_2(C,E)) = k1_vectsp_7(A,B,k7_rlvect_2(B,D)) ) ) ) ) ) ) ).
fof(t15_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ( ~ r1_rlvect_1(D,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& F = D )
=> r1_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) ) ) ) ) ) ) ) ) ).
fof(t16_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& D = F )
=> ( r1_rlvect_1(D,C)
| k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(F),u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))),k1_rlvect_1(F),E) ) ) ) ) ) ) ) ) ).
fof(t17_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& D = F )
=> ( r1_rlvect_1(D,C)
| ! [G] :
( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ( r1_rlvect_1(D,G)
=> k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))),u1_struct_0(B),G,k1_rlvect_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& ? [G] :
( m1_subset_1(G,u1_struct_0(B))
& k4_vectsp_5(A,B,C,D,E) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) ) ) ) ) ) ) ) ).
fof(t19_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& D = F )
=> ( r1_rlvect_1(D,C)
| ! [G] :
( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ? [H] :
( m1_subset_1(H,u1_struct_0(D))
& ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),H,k6_vectsp_1(A,B,I,C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& D = F )
=> ( r1_rlvect_1(D,C)
| ! [G] :
( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(D))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(D))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ( ( k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),I,k6_vectsp_1(A,B,K,C))
& k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),H,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),J,k6_vectsp_1(A,B,L,C)) )
=> k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k4_rlvect_1(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,H),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),k4_rlvect_1(D,I,J),k6_vectsp_1(A,B,k4_rlvect_1(A,K,L),C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [F] :
( m1_vectsp_4(F,A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))))
=> ( ( C = E
& D = F )
=> ( r1_rlvect_1(D,C)
| ! [G] :
( m1_subset_1(G,u1_struct_0(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),G,F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),H,k6_vectsp_1(A,B,J,C))
=> k4_vectsp_5(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k6_vectsp_1(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),I,G),F,k1_vectsp_7(A,k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),k7_rlvect_2(k1_vectsp_5(A,B,D,k1_vectsp_7(A,B,k7_rlvect_2(B,C))),E))) = k1_domain_1(u1_struct_0(D),u1_struct_0(B),k6_vectsp_1(A,D,I,H),k6_vectsp_1(A,B,k10_group_1(A,I,J),C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
& m2_relset_1(D,k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) )
=> ( D = k3_vectsp10(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
=> ! [F] :
( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( ( E = k3_vectsp_4(A,B,G,C)
& F = k3_vectsp_4(A,B,H,C) )
=> k2_binop_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),D,E,F) = k3_vectsp_4(A,B,k4_rlvect_1(B,G,H),C) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> k4_vectsp10(A,B,C) = u1_struct_0(C) ) ) ) ).
fof(d5_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) )
=> ( D = k5_vectsp10(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( F = k3_vectsp_4(A,B,G,C)
=> k2_binop_1(u1_struct_0(A),k2_vectsp10(A,B,C),k2_vectsp10(A,B,C),D,E,F) = k3_vectsp_4(A,B,k6_vectsp_1(A,B,E,G),C) ) ) ) ) ) ) ) ) ) ).
fof(d6_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v11_vectsp_1(D,A)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A) )
=> ( D = k6_vectsp10(A,B,C)
<=> ( u1_struct_0(D) = k2_vectsp10(A,B,C)
& u1_rlvect_1(D) = k3_vectsp10(A,B,C)
& u2_struct_0(D) = k4_vectsp10(A,B,C)
& u2_vectsp_1(A,D) = k5_vectsp10(A,B,C) ) ) ) ) ) ) ).
fof(t22_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ( k4_vectsp10(A,B,C) = k3_vectsp_4(A,B,k1_rlvect_1(B),C)
& k1_rlvect_1(k6_vectsp10(A,B,C)) = k4_vectsp10(A,B,C) ) ) ) ) ).
fof(t23_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
=> ( m2_vectsp_4(D,A,B,C)
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k3_vectsp_4(A,B,E,C) ) ) ) ) ) ) ).
fof(t24_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( m2_vectsp_4(k3_vectsp_4(A,B,D,C),A,B,C)
& m1_subset_1(k3_vectsp_4(A,B,D,C),u1_struct_0(k6_vectsp10(A,B,C))) ) ) ) ) ) ).
fof(t25_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m2_vectsp_4(D,A,B,C)
=> m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) ) ) ) ) ).
fof(t26_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( D = k3_vectsp_4(A,B,E,C)
=> k6_vectsp_1(A,k6_vectsp10(A,B,C),F,D) = k3_vectsp_4(A,B,k6_vectsp_1(A,B,F,E),C) ) ) ) ) ) ) ) ).
fof(t27_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_vectsp10(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( D = k3_vectsp_4(A,B,F,C)
& E = k3_vectsp_4(A,B,G,C) )
=> k4_rlvect_1(k6_vectsp10(A,B,C),D,E) = k3_vectsp_4(A,B,k4_rlvect_1(B,F,G),C) ) ) ) ) ) ) ) ) ).
fof(t28_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& v1_hahnban1(D,A,C)
& v2_hahnban1(D,A,C)
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))))
=> ( E = F
=> ( r1_rlvect_1(C,E)
| ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ? [H] :
( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A))
& v1_hahnban1(H,A,k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E))))
& v2_hahnban1(H,A,k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E))))
& m2_relset_1(H,u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A))
& k8_relset_1(u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A),H,u1_struct_0(C)) = D
& k8_funct_2(u1_struct_0(k1_vectsp_5(A,B,C,k1_vectsp_7(A,B,k7_rlvect_2(B,E)))),u1_struct_0(A),H,F) = G ) ) ) ) ) ) ) ) ) ) ).
fof(d7_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v5_seqm_3(C)
<=> C = k7_hahnban1(A,B) ) ) ) ) ).
fof(d8_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_5(D,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
=> ( C != k1_rlvect_1(B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(E)
& v1_hahnban1(E,A,B)
& v2_hahnban1(E,A,B)
& ~ v1_realset1(E)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( E = k7_vectsp10(A,B,C,D)
<=> ( k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C) = k2_group_1(A)
& k8_relset_1(u1_struct_0(B),u1_struct_0(A),E,u1_struct_0(D)) = k7_hahnban1(A,D) ) ) ) ) ) ) ) ) ).
fof(t29_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(C)
& v3_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& D != k1_rlvect_1(B)
& k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D) != k1_rlvect_1(A) ) ) ) ) ).
fof(t30_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_vectsp_5(E,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
=> ( C != k1_rlvect_1(B)
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,E),k6_vectsp_1(A,B,D,C)) = D ) ) ) ) ) ) ).
fof(t31_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_5(E,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
=> ( r1_rlvect_1(E,D)
=> ( C = k1_rlvect_1(B)
| k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,E),D) = k1_rlvect_1(A) ) ) ) ) ) ) ) ).
fof(t32_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_vectsp_5(F,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C)))
=> ( r1_rlvect_1(F,D)
=> ( C = k1_rlvect_1(B)
| k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_vectsp10(A,B,C,F),k4_rlvect_1(B,k6_vectsp_1(A,B,E,C),D)) = E ) ) ) ) ) ) ) ) ).
fof(t33_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k5_hahnban1(A,B,C,D),E) = k6_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E)) ) ) ) ) ) ).
fof(t34_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> v1_vectsp_4(k8_vectsp10(A,B,C),A,B) ) ) ) ).
fof(d10_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v2_vectsp10(C,A,B)
<=> k8_vectsp10(A,B,C) != k7_rlvect_2(B,k1_rlvect_1(B)) ) ) ) ) ).
fof(d11_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v11_vectsp_1(D,A)
& m1_vectsp_4(D,A,B) )
=> ( D = k9_vectsp10(A,B,C)
<=> u1_struct_0(D) = k8_vectsp10(A,B,C) ) ) ) ) ) ).
fof(d12_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( r1_tarski(u1_struct_0(C),k8_vectsp10(A,B,D))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A))
& v1_hahnban1(E,A,k6_vectsp10(A,B,C))
& m2_relset_1(E,u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A)) )
=> ( E = k10_vectsp10(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( F = k3_vectsp_4(A,B,G,C)
=> k8_funct_2(u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A),E,F) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( r1_tarski(u1_struct_0(C),k8_vectsp10(A,B,D))
=> v2_hahnban1(k10_vectsp10(A,B,C,D),A,k6_vectsp10(A,B,C)) ) ) ) ) ) ).
fof(d13_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> k11_vectsp10(A,B,C) = k10_vectsp10(A,B,k9_vectsp10(A,B,C),C) ) ) ) ).
fof(t36_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( D = k3_vectsp_4(A,B,E,k9_vectsp10(A,B,C))
=> k8_funct_2(u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A),k11_vectsp10(A,B,C),D) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) ) ) ) ) ) ) ).
fof(redefinition_v1_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_vectsp10(C,A,B)
<=> v5_seqm_3(C) ) ) ).
fof(dt_k1_vectsp10,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( v11_vectsp_1(k1_vectsp10(A),A)
& l4_vectsp_1(k1_vectsp10(A),A) ) ) ).
fof(dt_k2_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v1_xboole_0(k2_vectsp10(A,B,C))
& m1_subset_1(k2_vectsp10(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) ) ).
fof(dt_k3_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_funct_1(k3_vectsp10(A,B,C))
& v1_funct_2(k3_vectsp10(A,B,C),k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
& m2_relset_1(k3_vectsp10(A,B,C),k2_zfmisc_1(k2_vectsp10(A,B,C),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) ) ) ).
fof(dt_k4_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> m2_subset_1(k4_vectsp10(A,B,C),k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C)) ) ).
fof(dt_k5_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_funct_1(k5_vectsp10(A,B,C))
& v1_funct_2(k5_vectsp10(A,B,C),k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C))
& m2_relset_1(k5_vectsp10(A,B,C),k2_zfmisc_1(u1_struct_0(A),k2_vectsp10(A,B,C)),k2_vectsp10(A,B,C)) ) ) ).
fof(dt_k6_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v3_struct_0(k6_vectsp10(A,B,C))
& v3_rlvect_1(k6_vectsp10(A,B,C))
& v4_rlvect_1(k6_vectsp10(A,B,C))
& v5_rlvect_1(k6_vectsp10(A,B,C))
& v6_rlvect_1(k6_vectsp10(A,B,C))
& v11_vectsp_1(k6_vectsp10(A,B,C),A)
& v12_vectsp_1(k6_vectsp10(A,B,C),A)
& l4_vectsp_1(k6_vectsp10(A,B,C),A) ) ) ).
fof(dt_k7_vectsp10,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)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_vectsp_5(D,A,B,k1_vectsp_7(A,B,k7_rlvect_2(B,C))) )
=> ( v1_funct_1(k7_vectsp10(A,B,C,D))
& v1_funct_2(k7_vectsp10(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(k7_vectsp10(A,B,C,D))
& v1_hahnban1(k7_vectsp10(A,B,C,D),A,B)
& v2_hahnban1(k7_vectsp10(A,B,C,D),A,B)
& ~ v1_realset1(k7_vectsp10(A,B,C,D))
& m2_relset_1(k7_vectsp10(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k8_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> m1_subset_1(k8_vectsp10(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k9_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k9_vectsp10(A,B,C))
& v11_vectsp_1(k9_vectsp10(A,B,C),A)
& m1_vectsp_4(k9_vectsp10(A,B,C),A,B) ) ) ).
fof(dt_k10_vectsp10,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)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k10_vectsp10(A,B,C,D))
& v1_funct_2(k10_vectsp10(A,B,C,D),u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A))
& v1_hahnban1(k10_vectsp10(A,B,C,D),A,k6_vectsp10(A,B,C))
& m2_relset_1(k10_vectsp10(A,B,C,D),u1_struct_0(k6_vectsp10(A,B,C)),u1_struct_0(A)) ) ) ).
fof(dt_k11_vectsp10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k11_vectsp10(A,B,C))
& v1_funct_2(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A))
& v1_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& v2_hahnban1(k11_vectsp10(A,B,C),A,k6_vectsp10(A,B,k9_vectsp10(A,B,C)))
& m2_relset_1(k11_vectsp10(A,B,C),u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C))),u1_struct_0(A)) ) ) ).
fof(d2_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> k2_vectsp10(A,B,C) = a_3_0_vectsp10(A,B,C) ) ) ) ).
fof(d9_vectsp10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> k8_vectsp10(A,B,C) = a_3_1_vectsp10(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_vectsp10,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)
& v4_group_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,B)
& l4_vectsp_1(C,B)
& m1_vectsp_4(D,B,C) )
=> ( r2_hidden(A,a_3_0_vectsp10(B,C,D))
<=> ? [E] :
( m2_vectsp_4(E,B,C,D)
& A = E ) ) ) ).
fof(fraenkel_a_3_1_vectsp10,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,B)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_vectsp10(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = E
& k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) = k1_rlvect_1(B) ) ) ) ).
%------------------------------------------------------------------------------