SET007 Axioms: SET007+241.ax
%------------------------------------------------------------------------------
% File : SET007+241 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Rings and Left-, Right-, and Bi-Modules over a Ring
% 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 : vectsp_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 154 ( 68 unt; 0 def)
% Number of atoms : 1283 ( 127 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 1300 ( 171 ~; 1 |; 931 &)
% ( 8 <=>; 189 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 4 con; 0-7 aty)
% Number of variables : 243 ( 223 !; 20 ?)
% 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(cc1_vectsp_2,axiom,
! [A] :
( l1_vectsp_1(A)
=> ( ( ~ v3_struct_0(A)
& v1_vectsp_2(A) )
=> ( ~ v3_struct_0(A)
& v2_group_1(A)
& v6_vectsp_1(A)
& v8_vectsp_1(A) ) ) ) ).
fof(rc1_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A) ) ).
fof(rc2_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A) ) ).
fof(rc3_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A) ) ).
fof(rc4_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A) ) ).
fof(rc5_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v2_vectsp_2(A) ) ).
fof(rc6_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A) ) ).
fof(rc7_vectsp_2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A) ) ).
fof(cc2_vectsp_2,axiom,
! [A] :
( l1_vectsp_1(A)
=> ( ( ~ v3_struct_0(A)
& v7_group_1(A)
& v8_vectsp_1(A) )
=> ( ~ v3_struct_0(A)
& v2_group_1(A)
& v6_vectsp_1(A)
& v8_vectsp_1(A) ) ) ) ).
fof(cc3_vectsp_2,axiom,
! [A] :
( l1_vectsp_1(A)
=> ( ( ~ v3_struct_0(A)
& v7_group_1(A)
& v6_vectsp_1(A) )
=> ( ~ v3_struct_0(A)
& v2_group_1(A)
& v6_vectsp_1(A)
& v8_vectsp_1(A) ) ) ) ).
fof(rc8_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l1_vectsp_2(B,A)
& v3_vectsp_2(B,A) ) ) ).
fof(rc9_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l1_vectsp_2(B,A)
& ~ v3_struct_0(B) ) ) ).
fof(fc1_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( l1_struct_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& m1_subset_1(D,B)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
=> ( ~ v3_struct_0(g1_vectsp_2(A,B,C,D,E))
& v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) ) ) ).
fof(rc10_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] :
( l2_vectsp_2(C,A,B)
& v4_vectsp_2(C,A,B) ) ) ).
fof(rc11_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] :
( l2_vectsp_2(C,A,B)
& ~ v3_struct_0(C) ) ) ).
fof(fc2_vectsp_2,axiom,
! [A,B,C,D,E,F,G] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m1_relset_1(D,k2_zfmisc_1(C,C),C)
& m1_subset_1(E,C)
& v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
& m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
=> ( ~ v3_struct_0(g2_vectsp_2(A,B,C,D,E,F,G))
& v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) ) ) ).
fof(rc12_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_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) ) ) ).
fof(rc13_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l1_vectsp_2(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v3_vectsp_2(B,A) ) ) ).
fof(rc14_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ? [C] :
( l2_vectsp_2(C,A,B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_vectsp_2(C,A,B) ) ) ).
fof(rc15_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_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) ) ) ).
fof(fc3_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k4_vectsp_2(A))
& v3_rlvect_1(k4_vectsp_2(A))
& v4_rlvect_1(k4_vectsp_2(A))
& v5_rlvect_1(k4_vectsp_2(A))
& v6_rlvect_1(k4_vectsp_2(A))
& v11_vectsp_1(k4_vectsp_2(A),A)
& v12_vectsp_1(k4_vectsp_2(A),A) ) ) ).
fof(rc16_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l1_vectsp_2(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v3_vectsp_2(B,A)
& v5_vectsp_2(B,A) ) ) ).
fof(fc4_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k5_vectsp_2(A))
& v3_rlvect_1(k5_vectsp_2(A))
& v4_rlvect_1(k5_vectsp_2(A))
& v5_rlvect_1(k5_vectsp_2(A))
& v6_rlvect_1(k5_vectsp_2(A))
& v3_vectsp_2(k5_vectsp_2(A),A)
& v5_vectsp_2(k5_vectsp_2(A),A) ) ) ).
fof(rc17_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ? [C] :
( l2_vectsp_2(C,A,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,A)
& v4_vectsp_2(C,A,B)
& v5_vectsp_2(C,B)
& v6_vectsp_2(C,A,B) ) ) ).
fof(fc5_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ( ~ v3_struct_0(k9_vectsp_2(A,B))
& v3_rlvect_1(k9_vectsp_2(A,B))
& v4_rlvect_1(k9_vectsp_2(A,B))
& v5_rlvect_1(k9_vectsp_2(A,B))
& v6_rlvect_1(k9_vectsp_2(A,B))
& v12_vectsp_1(k9_vectsp_2(A,B),A)
& v4_vectsp_2(k9_vectsp_2(A,B),A,B)
& v5_vectsp_2(k9_vectsp_2(A,B),B)
& v6_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) ).
fof(d1_vectsp_2,axiom,
$true ).
fof(d2_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_vectsp_1(A) )
=> ( v1_vectsp_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k1_group_1(A,B,k2_vectsp_1(A)) = B
& k1_group_1(A,k2_vectsp_1(A),B) = B ) ) ) ) ).
fof(t1_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)
& k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))
& k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
& k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
& k1_group_1(A,B,k2_group_1(A)) = B
& k1_group_1(A,k2_group_1(A),B) = B
& k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
& k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
& k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) ) ) ) ).
fof(d3_vectsp_2,axiom,
$true ).
fof(d4_vectsp_2,axiom,
$true ).
fof(d5_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_vectsp_1(A) )
=> ( v2_vectsp_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_group_1(A,B,C) = k1_rlvect_1(A)
& B != k1_rlvect_1(A)
& C != k1_rlvect_1(A) ) ) ) ) ) ).
fof(t2_vectsp_2,axiom,
$true ).
fof(t3_vectsp_2,axiom,
$true ).
fof(t4_vectsp_2,axiom,
$true ).
fof(t5_vectsp_2,axiom,
$true ).
fof(t6_vectsp_2,axiom,
$true ).
fof(t7_vectsp_2,axiom,
$true ).
fof(t8_vectsp_2,axiom,
$true ).
fof(t9_vectsp_2,axiom,
$true ).
fof(t10_vectsp_2,axiom,
$true ).
fof(t11_vectsp_2,axiom,
$true ).
fof(t12_vectsp_2,axiom,
$true ).
fof(t13_vectsp_2,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) )
=> ( ~ 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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v2_vectsp_2(A)
& l3_vectsp_1(A) ) ) ).
fof(t14_vectsp_2,axiom,
$true ).
fof(t15_vectsp_2,axiom,
$true ).
fof(t16_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ ( B != k1_rlvect_1(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_group_1(A,B,C) != k2_group_1(A) ) )
& k1_rlvect_1(A) != k2_group_1(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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) ) ) ) ).
fof(t17_vectsp_2,axiom,
$true ).
fof(t18_vectsp_2,axiom,
$true ).
fof(t19_vectsp_2,axiom,
$true ).
fof(t20_vectsp_2,axiom,
$true ).
fof(t21_vectsp_2,axiom,
$true ).
fof(t22_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( k4_rlvect_1(A,B,C) = D
=> B = k6_rlvect_1(A,D,C) )
& ( B = k6_rlvect_1(A,D,C)
=> k4_rlvect_1(A,B,C) = D )
& ( k4_rlvect_1(A,B,C) = D
=> C = k6_rlvect_1(A,D,B) )
& ( C = k6_rlvect_1(A,D,B)
=> k4_rlvect_1(A,B,C) = D ) ) ) ) ) ) ).
fof(t23_vectsp_2,axiom,
$true ).
fof(t24_vectsp_2,axiom,
$true ).
fof(t25_vectsp_2,axiom,
$true ).
fof(t26_vectsp_2,axiom,
$true ).
fof(t27_vectsp_2,axiom,
$true ).
fof(t28_vectsp_2,axiom,
$true ).
fof(t29_vectsp_2,axiom,
$true ).
fof(t30_vectsp_2,axiom,
$true ).
fof(t31_vectsp_2,axiom,
$true ).
fof(t32_vectsp_2,axiom,
$true ).
fof(t33_vectsp_2,axiom,
$true ).
fof(t34_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k1_rlvect_1(A)
<=> k5_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(t35_vectsp_2,axiom,
$true ).
fof(t36_vectsp_2,axiom,
$true ).
fof(t37_vectsp_2,axiom,
$true ).
fof(t38_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k4_rlvect_1(A,C,D)
& B = k4_rlvect_1(A,D,C) ) ) ) ) ).
fof(t39_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_group_1(A,B,C) = k2_group_1(A)
=> ( B != k1_rlvect_1(A)
& C != k1_rlvect_1(A) ) ) ) ) ) ).
fof(t40_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( B != k1_rlvect_1(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_group_1(A,C,B) != k2_group_1(A) ) ) ) ) ).
fof(t41_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_group_1(A,B,C) = k2_group_1(A)
=> k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ).
fof(t42_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k1_group_1(A,B,C) = k1_group_1(A,B,D)
=> ( B = k1_rlvect_1(A)
| C = D ) ) ) ) ) ) ).
fof(d6_vectsp_2,axiom,
$true ).
fof(d7_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k1_vectsp_2(A,B)
<=> k1_group_1(A,B,C) = k2_group_1(A) ) ) ) ) ) ).
fof(d8_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_vectsp_2(A,B,C) = k1_group_1(A,B,k1_vectsp_2(A,C)) ) ) ) ).
fof(t43_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ( k1_group_1(A,B,k1_vectsp_2(A,B)) = k2_group_1(A)
& k1_group_1(A,k1_vectsp_2(A,B),B) = k2_group_1(A) ) ) ) ) ).
fof(t44_vectsp_2,axiom,
$true ).
fof(t45_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_group_1(A,B,C) = k2_group_1(A)
=> ( B = k1_vectsp_2(A,C)
& C = k1_vectsp_2(A,B) ) ) ) ) ) ).
fof(t46_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != k1_rlvect_1(A)
& C != k1_rlvect_1(A)
& k1_group_1(A,k1_vectsp_2(A,B),k1_vectsp_2(A,C)) != k1_vectsp_2(A,k1_group_1(A,C,B)) ) ) ) ) ).
fof(t47_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_group_1(A,B,C) = k1_rlvect_1(A)
& B != k1_rlvect_1(A)
& C != k1_rlvect_1(A) ) ) ) ) ).
fof(t48_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( B != k1_rlvect_1(A)
& k1_vectsp_2(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(t49_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> k1_vectsp_2(A,k1_vectsp_2(A,B)) = B ) ) ) ).
fof(t50_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ( k2_vectsp_2(A,k2_group_1(A),B) = k1_vectsp_2(A,B)
& k2_vectsp_2(A,k2_group_1(A),k1_vectsp_2(A,B)) = B ) ) ) ) ).
fof(t51_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ( k1_group_1(A,B,k2_vectsp_2(A,k2_group_1(A),B)) = k2_group_1(A)
& k1_group_1(A,k2_vectsp_2(A,k2_group_1(A),B),B) = k2_group_1(A) ) ) ) ) ).
fof(t52_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> k2_vectsp_2(A,B,B) = k2_group_1(A) ) ) ) ).
fof(t53_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( B != k1_rlvect_1(A)
& C != k1_rlvect_1(A)
& k2_vectsp_2(A,D,B) != k2_vectsp_2(A,k1_group_1(A,D,C),k1_group_1(A,B,C)) ) ) ) ) ) ).
fof(t54_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ( k5_rlvect_1(A,k2_vectsp_2(A,C,B)) = k2_vectsp_2(A,k5_rlvect_1(A,C),B)
& k2_vectsp_2(A,C,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_vectsp_2(A,C,B)) ) ) ) ) ) ).
fof(t55_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> ( k4_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) = k2_vectsp_2(A,k4_rlvect_1(A,C,D),B)
& k6_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) = k2_vectsp_2(A,k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) ).
fof(t56_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( B != k1_rlvect_1(A)
& C != k1_rlvect_1(A)
& k2_vectsp_2(A,D,k2_vectsp_2(A,B,C)) != k2_vectsp_2(A,k1_group_1(A,D,C),B) ) ) ) ) ) ).
fof(t57_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != k1_rlvect_1(A)
=> k1_group_1(A,k2_vectsp_2(A,C,B),B) = C ) ) ) ) ).
fof(d9_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k3_vectsp_2(A) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ).
fof(d10_vectsp_2,axiom,
$true ).
fof(d11_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> k4_vectsp_2(A) = g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) ).
fof(d12_vectsp_2,axiom,
$true ).
fof(d13_vectsp_2,axiom,
$true ).
fof(d14_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> k5_vectsp_2(A) = g1_vectsp_2(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) ) ).
fof(d15_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k6_vectsp_2(A,B,C,D) = k2_binop_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_vectsp_2(A,B),D,C) ) ) ) ) ).
fof(d16_vectsp_2,axiom,
$true ).
fof(d17_vectsp_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
& m2_relset_1(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) )
=> A = k7_vectsp_2 ) ).
fof(d18_vectsp_2,axiom,
! [A] :
( m1_subset_1(A,k1_tarski(k1_xboole_0))
=> A = k8_vectsp_2 ) ).
fof(d19_vectsp_2,axiom,
$true ).
fof(d20_vectsp_2,axiom,
$true ).
fof(d21_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> k9_vectsp_2(A,B) = g2_vectsp_2(A,B,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0)),k9_funct_3(k1_tarski(k1_xboole_0),u1_struct_0(B))) ) ) ).
fof(t58_vectsp_2,axiom,
$true ).
fof(t59_vectsp_2,axiom,
$true ).
fof(t60_vectsp_2,axiom,
$true ).
fof(t61_vectsp_2,axiom,
$true ).
fof(t62_vectsp_2,axiom,
$true ).
fof(t63_vectsp_2,axiom,
$true ).
fof(t64_vectsp_2,axiom,
$true ).
fof(t65_vectsp_2,axiom,
$true ).
fof(t66_vectsp_2,axiom,
$true ).
fof(t67_vectsp_2,axiom,
$true ).
fof(t68_vectsp_2,axiom,
$true ).
fof(t69_vectsp_2,axiom,
$true ).
fof(t70_vectsp_2,axiom,
$true ).
fof(t71_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k4_vectsp_2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k4_vectsp_2(A)))
=> ( k6_vectsp_1(A,k4_vectsp_2(A),B,k4_rlvect_1(k4_vectsp_2(A),D,E)) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),B,E))
& k6_vectsp_1(A,k4_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),C,D))
& k6_vectsp_1(A,k4_vectsp_2(A),k1_group_1(A,B,C),D) = k6_vectsp_1(A,k4_vectsp_2(A),B,k6_vectsp_1(A,k4_vectsp_2(A),C,D))
& k6_vectsp_1(A,k4_vectsp_2(A),k2_group_1(A),D) = D ) ) ) ) ) ) ).
fof(t72_vectsp_2,axiom,
$true ).
fof(t73_vectsp_2,axiom,
$true ).
fof(t74_vectsp_2,axiom,
$true ).
fof(t75_vectsp_2,axiom,
$true ).
fof(t76_vectsp_2,axiom,
$true ).
fof(t77_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_vectsp_2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_vectsp_2(A)))
=> ( k6_vectsp_2(A,k5_vectsp_2(A),B,k4_rlvect_1(k5_vectsp_2(A),D,E)) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),B,E))
& k6_vectsp_2(A,k5_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),C,D))
& k6_vectsp_2(A,k5_vectsp_2(A),k1_group_1(A,C,B),D) = k6_vectsp_2(A,k5_vectsp_2(A),B,k6_vectsp_2(A,k5_vectsp_2(A),C,D))
& k6_vectsp_2(A,k5_vectsp_2(A),k2_group_1(A),D) = D ) ) ) ) ) ) ).
fof(d22_vectsp_2,axiom,
$true ).
fof(d23_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) )
=> ( v5_vectsp_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( k6_vectsp_2(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,C,F))
& k6_vectsp_2(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,D,E))
& k6_vectsp_2(A,B,k1_group_1(A,D,C),E) = k6_vectsp_2(A,B,C,k6_vectsp_2(A,B,D,E))
& k6_vectsp_2(A,B,k2_group_1(A),E) = E ) ) ) ) ) ) ) ) ).
fof(d24_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_vectsp_2(C,A,B) )
=> ( v6_vectsp_2(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,E,F)) = k6_vectsp_2(B,C,E,k6_vectsp_1(A,C,D,F)) ) ) ) ) ) ) ) ).
fof(t78_vectsp_2,axiom,
$true ).
fof(t79_vectsp_2,axiom,
$true ).
fof(t80_vectsp_2,axiom,
$true ).
fof(t81_vectsp_2,axiom,
$true ).
fof(t82_vectsp_2,axiom,
$true ).
fof(t83_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_vectsp_2(C,A,B) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(C))
=> ( k6_vectsp_1(A,C,D,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,D,I))
& k6_vectsp_1(A,C,k4_rlvect_1(A,D,E),H) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,E,H))
& k6_vectsp_1(A,C,k1_group_1(A,D,E),H) = k6_vectsp_1(A,C,D,k6_vectsp_1(A,C,E,H))
& k6_vectsp_1(A,C,k2_group_1(A),H) = H
& k6_vectsp_2(B,C,F,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,F,I))
& k6_vectsp_2(B,C,k4_rlvect_1(B,F,G),H) = k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,G,H))
& k6_vectsp_2(B,C,k1_group_1(B,G,F),H) = k6_vectsp_2(B,C,F,k6_vectsp_2(B,C,G,H))
& k6_vectsp_2(B,C,k2_group_1(B),H) = H
& k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,F,H)) = k6_vectsp_2(B,C,F,k6_vectsp_1(A,C,D,H)) ) ) ) ) ) ) )
<=> ( v5_vectsp_2(C,B)
& v12_vectsp_1(C,A)
& v6_vectsp_2(C,A,B) ) ) ) ) ) ).
fof(t84_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ( ~ v3_struct_0(k9_vectsp_2(A,B))
& v3_rlvect_1(k9_vectsp_2(A,B))
& v4_rlvect_1(k9_vectsp_2(A,B))
& v5_rlvect_1(k9_vectsp_2(A,B))
& v6_rlvect_1(k9_vectsp_2(A,B))
& v12_vectsp_1(k9_vectsp_2(A,B),A)
& v5_vectsp_2(k9_vectsp_2(A,B),B)
& v6_vectsp_2(k9_vectsp_2(A,B),A,B)
& l2_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) ) ).
fof(t85_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_vectsp_1(A) )
=> ( v1_vectsp_2(A)
=> k2_vectsp_1(A) = k2_group_1(A) ) ) ).
fof(dt_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_vectsp_2(B,A)
=> l1_rlvect_1(B) ) ) ).
fof(existence_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] : l1_vectsp_2(B,A) ) ).
fof(dt_l2_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ! [C] :
( l2_vectsp_2(C,A,B)
=> ( l4_vectsp_1(C,A)
& l1_vectsp_2(C,B) ) ) ) ).
fof(existence_l2_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] : l2_vectsp_2(C,A,B) ) ).
fof(abstractness_v3_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_vectsp_2(B,A) )
=> ( v3_vectsp_2(B,A)
=> B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) ).
fof(abstractness_v4_vectsp_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& l2_vectsp_2(C,A,B) )
=> ( v4_vectsp_2(C,A,B)
=> C = g2_vectsp_2(A,B,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(B,C),u1_vectsp_2(B,C)) ) ) ).
fof(dt_k1_vectsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_vectsp_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_vectsp_2(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_vectsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ( ~ v3_struct_0(k3_vectsp_2(A))
& v1_rlvect_1(k3_vectsp_2(A))
& v3_rlvect_1(k3_vectsp_2(A))
& v4_rlvect_1(k3_vectsp_2(A))
& v5_rlvect_1(k3_vectsp_2(A))
& v6_rlvect_1(k3_vectsp_2(A))
& l1_rlvect_1(k3_vectsp_2(A)) ) ) ).
fof(dt_k4_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k4_vectsp_2(A))
& v3_rlvect_1(k4_vectsp_2(A))
& v4_rlvect_1(k4_vectsp_2(A))
& v5_rlvect_1(k4_vectsp_2(A))
& v6_rlvect_1(k4_vectsp_2(A))
& v11_vectsp_1(k4_vectsp_2(A),A)
& l4_vectsp_1(k4_vectsp_2(A),A) ) ) ).
fof(dt_k5_vectsp_2,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)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k5_vectsp_2(A))
& v3_rlvect_1(k5_vectsp_2(A))
& v4_rlvect_1(k5_vectsp_2(A))
& v5_rlvect_1(k5_vectsp_2(A))
& v6_rlvect_1(k5_vectsp_2(A))
& v3_vectsp_2(k5_vectsp_2(A),A)
& l1_vectsp_2(k5_vectsp_2(A),A) ) ) ).
fof(dt_k6_vectsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_vectsp_2(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k6_vectsp_2(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k7_vectsp_2,axiom,
( v1_funct_1(k7_vectsp_2)
& v1_funct_2(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
& m2_relset_1(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) ) ).
fof(dt_k8_vectsp_2,axiom,
m1_subset_1(k8_vectsp_2,k1_tarski(k1_xboole_0)) ).
fof(dt_k9_vectsp_2,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)
& v6_vectsp_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)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ( ~ v3_struct_0(k9_vectsp_2(A,B))
& v3_rlvect_1(k9_vectsp_2(A,B))
& v4_rlvect_1(k9_vectsp_2(A,B))
& v5_rlvect_1(k9_vectsp_2(A,B))
& v6_rlvect_1(k9_vectsp_2(A,B))
& v4_vectsp_2(k9_vectsp_2(A,B),A,B)
& l2_vectsp_2(k9_vectsp_2(A,B),A,B) ) ) ).
fof(dt_u1_vectsp_2,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_vectsp_2(B,A) )
=> ( v1_funct_1(u1_vectsp_2(A,B))
& v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B))
& m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) ) ) ).
fof(dt_g1_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( l1_struct_0(A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& m1_subset_1(D,B)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
=> ( v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A)
& l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) ) ) ).
fof(free_g1_vectsp_2,axiom,
! [A,B,C,D,E] :
( ( l1_struct_0(A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& m1_subset_1(D,B)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B)
& m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) )
=> ! [F,G,H,I,J] :
( g1_vectsp_2(A,B,C,D,E) = g1_vectsp_2(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(dt_g2_vectsp_2,axiom,
! [A,B,C,D,E,F,G] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m1_relset_1(D,k2_zfmisc_1(C,C),C)
& m1_subset_1(E,C)
& v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
& m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
=> ( v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B)
& l2_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) ) ) ).
fof(free_g2_vectsp_2,axiom,
! [A,B,C,D,E,F,G] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m1_relset_1(D,k2_zfmisc_1(C,C),C)
& m1_subset_1(E,C)
& v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C)
& v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C)
& m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) )
=> ! [H,I,J,K,L,M,N] :
( g2_vectsp_2(A,B,C,D,E,F,G) = g2_vectsp_2(H,I,J,K,L,M,N)
=> ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
%------------------------------------------------------------------------------