SET007 Axioms: SET007+215.ax
%------------------------------------------------------------------------------
% File : SET007+215 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Construction of a Bilinear Antisymmetric Form
% Version : [Urb08] axioms.
% English : Construction of a Bilinear Antisymmetric Form in symplectic vector
% space
% 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 : symsp_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 1356 ( 59 equ)
% Maximal formula atoms : 40 ( 19 avg)
% Number of connectives : 1551 ( 266 ~; 10 |;1002 &)
% ( 7 <=>; 266 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 14 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 0 con; 1-6 aty)
% Number of variables : 279 ( 273 !; 6 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_symsp_1,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] :
( l1_symsp_1(B,A)
& v1_symsp_1(B,A) ) ) ).
fof(rc2_symsp_1,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] :
( l1_symsp_1(B,A)
& ~ v3_struct_0(B) ) ) ).
fof(fc1_symsp_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& ~ 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(u1_struct_0(A),B),B)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B)
& m1_relset_1(F,B,B) )
=> ( ~ v3_struct_0(g1_symsp_1(A,B,C,D,E,F))
& v1_symsp_1(g1_symsp_1(A,B,C,D,E,F),A) ) ) ).
fof(rc3_symsp_1,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] :
( l1_symsp_1(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B) ) ) ).
fof(rc4_symsp_1,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] :
( l1_symsp_1(B,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)
& v1_symsp_1(B,A)
& v2_symsp_1(B,A) ) ) ).
fof(d1_symsp_1,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] :
( l1_symsp_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_symsp_1(A,B,C,D)
<=> r2_hidden(k4_tarski(C,D),u1_symsp_1(A,B)) ) ) ) ) ) ).
fof(d2_symsp_1,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)
& l1_symsp_1(B,A) )
=> ( v2_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ~ ( C != k1_rlvect_1(B)
& ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> r1_symsp_1(A,B,H,C) ) )
& ( r1_symsp_1(A,B,C,D)
=> r1_symsp_1(A,B,k6_vectsp_1(A,B,G,C),D) )
& ( ( r1_symsp_1(A,B,D,C)
& r1_symsp_1(A,B,E,C) )
=> r1_symsp_1(A,B,k4_rlvect_1(B,D,E),C) )
& ~ ( ~ r1_symsp_1(A,B,D,C)
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ~ r1_symsp_1(A,B,k6_rlvect_1(B,F,k6_vectsp_1(A,B,H,D)),C) ) )
& ( ( r1_symsp_1(A,B,C,k4_rlvect_1(B,D,E))
& r1_symsp_1(A,B,D,k4_rlvect_1(B,E,C)) )
=> r1_symsp_1(A,B,E,k4_rlvect_1(B,C,D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_symsp_1,axiom,
$true ).
fof(t2_symsp_1,axiom,
$true ).
fof(t3_symsp_1,axiom,
$true ).
fof(t4_symsp_1,axiom,
$true ).
fof(t5_symsp_1,axiom,
$true ).
fof(t6_symsp_1,axiom,
$true ).
fof(t7_symsp_1,axiom,
$true ).
fof(t8_symsp_1,axiom,
$true ).
fof(t9_symsp_1,axiom,
$true ).
fof(t10_symsp_1,axiom,
$true ).
fof(t11_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r1_symsp_1(A,B,k1_rlvect_1(B),C) ) ) ) ).
fof(t12_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_symsp_1(A,B,C,D)
=> r1_symsp_1(A,B,D,C) ) ) ) ) ) ).
fof(t13_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& r1_symsp_1(A,B,k4_rlvect_1(B,E,C),D)
& r1_symsp_1(A,B,E,D) ) ) ) ) ) ) ).
fof(t14_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& r1_symsp_1(A,B,E,D)
& r1_symsp_1(A,B,k4_rlvect_1(B,C,E),D) ) ) ) ) ) ) ).
fof(t15_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& E != k1_rlvect_1(A)
& ~ ( ~ r1_symsp_1(A,B,k6_vectsp_1(A,B,E,C),D)
& ~ r1_symsp_1(A,B,C,k6_vectsp_1(A,B,E,D)) ) ) ) ) ) ) ) ).
fof(t16_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_symsp_1(A,B,C,D)
=> r1_symsp_1(A,B,k5_rlvect_1(B,C),D) ) ) ) ) ) ).
fof(t17_symsp_1,axiom,
$true ).
fof(t18_symsp_1,axiom,
$true ).
fof(t19_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& r1_symsp_1(A,B,k4_rlvect_1(B,C,E),D)
& r1_symsp_1(A,B,k4_rlvect_1(B,k6_vectsp_1(A,B,k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)),C),E),D) ) ) ) ) ) ) ).
fof(t20_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_symsp_1(A,B,C,E)
& r1_symsp_1(A,B,F,D) )
=> ( r1_symsp_1(A,B,C,D)
| r1_symsp_1(A,B,F,E)
| ( ~ r1_symsp_1(A,B,k4_rlvect_1(B,C,F),D)
& ~ r1_symsp_1(A,B,k4_rlvect_1(B,C,F),E) ) ) ) ) ) ) ) ) ) ).
fof(t21_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ~ ( C != k1_rlvect_1(B)
& D != k1_rlvect_1(B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,E,C)
& ~ r1_symsp_1(A,B,E,D) ) ) ) ) ) ) ) ).
fof(t22_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& C != k1_rlvect_1(B)
& D != k1_rlvect_1(B)
& E != k1_rlvect_1(B)
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,F,C)
& ~ r1_symsp_1(A,B,F,D)
& ~ r1_symsp_1(A,B,F,E) ) ) ) ) ) ) ) ) ).
fof(t23_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_symsp_1(A,B,k6_rlvect_1(B,C,D),E)
& r1_symsp_1(A,B,k6_rlvect_1(B,C,F),E) )
=> r1_symsp_1(A,B,k6_rlvect_1(B,D,F),E) ) ) ) ) ) ) ) ).
fof(t24_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r1_symsp_1(A,B,k6_rlvect_1(B,E,k6_vectsp_1(A,B,F,C)),D)
& r1_symsp_1(A,B,k6_rlvect_1(B,E,k6_vectsp_1(A,B,G,C)),D) )
=> ( r1_symsp_1(A,B,C,D)
| F = G ) ) ) ) ) ) ) ) ) ).
fof(t25_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
=> r1_symsp_1(A,B,C,C) ) ) ) ) ).
fof(d3_symsp_1,axiom,
$true ).
fof(d4_symsp_1,axiom,
$true ).
fof(d5_symsp_1,axiom,
$true ).
fof(d6_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ( ~ r1_symsp_1(A,B,D,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( F = k1_symsp_1(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r1_symsp_1(A,B,k6_rlvect_1(B,E,k6_vectsp_1(A,B,G,D)),C)
=> F = G ) ) ) ) ) ) ) ) ) ) ).
fof(t26_symsp_1,axiom,
$true ).
fof(t27_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ( ~ r1_symsp_1(A,B,C,D)
=> r1_symsp_1(A,B,k6_rlvect_1(B,E,k6_vectsp_1(A,B,k1_symsp_1(A,B,D,C,E),C)),D) ) ) ) ) ) ) ).
fof(t28_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ~ r1_symsp_1(A,B,C,D)
=> k1_symsp_1(A,B,D,C,k6_vectsp_1(A,B,F,E)) = k10_group_1(A,F,k1_symsp_1(A,B,D,C,E)) ) ) ) ) ) ) ) ).
fof(t29_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ~ r1_symsp_1(A,B,C,D)
=> k1_symsp_1(A,B,D,C,k4_rlvect_1(B,E,F)) = k4_rlvect_1(A,k1_symsp_1(A,B,D,C,E),k1_symsp_1(A,B,D,C,F)) ) ) ) ) ) ) ) ).
fof(t30_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& F != k1_rlvect_1(A)
& k1_symsp_1(A,B,D,k6_vectsp_1(A,B,F,C),E) != k10_group_1(A,k4_vectsp_1(A,F),k1_symsp_1(A,B,D,C,E)) ) ) ) ) ) ) ) ).
fof(t31_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& F != k1_rlvect_1(A)
& k1_symsp_1(A,B,k6_vectsp_1(A,B,F,D),C,E) != k1_symsp_1(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t32_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_symsp_1(A,B,E,D)
=> ( r1_symsp_1(A,B,C,D)
| ( k1_symsp_1(A,B,D,k4_rlvect_1(B,C,E),F) = k1_symsp_1(A,B,D,C,F)
& k1_symsp_1(A,B,D,C,k4_rlvect_1(B,F,E)) = k1_symsp_1(A,B,D,C,F) ) ) ) ) ) ) ) ) ) ).
fof(t33_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_symsp_1(A,B,E,C)
& r1_symsp_1(A,B,E,F) )
=> ( r1_symsp_1(A,B,C,D)
| k1_symsp_1(A,B,k4_rlvect_1(B,D,E),C,F) = k1_symsp_1(A,B,D,C,F) ) ) ) ) ) ) ) ) ).
fof(t34_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ( r1_symsp_1(A,B,k6_rlvect_1(B,E,C),D)
=> ( r1_symsp_1(A,B,C,D)
| k1_symsp_1(A,B,D,C,E) = k2_group_1(A) ) ) ) ) ) ) ) ).
fof(t35_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ~ r1_symsp_1(A,B,C,D)
=> k1_symsp_1(A,B,D,C,C) = k2_group_1(A) ) ) ) ) ) ).
fof(t36_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ( ~ r1_symsp_1(A,B,C,D)
=> ( r1_symsp_1(A,B,E,D)
<=> k1_symsp_1(A,B,D,C,E) = k1_rlvect_1(A) ) ) ) ) ) ) ) ).
fof(t37_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,E,D)
& k10_group_1(A,k1_symsp_1(A,B,D,C,F),k4_vectsp_1(A,k1_symsp_1(A,B,D,C,E))) != k1_symsp_1(A,B,D,E,F) ) ) ) ) ) ) ) ).
fof(t38_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,E,D)
& k1_symsp_1(A,B,D,C,E) != k4_vectsp_1(A,k1_symsp_1(A,B,D,E,C)) ) ) ) ) ) ) ).
fof(t39_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ( r1_symsp_1(A,B,C,k4_rlvect_1(B,E,D))
=> ( r1_symsp_1(A,B,C,D)
| k1_symsp_1(A,B,D,C,E) = k1_symsp_1(A,B,E,C,D) ) ) ) ) ) ) ) ).
fof(t40_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,E,D)
& k1_symsp_1(A,B,E,D,C) != k10_group_1(A,k5_rlvect_1(A,k4_vectsp_1(A,k1_symsp_1(A,B,D,C,E))),k1_symsp_1(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t41_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,C,E)
& ~ r1_symsp_1(A,B,F,D)
& ~ r1_symsp_1(A,B,F,E)
& k10_group_1(A,k1_symsp_1(A,B,C,D,E),k1_symsp_1(A,B,F,E,D)) != k10_group_1(A,k1_symsp_1(A,B,D,C,F),k1_symsp_1(A,B,E,F,C)) ) ) ) ) ) ) ) ).
fof(t42_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,C,E)
& ~ r1_symsp_1(A,B,F,D)
& ~ r1_symsp_1(A,B,F,E)
& k10_group_1(A,k1_symsp_1(A,B,D,F,C),k1_symsp_1(A,B,C,D,E)) != k10_group_1(A,k1_symsp_1(A,B,E,F,C),k1_symsp_1(A,B,F,D,E)) ) ) ) ) ) ) ) ).
fof(t43_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [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(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,C,E)
& ~ r1_symsp_1(A,B,F,D)
& ~ r1_symsp_1(A,B,F,E)
& ~ r1_symsp_1(A,B,G,D)
& k10_group_1(A,k10_group_1(A,k1_symsp_1(A,B,D,G,C),k1_symsp_1(A,B,C,D,E)),k1_symsp_1(A,B,E,C,H)) != k10_group_1(A,k10_group_1(A,k1_symsp_1(A,B,D,G,F),k1_symsp_1(A,B,F,D,E)),k1_symsp_1(A,B,E,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t44_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,C,D)
& ~ r1_symsp_1(A,B,E,D)
& ~ r1_symsp_1(A,B,F,D)
& k10_group_1(A,k1_symsp_1(A,B,D,C,E),k1_symsp_1(A,B,E,D,F)) != k10_group_1(A,k5_rlvect_1(A,k1_symsp_1(A,B,D,C,F)),k1_symsp_1(A,B,F,D,E)) ) ) ) ) ) ) ) ).
fof(d7_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,F,E)
& k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( ? [H] :
( m1_subset_1(H,u1_struct_0(B))
& ~ r1_symsp_1(A,B,H,E)
& ~ r1_symsp_1(A,B,H,C) )
=> ( G = k2_symsp_1(A,B,C,D,E,F)
<=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,H,E)
& ~ r1_symsp_1(A,B,H,C)
& G != k10_group_1(A,k10_group_1(A,k1_symsp_1(A,B,E,F,H),k1_symsp_1(A,B,H,E,C)),k1_symsp_1(A,B,C,H,D)) ) ) ) )
& ( ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( r1_symsp_1(A,B,H,E)
| r1_symsp_1(A,B,H,C) ) )
=> ( G = k2_symsp_1(A,B,C,D,E,F)
<=> G = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_symsp_1,axiom,
$true ).
fof(t46_symsp_1,axiom,
$true ).
fof(t47_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( E = k1_rlvect_1(B)
=> ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) = k1_rlvect_1(A)
| r1_symsp_1(A,B,C,D)
| k2_symsp_1(A,B,E,F,D,C) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ).
fof(t48_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& ~ ( k2_symsp_1(A,B,E,F,D,C) = k1_rlvect_1(A)
<=> r1_symsp_1(A,B,F,E) ) ) ) ) ) ) ) ) ).
fof(t49_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& k2_symsp_1(A,B,E,F,D,C) != k5_rlvect_1(A,k2_symsp_1(A,B,F,E,D,C)) ) ) ) ) ) ) ) ).
fof(t50_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& k2_symsp_1(A,B,E,k6_vectsp_1(A,B,G,F),D,C) != k10_group_1(A,G,k2_symsp_1(A,B,E,F,D,C)) ) ) ) ) ) ) ) ) ).
fof(t51_symsp_1,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)
& v2_symsp_1(B,A)
& l1_symsp_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(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ r1_symsp_1(A,B,C,D)
& k2_symsp_1(A,B,E,k4_rlvect_1(B,F,G),D,C) != k4_rlvect_1(A,k2_symsp_1(A,B,E,F,D,C),k2_symsp_1(A,B,E,G,D,C)) ) ) ) ) ) ) ) ) ).
fof(dt_l1_symsp_1,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] :
( l1_symsp_1(B,A)
=> l4_vectsp_1(B,A) ) ) ).
fof(existence_l1_symsp_1,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] : l1_symsp_1(B,A) ) ).
fof(abstractness_v1_symsp_1,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)
& l1_symsp_1(B,A) )
=> ( v1_symsp_1(B,A)
=> B = g1_symsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B),u1_symsp_1(A,B)) ) ) ).
fof(dt_k1_symsp_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,u1_struct_0(B)) )
=> m1_subset_1(k1_symsp_1(A,B,C,D,E),u1_struct_0(A)) ) ).
fof(dt_k2_symsp_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& v2_symsp_1(B,A)
& l1_symsp_1(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B)) )
=> m1_subset_1(k2_symsp_1(A,B,C,D,E,F),u1_struct_0(A)) ) ).
fof(dt_u1_symsp_1,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)
& l1_symsp_1(B,A) )
=> m2_relset_1(u1_symsp_1(A,B),u1_struct_0(B),u1_struct_0(B)) ) ).
fof(dt_g1_symsp_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& 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(u1_struct_0(A),B),B)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B)
& m1_relset_1(F,B,B) )
=> ( v1_symsp_1(g1_symsp_1(A,B,C,D,E,F),A)
& l1_symsp_1(g1_symsp_1(A,B,C,D,E,F),A) ) ) ).
fof(free_g1_symsp_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& 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(u1_struct_0(A),B),B)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B)
& m1_relset_1(F,B,B) )
=> ! [G,H,I,J,K,L] :
( g1_symsp_1(A,B,C,D,E,F) = g1_symsp_1(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
%------------------------------------------------------------------------------