SET007 Axioms: SET007+216.ax
%------------------------------------------------------------------------------
% File : SET007+216 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Construction of a Bilinear Symmetric Form
% Version : [Urb08] axioms.
% English : Construction of a Bilinear Symmetric Form in orthogonal 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 : ortsp_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 57 ( 19 unt; 0 def)
% Number of atoms : 1048 ( 39 equ)
% Maximal formula atoms : 45 ( 18 avg)
% Number of connectives : 1186 ( 195 ~; 7 |; 747 &)
% ( 6 <=>; 231 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-6 aty)
% Number of variables : 215 ( 213 !; 2 ?)
% 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_ortsp_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)
& v1_ortsp_1(B,A) ) ) ).
fof(d1_ortsp_1,axiom,
$true ).
fof(d2_ortsp_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) )
=> ( v1_ortsp_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(A))
=> ( ~ ( C != k1_rlvect_1(B)
& D != k1_rlvect_1(B)
& E != k1_rlvect_1(B)
& F != k1_rlvect_1(B)
& ! [I] :
( m1_subset_1(I,u1_struct_0(B))
=> ~ ( ~ r1_symsp_1(A,B,I,C)
& ~ r1_symsp_1(A,B,I,D)
& ~ r1_symsp_1(A,B,I,E)
& ~ r1_symsp_1(A,B,I,F) ) ) )
& ( r1_symsp_1(A,B,C,D)
=> r1_symsp_1(A,B,k6_vectsp_1(A,B,H,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)
& ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ~ r1_symsp_1(A,B,k6_rlvect_1(B,G,k6_vectsp_1(A,B,I,D)),C) ) )
& ( ( r1_symsp_1(A,B,C,k6_rlvect_1(B,D,E))
& r1_symsp_1(A,B,D,k6_rlvect_1(B,E,C)) )
=> r1_symsp_1(A,B,E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_ortsp_1,axiom,
$true ).
fof(t2_ortsp_1,axiom,
$true ).
fof(t3_ortsp_1,axiom,
$true ).
fof(t4_ortsp_1,axiom,
$true ).
fof(t5_ortsp_1,axiom,
$true ).
fof(t6_ortsp_1,axiom,
$true ).
fof(t7_ortsp_1,axiom,
$true ).
fof(t8_ortsp_1,axiom,
$true ).
fof(t9_ortsp_1,axiom,
$true ).
fof(t10_ortsp_1,axiom,
$true ).
fof(t11_ortsp_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)
& v1_ortsp_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_ortsp_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)
& v1_ortsp_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_ortsp_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)
& v1_ortsp_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_ortsp_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)
& v1_ortsp_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_ortsp_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)
& v1_ortsp_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_ortsp_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)
& v1_ortsp_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_ortsp_1,axiom,
$true ).
fof(t18_ortsp_1,axiom,
$true ).
fof(t19_ortsp_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)
& v1_ortsp_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(t20_ortsp_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)
& v1_ortsp_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(t21_ortsp_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)
& v1_ortsp_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,C)
& r1_symsp_1(A,B,D,D) )
=> r1_symsp_1(A,B,k4_rlvect_1(B,C,D),k6_rlvect_1(B,C,D)) ) ) ) ) ) ).
fof(t22_ortsp_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)
& v1_ortsp_1(B,A)
& l1_symsp_1(B,A) )
=> ~ ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A)
& ~ ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> C = k1_rlvect_1(B) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r1_symsp_1(A,B,C,C) ) ) ) ) ).
fof(d3_ortsp_1,axiom,
$true ).
fof(d4_ortsp_1,axiom,
$true ).
fof(d5_ortsp_1,axiom,
$true ).
fof(d6_ortsp_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)
& v1_ortsp_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_ortsp_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(t23_ortsp_1,axiom,
$true ).
fof(t24_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E),C)),D) ) ) ) ) ) ) ).
fof(t25_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,k6_vectsp_1(A,B,F,E)) = k10_group_1(A,F,k1_ortsp_1(A,B,D,C,E)) ) ) ) ) ) ) ) ).
fof(t26_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,k4_rlvect_1(B,E,F)) = k4_rlvect_1(A,k1_ortsp_1(A,B,D,C,E),k1_ortsp_1(A,B,D,C,F)) ) ) ) ) ) ) ) ).
fof(t27_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,k6_vectsp_1(A,B,F,C),E) != k10_group_1(A,k4_vectsp_1(A,F),k1_ortsp_1(A,B,D,C,E)) ) ) ) ) ) ) ) ).
fof(t28_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,k6_vectsp_1(A,B,F,D),C,E) != k1_ortsp_1(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t29_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,k4_rlvect_1(B,C,E),F) = k1_ortsp_1(A,B,D,C,F)
& k1_ortsp_1(A,B,D,C,k4_rlvect_1(B,F,E)) = k1_ortsp_1(A,B,D,C,F) ) ) ) ) ) ) ) ) ) ).
fof(t30_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,k4_rlvect_1(B,D,E),C,F) = k1_ortsp_1(A,B,D,C,F) ) ) ) ) ) ) ) ) ).
fof(t31_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E) = k2_group_1(A) ) ) ) ) ) ) ) ).
fof(t32_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,C) = k2_group_1(A) ) ) ) ) ) ).
fof(t33_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E) = k1_rlvect_1(A) ) ) ) ) ) ) ) ).
fof(t34_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,F),k4_vectsp_1(A,k1_ortsp_1(A,B,D,C,E))) != k1_ortsp_1(A,B,D,E,F) ) ) ) ) ) ) ) ).
fof(t35_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E) != k4_vectsp_1(A,k1_ortsp_1(A,B,D,E,C)) ) ) ) ) ) ) ).
fof(t36_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E) = k5_rlvect_1(A,k1_ortsp_1(A,B,E,C,D)) ) ) ) ) ) ) ) ).
fof(t37_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,E,D,C) != k10_group_1(A,k4_vectsp_1(A,k1_ortsp_1(A,B,D,C,E)),k1_ortsp_1(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t38_ortsp_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)
& v1_ortsp_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,C,E)
& ~ r1_symsp_1(A,B,F,D)
& ~ r1_symsp_1(A,B,F,E)
& k10_group_1(A,k1_ortsp_1(A,B,D,F,C),k1_ortsp_1(A,B,C,D,E)) != k10_group_1(A,k1_ortsp_1(A,B,F,D,E),k1_ortsp_1(A,B,E,F,C)) ) ) ) ) ) ) ) ).
fof(t39_ortsp_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)
& v1_ortsp_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))
=> ~ ( ~ 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_ortsp_1(A,B,D,G,C),k1_ortsp_1(A,B,C,D,E)),k1_ortsp_1(A,B,E,C,H)) != k10_group_1(A,k10_group_1(A,k1_ortsp_1(A,B,D,G,F),k1_ortsp_1(A,B,F,D,E)),k1_ortsp_1(A,B,E,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t40_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,D,C,E),k1_ortsp_1(A,B,E,D,F)) != k10_group_1(A,k1_ortsp_1(A,B,D,C,F),k1_ortsp_1(A,B,F,D,E)) ) ) ) ) ) ) ) ).
fof(d7_ortsp_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)
& v1_ortsp_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)
=> ! [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_ortsp_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_ortsp_1(A,B,E,F,H),k1_ortsp_1(A,B,H,E,C)),k1_ortsp_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_ortsp_1(A,B,C,D,E,F)
<=> G = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_ortsp_1,axiom,
$true ).
fof(t42_ortsp_1,axiom,
$true ).
fof(t43_ortsp_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)
& v1_ortsp_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)
=> ( r1_symsp_1(A,B,C,D)
| k2_ortsp_1(A,B,E,F,D,C) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ).
fof(t44_ortsp_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)
& v1_ortsp_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)
=> ( k2_ortsp_1(A,B,E,F,D,C) = k1_rlvect_1(A)
<=> r1_symsp_1(A,B,F,E) ) ) ) ) ) ) ) ) ).
fof(t45_ortsp_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)
& v1_ortsp_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)
=> k2_ortsp_1(A,B,E,F,D,C) = k2_ortsp_1(A,B,F,E,D,C) ) ) ) ) ) ) ) ).
fof(t46_ortsp_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)
& v1_ortsp_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))
=> ( ~ r1_symsp_1(A,B,C,D)
=> k2_ortsp_1(A,B,E,k6_vectsp_1(A,B,G,F),D,C) = k10_group_1(A,G,k2_ortsp_1(A,B,E,F,D,C)) ) ) ) ) ) ) ) ) ).
fof(t47_ortsp_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)
& v1_ortsp_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))
=> ( ~ r1_symsp_1(A,B,C,D)
=> k2_ortsp_1(A,B,E,k4_rlvect_1(B,F,G),D,C) = k4_rlvect_1(A,k2_ortsp_1(A,B,E,F,D,C),k2_ortsp_1(A,B,E,G,D,C)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,C,D,E),u1_struct_0(A)) ) ).
fof(dt_k2_ortsp_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)
& v1_ortsp_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_ortsp_1(A,B,C,D,E,F),u1_struct_0(A)) ) ).
%------------------------------------------------------------------------------