SET007 Axioms: SET007+216.ax


%------------------------------------------------------------------------------
% File     : SET007+216 : TPTP v7.5.0. 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 unit)
%            Number of atoms       : 1048 (  39 equality)
%            Maximal formula depth :   31 (  12 average)
%            Number of connectives : 1186 ( 195 ~  ;   7  |; 747  &)
%                                         (   6 <=>; 231 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-4 arity)
%            Number of functors    :   11 (   0 constant; 1-6 arity)
%            Number of variables   :  215 (   0 singleton; 213 !;   2 ?)
%            Maximal term depth    :    4 (   1 average)
% 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)) ) )).
%------------------------------------------------------------------------------