SET007 Axioms: SET007+210.ax


%------------------------------------------------------------------------------
% File     : SET007+210 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Vectors in Real Linear Space
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : rlvect_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  142 (  20 unit)
%            Number of atoms       : 1008 ( 165 equality)
%            Maximal formula depth :   20 (   7 average)
%            Number of connectives :  979 ( 113 ~  ;   6  |; 501  &)
%                                         (   9 <=>; 350 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   28 (   1 propositional; 0-3 arity)
%            Number of functors    :   41 (   6 constant; 0-6 arity)
%            Number of variables   :  379 (   0 singleton; 366 !;  13 ?)
%            Maximal term depth    :    6 (   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_rlvect_1,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & v1_rlvect_1(A) ) )).

fof(rc2_rlvect_1,axiom,(
    ? [A] :
      ( l2_rlvect_1(A)
      & v2_rlvect_1(A) ) )).

fof(rc3_rlvect_1,axiom,(
    ? [A] :
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A) ) )).

fof(rc4_rlvect_1,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A) ) )).

fof(fc1_rlvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ( ~ v3_struct_0(g2_rlvect_1(A,B,C,D))
        & v2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) )).

fof(rc5_rlvect_1,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A) ) )).

fof(rc6_rlvect_1,axiom,(
    ? [A] :
      ( l2_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v2_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v7_rlvect_1(A) ) )).

fof(d1_rlvect_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( r1_rlvect_1(A,B)
        <=> r2_hidden(B,u1_struct_0(A)) ) ) )).

fof(t1_rlvect_1,axiom,(
    $true )).

fof(t2_rlvect_1,axiom,(
    $true )).

fof(t3_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_rlvect_1(A,B) ) ) )).

fof(d2_rlvect_1,axiom,(
    ! [A] :
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) )).

fof(d3_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) )).

fof(d4_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) )).

fof(t4_rlvect_1,axiom,(
    $true )).

fof(t5_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) )).

fof(d5_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v3_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) ) ) ) )).

fof(d6_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) )).

fof(d7_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v5_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) )).

fof(d8_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v6_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) )).

fof(d9_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ( v7_rlvect_1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => k3_rlvect_1(A,B,np__1) = B ) ) ) ) )).

fof(t6_rlvect_1,axiom,(
    $true )).

fof(t7_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ( ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                  & k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => k3_rlvect_1(A,B,np__1) = B ) )
       => ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v7_rlvect_1(A)
          & l2_rlvect_1(A) ) ) ) )).

fof(t8_rlvect_1,axiom,(
    $true )).

fof(t9_rlvect_1,axiom,(
    $true )).

fof(t10_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) )).

fof(d10_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v4_rlvect_1(A)
              & v5_rlvect_1(A)
              & v6_rlvect_1(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k5_rlvect_1(A,B)
                <=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) )).

fof(d11_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) )).

fof(t11_rlvect_1,axiom,(
    $true )).

fof(t12_rlvect_1,axiom,(
    $true )).

fof(t13_rlvect_1,axiom,(
    $true )).

fof(t14_rlvect_1,axiom,(
    $true )).

fof(t15_rlvect_1,axiom,(
    $true )).

fof(t16_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
            & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) )).

fof(t17_rlvect_1,axiom,(
    $true )).

fof(t18_rlvect_1,axiom,(
    $true )).

fof(t19_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = k5_rlvect_1(A,C) ) ) ) ) )).

fof(t20_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & k2_rlvect_1(A,B,D) = C ) ) ) ) )).

fof(t21_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
                          | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
                       => D = E ) ) ) ) ) ) )).

fof(t22_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( k2_rlvect_1(A,B,C) = B
                  | k2_rlvect_1(A,C,B) = B )
               => C = k1_rlvect_1(A) ) ) ) ) )).

fof(t23_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ( A = np__0
                  | C = k1_rlvect_1(B) )
               => k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) )).

fof(t24_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ~ ( k3_rlvect_1(B,C,A) = k1_rlvect_1(B)
                  & A != np__0
                  & C != k1_rlvect_1(B) ) ) ) ) )).

fof(t25_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k5_rlvect_1(A,k1_rlvect_1(A)) = k1_rlvect_1(A) ) )).

fof(t26_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) )).

fof(t27_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B) ) ) )).

fof(t28_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) )).

fof(t29_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(np__1)) ) ) )).

fof(t30_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,k5_rlvect_1(A,B)) = B ) ) )).

fof(t31_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k5_rlvect_1(A,B) = k5_rlvect_1(A,C)
               => B = C ) ) ) ) )).

fof(t32_rlvect_1,axiom,(
    $true )).

fof(t33_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B = k5_rlvect_1(A,B)
           => B = k1_rlvect_1(A) ) ) ) )).

fof(t34_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k4_rlvect_1(A,B,B) = k1_rlvect_1(A)
           => B = k1_rlvect_1(A) ) ) ) )).

fof(t35_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = C ) ) ) ) )).

fof(t36_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & k6_rlvect_1(A,C,D) = B ) ) ) ) )).

fof(t37_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t38_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) )).

fof(t39_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)) ) ) ) )).

fof(t40_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)) = k3_rlvect_1(B,C,A) ) ) ) )).

fof(t41_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) )).

fof(t42_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) ) ) ) ) )).

fof(t43_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) ) ) ) ) )).

fof(t44_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) )).

fof(t45_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) ) ) ) )).

fof(t46_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k6_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) )).

fof(t47_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)) ) ) ) )).

fof(t48_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) ) ) ) ) )).

fof(t49_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) ) ) ) ) )).

fof(t50_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( k3_rlvect_1(B,C,A) = k3_rlvect_1(B,D,A)
                   => ( A = np__0
                      | C = D ) ) ) ) ) ) )).

fof(t51_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( k3_rlvect_1(C,D,A) = k3_rlvect_1(C,D,B)
                   => ( D = k1_rlvect_1(C)
                      | A = B ) ) ) ) ) ) )).

fof(d12_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C = k9_rlvect_1(A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A))
                    & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B))
                    & k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) = k1_rlvect_1(A)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( F = k1_funct_1(B,k1_nat_1(E,np__1))
                             => ( r1_xreal_0(k3_finseq_1(B),E)
                                | k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ) )).

fof(t52_rlvect_1,axiom,(
    $true )).

fof(t53_rlvect_1,axiom,(
    $true )).

fof(t54_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(C,k2_finseq_1(D))
                      & k3_finseq_1(B) = D )
                   => m1_subset_1(k1_funct_1(B,C),u1_struct_0(A)) ) ) ) ) ) )).

fof(t55_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1)
                      & C = k7_relat_1(B,k4_finseq_1(C))
                      & D = k1_funct_1(B,k3_finseq_1(B)) )
                   => k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D) ) ) ) ) ) )).

fof(t56_rlvect_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ( ( k3_finseq_1(C) = k3_finseq_1(D)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ( ( r2_hidden(E,k4_finseq_1(C))
                                  & F = k1_funct_1(D,E) )
                               => k1_funct_1(C,E) = k3_rlvect_1(B,F,A) ) ) ) )
                   => k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A) ) ) ) ) ) )).

fof(t57_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_hidden(D,k4_finseq_1(B))
                              & E = k1_funct_1(C,D) )
                           => k1_funct_1(B,D) = k5_rlvect_1(A,E) ) ) ) )
               => k9_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,C)) ) ) ) ) )).

fof(t58_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) )).

fof(t59_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( ( k2_relat_1(B) = k2_relat_1(C)
                  & v2_funct_1(B)
                  & v2_funct_1(C) )
               => k9_rlvect_1(A,B) = k9_rlvect_1(A,C) ) ) ) ) )).

fof(t60_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A) ) )).

fof(t61_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) )).

fof(t62_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,B,C) ) ) ) )).

fof(t63_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) ) ) ) ) )).

fof(t64_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A) ) ) )).

fof(t65_rlvect_1,axiom,(
    $true )).

fof(t66_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) ) ) )).

fof(t67_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B) = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) ) ) ) ) ) )).

fof(t68_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A) ) )).

fof(t69_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))) = k5_rlvect_1(A,B) ) ) )).

fof(t70_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))) = k6_rlvect_1(A,k5_rlvect_1(A,B),C) ) ) ) )).

fof(t71_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))) = k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D) ) ) ) ) )).

fof(t72_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k9_rlvect_1(A,k7_rlvect_1(A,C,B)) ) ) ) )).

fof(t73_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))) ) ) ) )).

fof(t74_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A) ) )).

fof(t75_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)) = B
            & k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B ) ) ) )).

fof(t76_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) = k1_rlvect_1(A)
            & k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)) = k1_rlvect_1(A) ) ) ) )).

fof(t77_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))) = k6_rlvect_1(A,B,C) ) ) ) )).

fof(t78_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)) ) ) ) )).

fof(t79_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2) ) ) )).

fof(t80_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)) ) ) )).

fof(t81_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) ) ) ) ) )).

fof(t82_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) ) ) ) ) )).

fof(t83_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C) ) ) ) ) )).

fof(t84_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) ) ) ) ) )).

fof(t85_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) ) ) ) ) )).

fof(t86_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) ) ) ) ) )).

fof(t87_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) ) ) ) ) )).

fof(t88_rlvect_1,axiom,(
    $true )).

fof(t89_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)) ) ) ) ) )).

fof(t90_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A) ) )).

fof(t91_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)) = B
            & k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))) = B
            & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) = B ) ) ) )).

fof(t92_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) = k2_rlvect_1(A,B,C)
                & k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) = k2_rlvect_1(A,B,C)
                & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C) ) ) ) ) )).

fof(t93_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)) = k3_rlvect_1(A,B,np__3) ) ) )).

fof(t94_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( k3_finseq_1(B) = np__0
           => k9_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(t95_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( k3_finseq_1(B) = np__1
           => k9_rlvect_1(A,B) = k1_funct_1(B,np__1) ) ) ) )).

fof(t96_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( k3_finseq_1(B) = np__2
                      & C = k1_funct_1(B,np__1)
                      & D = k1_funct_1(B,np__2) )
                   => k9_rlvect_1(A,B) = k2_rlvect_1(A,C,D) ) ) ) ) ) )).

fof(t97_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( k3_finseq_1(B) = np__3
                          & C = k1_funct_1(B,np__1)
                          & D = k1_funct_1(B,np__2)
                          & E = k1_funct_1(B,np__3) )
                       => k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E) ) ) ) ) ) ) )).

fof(d13_rlvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v8_rlvect_1(B,A)
          <=> B != k1_rlvect_1(A) ) ) ) )).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) )).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) )).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] :
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) )).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) )).

fof(abstractness_v1_rlvect_1,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( v1_rlvect_1(A)
       => A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) )).

fof(abstractness_v2_rlvect_1,axiom,(
    ! [A] :
      ( l2_rlvect_1(A)
     => ( v2_rlvect_1(A)
       => A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) )).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] :
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) )).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k4_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) )).

fof(redefinition_k4_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) )).

fof(dt_k5_rlvect_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k6_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k7_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)) ) )).

fof(redefinition_k7_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k7_rlvect_1(A,B,C) = k10_finseq_1(B,C) ) )).

fof(dt_k8_rlvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)) ) )).

fof(redefinition_k8_rlvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D) ) )).

fof(dt_k9_rlvect_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,u1_struct_0(A)) )
     => m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)) ) )).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_u2_rlvect_1,axiom,(
    ! [A] :
      ( l2_rlvect_1(A)
     => ( v1_funct_1(u2_rlvect_1(A))
        & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_g1_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( v1_rlvect_1(g1_rlvect_1(A,B,C))
        & l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) )).

fof(free_g1_rlvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ! [D,E,F] :
          ( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

fof(dt_g2_rlvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ( v2_rlvect_1(g2_rlvect_1(A,B,C,D))
        & l2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) )).

fof(free_g2_rlvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) )
     => ! [E,F,G,H] :
          ( g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).
%------------------------------------------------------------------------------