SET007 Axioms: SET007+244.ax


%------------------------------------------------------------------------------
% File     : SET007+244 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Basis of 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   49 (   7 unit)
%            Number of atoms       :  466 (  42 equality)
%            Maximal formula depth :   14 (   9 average)
%            Number of connectives :  483 (  66 ~  ;   2  |; 283  &)
%                                         (   8 <=>; 124 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (   3 constant; 0-4 arity)
%            Number of variables   :  118 (   0 singleton; 114 !;   4 ?)
%            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_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
          & v1_rlvect_3(B,A) ) ) )).

fof(t1_rlvect_3,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_rlvect_2(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,A)
             => k13_rlvect_2(A,k14_rlvect_2(A,B,C)) = k4_rlvect_1(A,k13_rlvect_2(A,B),k13_rlvect_2(A,C)) ) ) ) )).

fof(t2_rlvect_3,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_rlvect_2(C,B)
             => k13_rlvect_2(B,k15_rlvect_2(B,A,C)) = k3_rlvect_1(B,k13_rlvect_2(B,C),A) ) ) ) )).

fof(t3_rlvect_3,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_rlvect_2(B,A)
         => k13_rlvect_2(A,k16_rlvect_2(A,B)) = k5_rlvect_1(A,k13_rlvect_2(A,B)) ) ) )).

fof(t4_rlvect_3,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_rlvect_2(B,A)
         => ! [C] :
              ( m1_rlvect_2(C,A)
             => k13_rlvect_2(A,k17_rlvect_2(A,B,C)) = k6_rlvect_1(A,k13_rlvect_2(A,B),k13_rlvect_2(A,C)) ) ) ) )).

fof(d1_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlvect_3(B,A)
          <=> ! [C] :
                ( m2_rlvect_2(C,A,B)
               => ( k13_rlvect_2(A,C) = k1_rlvect_1(A)
                 => k10_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) )).

fof(t5_rlvect_3,axiom,(
    $true )).

fof(t6_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( r1_tarski(B,C)
                  & v1_rlvect_3(C,A) )
               => v1_rlvect_3(B,A) ) ) ) ) )).

fof(t7_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_rlvect_3(B,A)
              & r2_hidden(k1_rlvect_1(A),B) ) ) ) )).

fof(t8_rlvect_3,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) )
     => v1_rlvect_3(k1_subset_1(u1_struct_0(A)),A) ) )).

fof(t9_rlvect_3,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))
         => ( v1_rlvect_3(k7_rlvect_2(A,B),A)
          <=> B != k1_rlvect_1(A) ) ) ) )).

fof(t10_rlvect_3,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) )
     => ~ v1_rlvect_3(k7_rlvect_2(A,k1_rlvect_1(A)),A) ) )).

fof(t11_rlvect_3,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
               => ( B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A) ) ) ) ) ) )).

fof(t12_rlvect_3,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))
         => ( ~ v1_rlvect_3(k8_rlvect_2(A,B,k1_rlvect_1(A)),A)
            & ~ v1_rlvect_3(k8_rlvect_2(A,k1_rlvect_1(A),B),A) ) ) ) )).

fof(t13_rlvect_3,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
                 => ( B = C
                    | ( C != k1_rlvect_1(A)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => B != k3_rlvect_1(A,C,D) ) ) ) )
                & ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => B != k3_rlvect_1(A,C,D) )
                 => ( C = k1_rlvect_1(A)
                    | ( B != C
                      & v1_rlvect_3(k8_rlvect_2(A,B,C),A) ) ) ) ) ) ) ) )).

fof(t14_rlvect_3,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( B != C
                  & v1_rlvect_3(k8_rlvect_2(A,B,C),A) )
              <=> ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = np__0
                            & E = np__0 ) ) ) ) ) ) ) ) )).

fof(t15_rlvect_3,axiom,(
    $true )).

fof(t16_rlvect_3,axiom,(
    $true )).

fof(t17_rlvect_3,axiom,(
    ! [A,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,k1_zfmisc_1(u1_struct_0(B)))
         => ( r1_rlvect_1(k1_rlvect_3(B,C),A)
          <=> ? [D] :
                ( m2_rlvect_2(D,B,C)
                & A = k13_rlvect_2(B,D) ) ) ) ) )).

fof(t18_rlvect_3,axiom,(
    ! [A,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,k1_zfmisc_1(u1_struct_0(B)))
         => ( r2_hidden(A,C)
           => r1_rlvect_1(k1_rlvect_3(B,C),A) ) ) ) )).

fof(t19_rlvect_3,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) )
     => k1_rlvect_3(A,k1_subset_1(u1_struct_0(A))) = k1_rlsub_1(A) ) )).

fof(t20_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ~ ( k1_rlvect_3(A,B) = k1_rlsub_1(A)
              & B != k1_xboole_0
              & B != k7_rlvect_2(A,k1_rlvect_1(A)) ) ) ) )).

fof(t21_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( B = u1_struct_0(C)
               => k1_rlvect_3(A,B) = C ) ) ) ) )).

fof(t22_rlvect_3,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = u1_struct_0(A)
           => k1_rlvect_3(A,B) = A ) ) ) )).

fof(t23_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => m1_rlsub_1(k1_rlvect_3(A,B),k1_rlvect_3(A,C)) ) ) ) ) )).

fof(t24_rlvect_3,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( k1_rlvect_3(A,B) = A
                  & r1_tarski(B,C) )
               => k1_rlvect_3(A,C) = A ) ) ) ) )).

fof(t25_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k1_rlvect_3(A,k4_subset_1(u1_struct_0(A),B,C)) = k1_rlsub_2(A,k1_rlvect_3(A,B),k1_rlvect_3(A,C)) ) ) ) )).

fof(t26_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => m1_rlsub_1(k1_rlvect_3(A,k5_subset_1(u1_struct_0(A),B,C)),k2_rlsub_2(A,k1_rlvect_3(A,B),k1_rlvect_3(A,C))) ) ) ) )).

fof(t27_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_rlvect_3(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r1_tarski(B,C)
                      & v1_rlvect_3(C,A)
                      & k1_rlvect_3(A,C) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ) ) ) )).

fof(t28_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ~ ( k1_rlvect_3(A,B) = A
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r1_tarski(C,B)
                      & v1_rlvect_3(C,A)
                      & k1_rlvect_3(A,C) = A ) ) ) ) ) )).

fof(d3_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ( m1_rlvect_3(B,A)
          <=> ( v1_rlvect_3(B,A)
              & k1_rlvect_3(A,B) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ) ) )).

fof(t29_rlvect_3,axiom,(
    $true )).

fof(t30_rlvect_3,axiom,(
    $true )).

fof(t31_rlvect_3,axiom,(
    $true )).

fof(t32_rlvect_3,axiom,(
    ! [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)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_rlvect_3(B,A)
              & ! [C] :
                  ( m1_rlvect_3(C,A)
                 => ~ r1_tarski(B,C) ) ) ) ) )).

fof(t33_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ~ ( k1_rlvect_3(A,B) = A
              & ! [C] :
                  ( m1_rlvect_3(C,A)
                 => ~ r1_tarski(C,B) ) ) ) ) )).

fof(t34_rlvect_3,axiom,(
    $true )).

fof(t35_rlvect_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_orders_1(B,A)
         => ( ~ r2_hidden(k1_xboole_0,A)
           => ( k1_relat_1(B) = A
              & r1_tarski(k2_relat_1(B),k3_tarski(A)) ) ) ) ) )).

fof(t36_rlvect_3,axiom,(
    ! [A,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) )
     => ( r1_rlvect_1(k1_rlsub_1(B),A)
      <=> A = k1_rlvect_1(B) ) ) )).

fof(t37_rlvect_3,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( m1_rlsub_1(B,C)
                   => m1_rlsub_1(k2_rlsub_2(A,B,D),C) ) ) ) ) ) )).

fof(t38_rlvect_3,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ( m1_rlsub_1(B,C)
                      & m1_rlsub_1(B,D) )
                   => m1_rlsub_1(B,k2_rlsub_2(A,C,D)) ) ) ) ) ) )).

fof(t39_rlvect_3,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( ( m1_rlsub_1(B,C)
                      & m1_rlsub_1(D,C) )
                   => m1_rlsub_1(k1_rlsub_2(A,B,D),C) ) ) ) ) ) )).

fof(t40_rlvect_3,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( m1_rlsub_1(B,C)
                   => m1_rlsub_1(B,k1_rlsub_2(A,C,D)) ) ) ) ) ) )).

fof(t41_rlvect_3,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] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                    & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                 => k12_rlvect_2(A,k8_finseq_1(u1_struct_0(A),B,C),D) = k8_finseq_1(u1_struct_0(A),k12_rlvect_2(A,B,D),k12_rlvect_2(A,C,D)) ) ) ) ) )).

fof(dt_m1_rlvect_3,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_rlvect_3(B,A)
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_rlvect_3,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_rlvect_3(B,A) ) )).

fof(dt_k1_rlvect_3,axiom,(
    ! [A,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)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v2_rlvect_1(k1_rlvect_3(A,B))
        & m1_rlsub_1(k1_rlvect_3(A,B),A) ) ) )).

fof(d2_rlvect_3,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_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( C = k1_rlvect_3(A,B)
              <=> u1_struct_0(C) = a_2_0_rlvect_3(A,B) ) ) ) ) )).

fof(fraenkel_a_2_0_rlvect_3,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_rlvect_3(B,C))
      <=> ? [D] :
            ( m2_rlvect_2(D,B,C)
            & A = k13_rlvect_2(B,D) ) ) ) )).
%------------------------------------------------------------------------------