SET007 Axioms: SET007+260.ax


%------------------------------------------------------------------------------
% File     : SET007+260 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Directed Geometrical Bundles and Their Analytical Representation
% 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    : afvect0 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  105 (  24 unit)
%            Number of atoms       :  885 (  63 equality)
%            Maximal formula depth :   27 (   9 average)
%            Number of connectives :  969 ( 189 ~  ;   3  |; 420  &)
%                                         (  19 <=>; 338 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-5 arity)
%            Number of functors    :   20 (   0 constant; 1-6 arity)
%            Number of variables   :  339 (   0 singleton; 325 !;  14 ?)
%            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_afvect0,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v1_afvect0(A) ) )).

fof(cc1_afvect0,axiom,(
    ! [A] :
      ( l1_analoaf(A)
     => ( ( ~ v3_struct_0(A)
          & v2_tdgroup(A) )
       => ( ~ v3_struct_0(A)
          & v1_afvect0(A) ) ) ) )).

fof(fc1_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_afvect0(A,B))
        & v1_rlvect_1(k5_afvect0(A,B)) ) ) )).

fof(fc2_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_afvect0(A,B))
        & v1_rlvect_1(k5_afvect0(A,B))
        & v3_rlvect_1(k5_afvect0(A,B))
        & v4_rlvect_1(k5_afvect0(A,B))
        & v5_rlvect_1(k5_afvect0(A,B))
        & v6_rlvect_1(k5_afvect0(A,B)) ) ) )).

fof(fc3_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_afvect0(A,B))
        & v1_rlvect_1(k5_afvect0(A,B))
        & v3_rlvect_1(k5_afvect0(A,B))
        & v4_rlvect_1(k5_afvect0(A,B))
        & v5_rlvect_1(k5_afvect0(A,B))
        & v6_rlvect_1(k5_afvect0(A,B))
        & v1_tdgroup(k5_afvect0(A,B)) ) ) )).

fof(fc4_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_afvect0(A,B))
        & v1_rlvect_1(k5_afvect0(A,B))
        & v3_rlvect_1(k5_afvect0(A,B))
        & v4_rlvect_1(k5_afvect0(A,B))
        & v5_rlvect_1(k5_afvect0(A,B))
        & v6_rlvect_1(k5_afvect0(A,B))
        & v13_vectsp_1(k5_afvect0(A,B))
        & v1_tdgroup(k5_afvect0(A,B)) ) ) )).

fof(rc2_afvect0,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)
      & v13_vectsp_1(A)
      & ~ v3_realset2(A)
      & v1_tdgroup(A) ) )).

fof(fc5_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_afvect0(A,B))
        & v1_rlvect_1(k5_afvect0(A,B))
        & v3_rlvect_1(k5_afvect0(A,B))
        & v4_rlvect_1(k5_afvect0(A,B))
        & v5_rlvect_1(k5_afvect0(A,B))
        & v6_rlvect_1(k5_afvect0(A,B))
        & v13_vectsp_1(k5_afvect0(A,B))
        & ~ v3_realset2(k5_afvect0(A,B))
        & v1_tdgroup(k5_afvect0(A,B)) ) ) )).

fof(fc6_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ v3_struct_0(k2_tdgroup(A))
        & ~ v3_realset2(k2_tdgroup(A))
        & v1_analoaf(k2_tdgroup(A))
        & v2_tdgroup(k2_tdgroup(A))
        & v1_afvect0(k2_tdgroup(A)) ) ) )).

fof(d1_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_afvect0(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))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [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))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [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))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [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))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [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))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [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))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).

fof(t1_afvect0,axiom,(
    $true )).

fof(t2_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,C,B,C) ) ) ) )).

fof(t3_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_analoaf(A,B,B,B,B) ) ) )).

fof(t4_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t5_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_analoaf(A,B,C,B,D)
                   => C = D ) ) ) ) ) )).

fof(t6_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) )).

fof(t7_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,B,C,C) ) ) ) )).

fof(t8_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => r2_analoaf(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t9_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,D,F,E) )
                           => C = F ) ) ) ) ) ) ) )).

fof(t10_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,F,G,B,C)
                                      & r2_analoaf(A,F,H,D,E) )
                                   => G = H ) ) ) ) ) ) ) ) ) )).

fof(t11_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,F,G,C,B)
                                      & r2_analoaf(A,F,H,E,D) )
                                   => G = H ) ) ) ) ) ) ) ) ) )).

fof(t12_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ( ( r2_analoaf(A,B,C,D,E)
                                                  & r2_analoaf(A,F,G,H,I)
                                                  & r2_analoaf(A,C,J,F,G)
                                                  & r2_analoaf(A,E,K,H,I) )
                                               => r2_analoaf(A,B,J,D,K) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r2_analoaf(A,B,C,D,E)
                                  & r2_analoaf(A,B,F,G,E) )
                               => r2_analoaf(A,C,F,G,D) ) ) ) ) ) ) ) ) )).

fof(d2_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_afvect0(A,B,C)
              <=> ( r2_analoaf(A,B,C,C,B)
                  & B != C ) ) ) ) ) )).

fof(t14_afvect0,axiom,(
    $true )).

fof(t15_afvect0,axiom,(
    $true )).

fof(t16_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(A))
          & ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & B != C
              & ~ r1_afvect0(A,B,C) ) ) ) )).

fof(t17_afvect0,axiom,(
    $true )).

fof(t18_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ~ ( r1_afvect0(A,B,C)
                      & r1_afvect0(A,B,D)
                      & C != D
                      & ~ r1_afvect0(A,C,D) ) ) ) ) ) )).

fof(t19_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r1_afvect0(A,B,C)
                          & r2_analoaf(A,B,C,D,E) )
                       => r1_afvect0(A,D,E) ) ) ) ) ) ) )).

fof(d3_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_afvect0(A,B,C,D)
                  <=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) )).

fof(t20_afvect0,axiom,(
    $true )).

fof(t21_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_afvect0(A,B,C,D)
                   => r2_afvect0(A,D,C,B) ) ) ) ) ) )).

fof(t22_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_afvect0(A,B,C,C)
              <=> B = C ) ) ) ) )).

fof(t23_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_afvect0(A,B,C,B)
              <=> ( B = C
                  | r1_afvect0(A,B,C) ) ) ) ) ) )).

fof(t24_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & r2_afvect0(A,B,D,C) ) ) ) ) )).

fof(t25_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ~ ( r2_afvect0(A,B,C,D)
                          & r2_afvect0(A,B,E,D)
                          & C != E
                          & ~ r1_afvect0(A,C,E) ) ) ) ) ) ) )).

fof(t26_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & r2_afvect0(A,B,C,D) ) ) ) ) )).

fof(t27_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r2_afvect0(A,B,C,D)
                          & r2_afvect0(A,B,C,E) )
                       => D = E ) ) ) ) ) ) )).

fof(t28_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r2_afvect0(A,B,C,D)
                          & r1_afvect0(A,C,E) )
                       => r2_afvect0(A,B,E,D) ) ) ) ) ) ) )).

fof(t29_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_afvect0(A,B,C,D)
                              & r2_afvect0(A,B,E,F)
                              & r1_afvect0(A,C,E) )
                           => D = F ) ) ) ) ) ) ) )).

fof(t30_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_afvect0(A,B,C,D)
                              & r2_afvect0(A,E,C,F) )
                           => r2_analoaf(A,B,E,F,D) ) ) ) ) ) ) ) )).

fof(t31_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r2_afvect0(A,B,C,D)
                                  & r2_afvect0(A,E,F,G)
                                  & r1_afvect0(A,C,F) )
                               => r2_analoaf(A,B,E,G,D) ) ) ) ) ) ) ) ) )).

fof(d4_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( D = k1_afvect0(A,B,C)
                  <=> r2_afvect0(A,C,B,D) ) ) ) ) ) )).

fof(t32_afvect0,axiom,(
    $true )).

fof(t33_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = D
                  <=> r2_analoaf(A,C,B,B,D) ) ) ) ) ) )).

fof(t34_afvect0,axiom,(
    $true )).

fof(t35_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_afvect0(A,B,C) = C
              <=> ( C = B
                  | r1_afvect0(A,C,B) ) ) ) ) ) )).

fof(t36_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_afvect0(A,B,k1_afvect0(A,B,C)) = C ) ) ) )).

fof(t37_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = k1_afvect0(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t38_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & k1_afvect0(A,B,D) = C ) ) ) ) )).

fof(t39_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => r2_analoaf(A,B,C,k1_afvect0(A,D,C),k1_afvect0(A,D,B)) ) ) ) ) )).

fof(t40_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r2_analoaf(A,B,C,D,E)
                          <=> r2_analoaf(A,k1_afvect0(A,F,B),k1_afvect0(A,F,C),k1_afvect0(A,F,D),k1_afvect0(A,F,E)) ) ) ) ) ) ) ) )).

fof(t41_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r1_afvect0(A,B,C)
                  <=> r1_afvect0(A,k1_afvect0(A,D,B),k1_afvect0(A,D,C)) ) ) ) ) ) )).

fof(t42_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_afvect0(A,B,C,D)
                      <=> r2_afvect0(A,k1_afvect0(A,E,B),k1_afvect0(A,E,C),k1_afvect0(A,E,D)) ) ) ) ) ) ) )).

fof(t43_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = k1_afvect0(A,D,C)
                  <=> ( B = D
                      | r1_afvect0(A,B,D) ) ) ) ) ) ) )).

fof(t44_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,B,D))) = k1_afvect0(A,k1_afvect0(A,B,C),D) ) ) ) ) )).

fof(t45_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,k1_afvect0(A,C,D)) = k1_afvect0(A,C,k1_afvect0(A,B,D))
                  <=> ~ ( B != C
                        & ~ r1_afvect0(A,B,C)
                        & ~ r1_afvect0(A,C,k1_afvect0(A,B,C)) ) ) ) ) ) ) )).

fof(t46_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,D,k1_afvect0(A,C,k1_afvect0(A,B,E))) ) ) ) ) ) )).

fof(t47_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ? [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                          & k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,F,E) ) ) ) ) ) ) )).

fof(t48_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                      & k1_afvect0(A,B,k1_afvect0(A,E,C)) = k1_afvect0(A,E,k1_afvect0(A,D,C)) ) ) ) ) ) )).

fof(d5_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( E = k2_afvect0(A,B,C,D)
                      <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).

fof(d6_afvect0,axiom,(
    $true )).

fof(d7_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
             => ( C = k3_afvect0(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D,E) = k2_afvect0(A,B,D,E) ) ) ) ) ) ) )).

fof(d8_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k4_afvect0(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_afvect0(A,B,D) ) ) ) ) ) )).

fof(d9_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_afvect0(A,B) = g1_rlvect_1(u1_struct_0(A),k3_afvect0(A,B),B) ) ) )).

fof(t49_afvect0,axiom,(
    $true )).

fof(t50_afvect0,axiom,(
    $true )).

fof(t51_afvect0,axiom,(
    $true )).

fof(t52_afvect0,axiom,(
    $true )).

fof(t53_afvect0,axiom,(
    $true )).

fof(t54_afvect0,axiom,(
    $true )).

fof(t55_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( u1_struct_0(k5_afvect0(A,B)) = u1_struct_0(A)
            & u1_rlvect_1(k5_afvect0(A,B)) = k3_afvect0(A,B)
            & u2_struct_0(k5_afvect0(A,B)) = B ) ) ) )).

fof(t56_afvect0,axiom,(
    $true )).

fof(t57_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( C = E
                              & D = F )
                           => k2_rlvect_1(k5_afvect0(A,B),C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k3_afvect0(A,B),E,F) ) ) ) ) ) ) ) )).

fof(t58_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( C = D
                   => k5_rlvect_1(k5_afvect0(A,B),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),k4_afvect0(A,B),D) ) ) ) ) ) )).

fof(t59_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_rlvect_1(k5_afvect0(A,B)) = B ) ) )).

fof(t60_afvect0,axiom,(
    $true )).

fof(t61_afvect0,axiom,(
    $true )).

fof(t62_afvect0,axiom,(
    $true )).

fof(t63_afvect0,axiom,(
    $true )).

fof(t64_afvect0,axiom,(
    $true )).

fof(t65_afvect0,axiom,(
    $true )).

fof(t66_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                  & k4_rlvect_1(k5_afvect0(A,B),D,D) = C ) ) ) ) )).

fof(t67_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ( k4_rlvect_1(k5_afvect0(A,B),C,C) = k1_rlvect_1(k5_afvect0(A,B))
               => C = k1_rlvect_1(k5_afvect0(A,B)) ) ) ) ) )).

fof(t68_afvect0,axiom,(
    $true )).

fof(t69_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ~ v3_struct_0(k5_afvect0(A,B))
            & v3_rlvect_1(k5_afvect0(A,B))
            & v4_rlvect_1(k5_afvect0(A,B))
            & v5_rlvect_1(k5_afvect0(A,B))
            & v6_rlvect_1(k5_afvect0(A,B))
            & v13_vectsp_1(k5_afvect0(A,B))
            & ~ v3_realset2(k5_afvect0(A,B))
            & v1_tdgroup(k5_afvect0(A,B))
            & l1_rlvect_1(k5_afvect0(A,B)) ) ) ) )).

fof(t70_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ v3_struct_0(k2_tdgroup(A))
        & ~ v3_realset2(k2_tdgroup(A))
        & v2_tdgroup(k2_tdgroup(A))
        & l1_analoaf(k2_tdgroup(A)) ) ) )).

fof(t71_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_analoaf(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => A = k2_tdgroup(k5_afvect0(A,B)) ) ) )).

fof(t72_afvect0,axiom,(
    ! [A] :
      ( ( v1_analoaf(A)
        & l1_analoaf(A) )
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_tdgroup(A)
          & l1_analoaf(A) )
      <=> ? [B] :
            ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v13_vectsp_1(B)
            & ~ v3_realset2(B)
            & v1_tdgroup(B)
            & l1_rlvect_1(B)
            & A = k2_tdgroup(B) ) ) ) )).

fof(d10_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r3_afvect0(A,B,C)
              <=> ( v2_funct_1(C)
                  & k2_relat_1(C) = u1_struct_0(B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_rlvect_1(A)) = k1_rlvect_1(B)
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_rlvect_1(A,D)) = k5_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) ) ) )).

fof(d11_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ( r4_afvect0(A,B)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & r3_afvect0(A,B,C) ) ) ) ) )).

fof(t73_afvect0,axiom,(
    $true )).

fof(t74_afvect0,axiom,(
    $true )).

fof(t75_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                 => ( ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
                      & D = C )
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_rlvect_1(A,E,F)) = k1_binop_1(k3_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F))
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k1_rlvect_1(A)) = k1_rlvect_1(k5_afvect0(k2_tdgroup(A),D))
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k5_rlvect_1(A,E)) = k1_funct_1(k4_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ) )).

fof(t76_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = k4_rlvect_1(A,C,D) )
               => v2_funct_1(B) ) ) ) ) )).

fof(t77_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
                   => k2_relat_1(B) = u1_struct_0(k5_afvect0(k2_tdgroup(A),D)) ) ) ) ) ) )).

fof(t78_afvect0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
             => ( C = B
               => r4_afvect0(A,k5_afvect0(k2_tdgroup(A),C)) ) ) ) ) )).

fof(symmetry_r1_afvect0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_afvect0(A,B,C)
       => r1_afvect0(A,C,B) ) ) )).

fof(irreflexivity_r1_afvect0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ r1_afvect0(A,B,B) ) )).

fof(dt_k1_afvect0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_afvect0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_afvect0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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)) )
     => m1_subset_1(k2_afvect0(A,B,C,D),u1_struct_0(A)) ) )).

fof(dt_k3_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k3_afvect0(A,B))
        & v1_funct_2(k3_afvect0(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(k3_afvect0(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_k4_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k4_afvect0(A,B))
        & v1_funct_2(k4_afvect0(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k4_afvect0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k5_afvect0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_rlvect_1(k5_afvect0(A,B))
        & l1_rlvect_1(k5_afvect0(A,B)) ) ) )).
%------------------------------------------------------------------------------