SET007 Axioms: SET007+240.ax


%------------------------------------------------------------------------------
% File     : SET007+240 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Projective Spaces
% 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    : anproj_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   1 unit)
%            Number of atoms       : 1422 ( 280 equality)
%            Maximal formula depth :   43 (  22 average)
%            Number of connectives : 1573 ( 213 ~  ;  51  |; 799  &)
%                                         (  17 <=>; 493 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   1 propositional; 0-8 arity)
%            Number of functors    :   19 (   3 constant; 0-6 arity)
%            Number of variables   :  540 (   0 singleton; 413 !; 127 ?)
%            Maximal term depth    :    7 (   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_anproj_2,axiom,(
    ? [A] :
      ( l2_rlvect_1(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)
      & v1_anproj_2(A) ) )).

fof(cc1_anproj_2,axiom,(
    ! [A] :
      ( l2_rlvect_1(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)
          & v1_anproj_2(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)
          & ~ v3_realset2(A) ) ) ) )).

fof(fc1_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A)) ) ) )).

fof(fc2_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A))
        & v2_anproj_2(k6_anproj_1(A)) ) ) )).

fof(fc3_anproj_2,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)
        & v1_anproj_2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A))
        & v4_collsp(k6_anproj_1(A))
        & v2_anproj_2(k6_anproj_1(A)) ) ) )).

fof(fc4_anproj_2,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)
        & v1_anproj_2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A))
        & v4_collsp(k6_anproj_1(A))
        & v2_anproj_2(k6_anproj_1(A))
        & v3_anproj_2(k6_anproj_1(A)) ) ) )).

fof(rc2_anproj_2,axiom,(
    ? [A] :
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v2_collsp(A)
      & v3_collsp(A)
      & v4_collsp(A)
      & v2_anproj_2(A)
      & v3_anproj_2(A) ) )).

fof(fc5_anproj_2,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)
        & v1_anproj_2(A)
        & l2_rlvect_1(A) )
     => ( ~ v3_struct_0(k6_anproj_1(A))
        & v1_collsp(k6_anproj_1(A))
        & v2_collsp(k6_anproj_1(A))
        & v3_collsp(k6_anproj_1(A))
        & v4_collsp(k6_anproj_1(A))
        & v2_anproj_2(k6_anproj_1(A))
        & v3_anproj_2(k6_anproj_1(A))
        & v4_anproj_2(k6_anproj_1(A))
        & v5_anproj_2(k6_anproj_1(A))
        & v6_anproj_2(k6_anproj_1(A)) ) ) )).

fof(rc3_anproj_2,axiom,(
    ? [A] :
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v1_collsp(A)
      & v2_collsp(A)
      & v3_collsp(A)
      & v4_collsp(A)
      & v2_anproj_2(A)
      & v3_anproj_2(A)
      & v4_anproj_2(A)
      & v5_anproj_2(A)
      & v6_anproj_2(A)
      & v7_anproj_2(A) ) )).

fof(rc4_anproj_2,axiom,(
    ? [A] :
      ( l1_collsp(A)
      & ~ v3_struct_0(A)
      & v1_collsp(A)
      & v2_collsp(A)
      & v3_collsp(A)
      & v4_collsp(A)
      & v2_anproj_2(A)
      & v3_anproj_2(A)
      & v4_anproj_2(A)
      & v5_anproj_2(A)
      & v6_anproj_2(A)
      & ~ v7_anproj_2(A)
      & v8_anproj_2(A) ) )).

fof(t1_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                 => ( E = np__0
                                    & F = np__0
                                    & G = np__0 ) ) ) ) )
                   => ( v8_rlvect_1(B,A)
                      & v8_rlvect_1(C,A)
                      & v8_rlvect_1(D,A)
                      & ~ r2_anproj_1(A,B,C,D)
                      & ~ r1_anproj_1(A,B,C) ) ) ) ) ) ) )).

fof(t2_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ! [H] :
                                    ( m1_subset_1(H,k1_numbers)
                                   => ! [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                         => ( F = np__0
                                            & G = np__0
                                            & H = np__0
                                            & I = np__0 ) ) ) ) ) )
                       => ( v8_rlvect_1(B,A)
                          & v8_rlvect_1(C,A)
                          & ~ r1_anproj_1(A,B,C)
                          & v8_rlvect_1(D,A)
                          & v8_rlvect_1(E,A)
                          & ~ r1_anproj_1(A,D,E)
                          & ~ r2_anproj_1(A,B,C,D)
                          & ~ r2_anproj_1(A,D,E,B) ) ) ) ) ) ) ) )).

fof(t3_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) )
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                   => ( E = np__0
                                      & F = np__0
                                      & G = np__0 ) ) ) ) ) )
                   => ! [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_anproj_1(A,B,C,G)
                                & r2_anproj_1(A,E,F,G)
                                & v8_rlvect_1(G,A) ) ) ) ) ) ) ) ) )).

fof(t4_anproj_2,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))
             => ! [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,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                           => ( F = np__0
                                              & G = np__0
                                              & H = np__0
                                              & I = np__0 ) ) ) ) ) ) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ~ ( v8_rlvect_1(F,A)
                                    & v8_rlvect_1(G,A)
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_struct_0(A))
                                           => ~ ( r2_anproj_1(A,F,G,I)
                                                & r2_anproj_1(A,C,D,H)
                                                & r2_anproj_1(A,B,I,H)
                                                & v8_rlvect_1(H,A)
                                                & v8_rlvect_1(I,A) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ! [H] :
                                    ( m1_subset_1(H,k1_numbers)
                                   => ! [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                         => ( F = np__0
                                            & G = np__0
                                            & H = np__0
                                            & I = np__0 ) ) ) ) ) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( v8_rlvect_1(F,A)
                                & r2_anproj_1(A,B,C,F)
                                & r2_anproj_1(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(d1_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_anproj_2(A,B,C,D)
                  <=> ( v8_rlvect_1(B,A)
                      & v8_rlvect_1(C,A)
                      & v8_rlvect_1(D,A) ) ) ) ) ) ) )).

fof(d2_anproj_2,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))
             => ! [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_anproj_2(A,B,C,D,E,F,G)
                              <=> ( r2_anproj_1(A,B,C,G)
                                  & r2_anproj_1(A,B,D,F)
                                  & r2_anproj_1(A,C,D,E) ) ) ) ) ) ) ) ) ) )).

fof(d3_anproj_2,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))
             => ! [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))
                                 => ( r3_anproj_2(A,B,C,D,E,F,G,H)
                                  <=> ( r2_anproj_1(A,B,C,F)
                                      & r2_anproj_1(A,B,D,G)
                                      & r2_anproj_1(A,B,E,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_anproj_1(A,B,C,D)
                      & r1_anproj_2(A,B,C,D) )
                   => ( r1_anproj_1(A,B,C)
                      | r1_anproj_1(A,B,D)
                      | r1_anproj_1(A,C,D)
                      | ( ? [E] :
                            ( m1_subset_1(E,k1_numbers)
                            & ? [F] :
                                ( m1_subset_1(F,k1_numbers)
                                & k3_rlvect_1(A,D,F) = k4_rlvect_1(A,B,k3_rlvect_1(A,C,E))
                                & E != np__0
                                & F != np__0 ) )
                        & ? [E] :
                            ( m1_subset_1(E,k1_numbers)
                            & ? [F] :
                                ( m1_subset_1(F,k1_numbers)
                                & D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,E))
                                & F != np__0
                                & E != np__0 ) ) ) ) ) ) ) ) ) )).

fof(t7_anproj_2,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))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_anproj_1(A,B,C,D)
                      & ~ r1_anproj_1(A,B,C)
                      & r1_anproj_2(A,B,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => D != k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) )).

fof(t8_anproj_2,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))
             => ! [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))
                                             => ( ( v8_rlvect_1(B,A)
                                                  & r1_anproj_2(A,C,D,E)
                                                  & r1_anproj_2(A,F,G,H)
                                                  & r1_anproj_2(A,I,J,K)
                                                  & r3_anproj_2(A,B,C,D,E,F,G,H)
                                                  & r2_anproj_2(A,C,D,E,I,J,K)
                                                  & r2_anproj_2(A,F,G,H,I,J,K) )
                                               => ( r1_anproj_1(A,B,F)
                                                  | r1_anproj_1(A,B,G)
                                                  | r1_anproj_1(A,B,H)
                                                  | r1_anproj_1(A,C,F)
                                                  | r1_anproj_1(A,D,G)
                                                  | r1_anproj_1(A,E,H)
                                                  | r2_anproj_1(A,B,C,D)
                                                  | r2_anproj_1(A,B,C,E)
                                                  | r2_anproj_1(A,B,D,E)
                                                  | r2_anproj_1(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_anproj_2,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))
             => ! [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))
                                 => ( r4_anproj_2(A,B,C,D,E,F,G,H)
                                  <=> ( ~ r2_anproj_1(A,B,C,F)
                                      & r2_anproj_1(A,B,C,D)
                                      & r2_anproj_1(A,B,C,E)
                                      & r2_anproj_1(A,B,F,G)
                                      & r2_anproj_1(A,B,F,H) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_anproj_2,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))
             => ! [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))
                                 => ( r5_anproj_2(A,B,C,D,E,F,G,H)
                                  <=> ( ~ r1_anproj_1(A,B,D)
                                      & ~ r1_anproj_1(A,B,E)
                                      & ~ r1_anproj_1(A,B,G)
                                      & ~ r1_anproj_1(A,B,H)
                                      & ~ r1_anproj_1(A,C,D)
                                      & ~ r1_anproj_1(A,C,E)
                                      & ~ r1_anproj_1(A,F,G)
                                      & ~ r1_anproj_1(A,F,H)
                                      & ~ r1_anproj_1(A,D,E)
                                      & ~ r1_anproj_1(A,G,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_anproj_2,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))
             => ! [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))
                                             => ( ( v8_rlvect_1(B,A)
                                                  & r1_anproj_2(A,C,D,E)
                                                  & r1_anproj_2(A,F,G,H)
                                                  & r1_anproj_2(A,I,J,K)
                                                  & r4_anproj_2(A,B,C,D,E,F,G,H)
                                                  & r5_anproj_2(A,B,C,D,E,F,G,H)
                                                  & r2_anproj_1(A,C,G,K)
                                                  & r2_anproj_1(A,F,D,K)
                                                  & r2_anproj_1(A,C,H,J)
                                                  & r2_anproj_1(A,E,F,J)
                                                  & r2_anproj_1(A,D,H,I)
                                                  & r2_anproj_1(A,E,G,I) )
                                               => r2_anproj_1(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ? [E] :
                      ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                      & ? [F] :
                          ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                          & ? [G] :
                              ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                              & ! [H] :
                                  ( r2_hidden(H,A)
                                 => ( ( H = B
                                     => k1_funct_1(E,H) = np__1 )
                                    & ( H != B
                                     => k1_funct_1(E,H) = np__0 ) ) )
                              & ! [H] :
                                  ( r2_hidden(H,A)
                                 => ( ( H = C
                                     => k1_funct_1(F,H) = np__1 )
                                    & ( H != C
                                     => k1_funct_1(F,H) = np__0 ) ) )
                              & ! [H] :
                                  ( r2_hidden(H,A)
                                 => ( ( H = D
                                     => k1_funct_1(G,H) = np__1 )
                                    & ( H != D
                                     => k1_funct_1(G,H) = np__0 ) ) ) ) ) ) ) ) ) ) )).

fof(t11_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,A)
                             => ( ( r2_hidden(E,A)
                                  & r2_hidden(F,A)
                                  & r2_hidden(G,A)
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = E
                                         => k1_funct_1(B,H) = np__1 )
                                        & ( H != E
                                         => k1_funct_1(B,H) = np__0 ) ) )
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = F
                                         => k1_funct_1(C,H) = np__1 )
                                        & ( H != F
                                         => k1_funct_1(C,H) = np__0 ) ) )
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = G
                                         => k1_funct_1(D,H) = np__1 )
                                        & ( H != G
                                         => k1_funct_1(D,H) = np__0 ) ) ) )
                               => ( E = F
                                  | E = G
                                  | F = G
                                  | ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,D))) = k9_funcsdom(A)
                                               => ( H = np__0
                                                  & I = np__0
                                                  & J = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ~ ( r2_hidden(B,A)
                      & r2_hidden(C,A)
                      & r2_hidden(D,A)
                      & B != C
                      & B != D
                      & C != D
                      & ! [E] :
                          ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                         => ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,G))) = k9_funcsdom(A)
                                              & ~ ( H = np__0
                                                  & I = np__0
                                                  & J = np__0 ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,A)
                             => ( ( A = k8_domain_1(A,E,F,G)
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = E
                                         => k1_funct_1(B,H) = np__1 )
                                        & ( H != E
                                         => k1_funct_1(B,H) = np__0 ) ) )
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = F
                                         => k1_funct_1(C,H) = np__1 )
                                        & ( H != F
                                         => k1_funct_1(C,H) = np__0 ) ) )
                                  & ! [H] :
                                      ( r2_hidden(H,A)
                                     => ( ( H = G
                                         => k1_funct_1(D,H) = np__1 )
                                        & ( H != G
                                         => k1_funct_1(D,H) = np__0 ) ) ) )
                               => ( E = F
                                  | E = G
                                  | F = G
                                  | ! [H] :
                                      ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                     => ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & ? [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                  & H = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ~ ( A = k8_domain_1(A,B,C,D)
                      & B != C
                      & B != D
                      & C != D
                      & ! [E] :
                          ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                         => ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ? [H] :
                                      ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                      & ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ! [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                 => H != k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ~ ( A = k8_domain_1(A,B,C,D)
                      & B != C
                      & B != D
                      & C != D
                      & ! [E] :
                          ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                         => ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ~ ( ! [H] :
                                          ( m1_subset_1(H,k1_numbers)
                                         => ! [I] :
                                              ( m1_subset_1(I,k1_numbers)
                                             => ! [J] :
                                                  ( m1_subset_1(J,k1_numbers)
                                                 => ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),H,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,G))) = k9_funcsdom(A)
                                                   => ( H = np__0
                                                      & I = np__0
                                                      & J = np__0 ) ) ) ) )
                                      & ! [H] :
                                          ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                         => ? [I] :
                                              ( m1_subset_1(I,k1_numbers)
                                              & ? [J] :
                                                  ( m1_subset_1(J,k1_numbers)
                                                  & ? [K] :
                                                      ( m1_subset_1(K,k1_numbers)
                                                      & H = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),I,E)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_anproj_2,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)
      & ~ v3_realset2(A)
      & l2_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,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                               => ( E = np__0
                                  & F = np__0
                                  & G = np__0 ) ) ) ) )
                  & ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ? [F] :
                          ( m1_subset_1(F,k1_numbers)
                          & ? [G] :
                              ( m1_subset_1(G,k1_numbers)
                              & ? [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                  & E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) ) ) )).

fof(t17_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ? [F] :
                          ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                          & ? [G] :
                              ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                              & ? [H] :
                                  ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                  & ? [I] :
                                      ( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                      & ! [J] :
                                          ( r2_hidden(J,A)
                                         => ( ( J = B
                                             => k1_funct_1(F,J) = np__1 )
                                            & ( J != B
                                             => k1_funct_1(F,J) = np__0 ) ) )
                                      & ! [J] :
                                          ( r2_hidden(J,A)
                                         => ( ( J = C
                                             => k1_funct_1(G,J) = np__1 )
                                            & ( J != C
                                             => k1_funct_1(G,J) = np__0 ) ) )
                                      & ! [J] :
                                          ( r2_hidden(J,A)
                                         => ( ( J = D
                                             => k1_funct_1(H,J) = np__1 )
                                            & ( J != D
                                             => k1_funct_1(H,J) = np__0 ) ) )
                                      & ! [J] :
                                          ( r2_hidden(J,A)
                                         => ( ( J = E
                                             => k1_funct_1(I,J) = np__1 )
                                            & ( J != E
                                             => k1_funct_1(I,J) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,A)
                             => ! [H] :
                                  ( m1_subset_1(H,A)
                                 => ! [I] :
                                      ( m1_subset_1(I,A)
                                     => ( ( r2_hidden(F,A)
                                          & r2_hidden(G,A)
                                          & r2_hidden(H,A)
                                          & r2_hidden(I,A)
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = F
                                                 => k1_funct_1(B,J) = np__1 )
                                                & ( J != F
                                                 => k1_funct_1(B,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = G
                                                 => k1_funct_1(C,J) = np__1 )
                                                & ( J != G
                                                 => k1_funct_1(C,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = H
                                                 => k1_funct_1(D,J) = np__1 )
                                                & ( J != H
                                                 => k1_funct_1(D,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = I
                                                 => k1_funct_1(E,J) = np__1 )
                                                & ( J != I
                                                 => k1_funct_1(E,J) = np__0 ) ) ) )
                                       => ( F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ! [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                 => ! [L] :
                                                      ( m1_subset_1(L,k1_numbers)
                                                     => ! [M] :
                                                          ( m1_subset_1(M,k1_numbers)
                                                         => ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,D))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,E))) = k9_funcsdom(A)
                                                           => ( J = np__0
                                                              & K = np__0
                                                              & L = np__0
                                                              & M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ~ ( r2_hidden(B,A)
                          & r2_hidden(C,A)
                          & r2_hidden(D,A)
                          & r2_hidden(E,A)
                          & B != C
                          & B != D
                          & B != E
                          & C != D
                          & C != E
                          & D != E
                          & ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ! [H] :
                                      ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                     => ! [I] :
                                          ( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                         => ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & ? [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                  & ? [L] :
                                                      ( m1_subset_1(L,k1_numbers)
                                                      & ? [M] :
                                                          ( m1_subset_1(M,k1_numbers)
                                                          & k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,I))) = k9_funcsdom(A)
                                                          & ~ ( J = np__0
                                                              & K = np__0
                                                              & L = np__0
                                                              & M = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,A)
                             => ! [H] :
                                  ( m1_subset_1(H,A)
                                 => ! [I] :
                                      ( m1_subset_1(I,A)
                                     => ( ( A = k9_domain_1(A,F,G,H,I)
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = F
                                                 => k1_funct_1(B,J) = np__1 )
                                                & ( J != F
                                                 => k1_funct_1(B,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = G
                                                 => k1_funct_1(C,J) = np__1 )
                                                & ( J != G
                                                 => k1_funct_1(C,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = H
                                                 => k1_funct_1(D,J) = np__1 )
                                                & ( J != H
                                                 => k1_funct_1(D,J) = np__0 ) ) )
                                          & ! [J] :
                                              ( r2_hidden(J,A)
                                             => ( ( J = I
                                                 => k1_funct_1(E,J) = np__1 )
                                                & ( J != I
                                                 => k1_funct_1(E,J) = np__0 ) ) ) )
                                       => ( F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | ! [J] :
                                              ( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                             => ? [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                  & ? [L] :
                                                      ( m1_subset_1(L,k1_numbers)
                                                      & ? [M] :
                                                          ( m1_subset_1(M,k1_numbers)
                                                          & ? [N] :
                                                              ( m1_subset_1(N,k1_numbers)
                                                              & J = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,C))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,D))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ~ ( A = k9_domain_1(A,B,C,D,E)
                          & B != C
                          & B != D
                          & B != E
                          & C != D
                          & C != E
                          & D != E
                          & ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ! [H] :
                                      ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                     => ! [I] :
                                          ( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                         => ? [J] :
                                              ( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                              & ! [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                 => ! [L] :
                                                      ( m1_subset_1(L,k1_numbers)
                                                     => ! [M] :
                                                          ( m1_subset_1(M,k1_numbers)
                                                         => ! [N] :
                                                              ( m1_subset_1(N,k1_numbers)
                                                             => J != k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_anproj_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ~ ( A = k9_domain_1(A,B,C,D,E)
                          & B != C
                          & B != D
                          & B != E
                          & C != D
                          & C != E
                          & D != E
                          & ! [F] :
                              ( m2_fraenkel(F,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                             => ! [G] :
                                  ( m2_fraenkel(G,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                 => ! [H] :
                                      ( m2_fraenkel(H,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                     => ! [I] :
                                          ( m2_fraenkel(I,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                         => ~ ( ! [J] :
                                                  ( m1_subset_1(J,k1_numbers)
                                                 => ! [K] :
                                                      ( m1_subset_1(K,k1_numbers)
                                                     => ! [L] :
                                                          ( m1_subset_1(L,k1_numbers)
                                                         => ! [M] :
                                                              ( m1_subset_1(M,k1_numbers)
                                                             => ( k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),J,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,I))) = k9_funcsdom(A)
                                                               => ( J = np__0
                                                                  & K = np__0
                                                                  & L = np__0
                                                                  & M = np__0 ) ) ) ) ) )
                                              & ! [J] :
                                                  ( m2_fraenkel(J,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                                                 => ? [K] :
                                                      ( m1_subset_1(K,k1_numbers)
                                                      & ? [L] :
                                                          ( m1_subset_1(L,k1_numbers)
                                                          & ? [M] :
                                                              ( m1_subset_1(M,k1_numbers)
                                                              & ? [N] :
                                                                  ( m1_subset_1(N,k1_numbers)
                                                                  & J = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),K,F)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),L,G))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),M,H))),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_anproj_2,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)
      & ~ v3_realset2(A)
      & l2_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))
                      & ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                 => ! [I] :
                                      ( m1_subset_1(I,k1_numbers)
                                     => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                       => ( F = np__0
                                          & G = np__0
                                          & H = np__0
                                          & I = np__0 ) ) ) ) ) )
                      & ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ? [G] :
                              ( m1_subset_1(G,k1_numbers)
                              & ? [H] :
                                  ( m1_subset_1(H,k1_numbers)
                                  & ? [I] :
                                      ( m1_subset_1(I,k1_numbers)
                                      & ? [J] :
                                          ( m1_subset_1(J,k1_numbers)
                                          & F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_anproj_2,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_anproj_2(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,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                 => ( E = np__0
                                    & F = np__0
                                    & G = np__0 ) ) ) ) ) ) ) ) ) ) )).

fof(d7_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v2_collsp(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_collsp(A,B,C,B)
                      & r1_collsp(A,B,B,C)
                      & r1_collsp(A,B,C,C) ) ) ) ) ) ) )).

fof(d8_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v3_collsp(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))
                           => ( ( r1_collsp(A,B,C,D)
                                & r1_collsp(A,B,C,E)
                                & r1_collsp(A,B,C,F) )
                             => ( B = C
                                | r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ) )).

fof(d9_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v2_anproj_2(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))
                           => ~ ( r1_collsp(A,B,C,E)
                                & r1_collsp(A,C,D,F)
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ~ ( r1_collsp(A,B,D,G)
                                        & r1_collsp(A,E,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d10_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v3_anproj_2(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))
                    & B != D
                    & C != D
                    & r1_collsp(A,B,C,D) ) ) ) ) ) )).

fof(t24_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                 => ( r1_collsp(k6_anproj_1(A),B,C,D)
                  <=> ? [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))
                                & B = k3_anproj_1(A,E)
                                & C = k3_anproj_1(A,F)
                                & D = k3_anproj_1(A,G)
                                & v8_rlvect_1(E,A)
                                & v8_rlvect_1(F,A)
                                & v8_rlvect_1(G,A)
                                & r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t25_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                 => ( r1_collsp(k6_anproj_1(A),B,C,D)
                   => ( r1_collsp(k6_anproj_1(A),B,D,C)
                      & r1_collsp(k6_anproj_1(A),C,B,D)
                      & r1_collsp(k6_anproj_1(A),D,C,B)
                      & r1_collsp(k6_anproj_1(A),D,B,C)
                      & r1_collsp(k6_anproj_1(A),C,D,B) ) ) ) ) ) ) )).

fof(t26_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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,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 ) ) ) ) ) )
       => v3_anproj_2(k6_anproj_1(A)) ) ) )).

fof(d11_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v4_anproj_2(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))
                                   => ~ ( r1_collsp(A,B,C,D)
                                        & r1_collsp(A,E,F,D)
                                        & r1_collsp(A,B,E,G)
                                        & r1_collsp(A,C,F,G)
                                        & r1_collsp(A,B,F,H)
                                        & r1_collsp(A,C,E,H)
                                        & r1_collsp(A,G,D,H)
                                        & ~ r1_collsp(A,B,C,F)
                                        & ~ r1_collsp(A,B,C,E)
                                        & ~ r1_collsp(A,B,E,F)
                                        & ~ r1_collsp(A,C,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v5_anproj_2(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))
                                               => ( ( r1_collsp(A,C,D,K)
                                                    & r1_collsp(A,F,G,K)
                                                    & r1_collsp(A,D,E,I)
                                                    & r1_collsp(A,G,H,I)
                                                    & r1_collsp(A,C,E,J)
                                                    & r1_collsp(A,F,H,J)
                                                    & r1_collsp(A,B,C,F)
                                                    & r1_collsp(A,B,D,G)
                                                    & r1_collsp(A,B,E,H) )
                                                 => ( B = F
                                                    | C = F
                                                    | B = G
                                                    | D = G
                                                    | B = H
                                                    | E = H
                                                    | r1_collsp(A,B,C,D)
                                                    | r1_collsp(A,B,C,E)
                                                    | r1_collsp(A,B,D,E)
                                                    | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d13_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v6_anproj_2(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))
                                               => ( ( r1_collsp(A,B,C,D)
                                                    & r1_collsp(A,B,C,E)
                                                    & r1_collsp(A,B,F,G)
                                                    & r1_collsp(A,B,F,H)
                                                    & r1_collsp(A,C,G,K)
                                                    & r1_collsp(A,F,D,K)
                                                    & r1_collsp(A,C,H,J)
                                                    & r1_collsp(A,E,F,J)
                                                    & r1_collsp(A,D,H,I)
                                                    & r1_collsp(A,E,G,I) )
                                                 => ( B = D
                                                    | B = E
                                                    | D = E
                                                    | C = D
                                                    | C = E
                                                    | B = G
                                                    | B = H
                                                    | G = H
                                                    | F = G
                                                    | F = H
                                                    | r1_collsp(A,B,C,F)
                                                    | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d14_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v7_anproj_2(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))
                            & r1_collsp(A,B,C,F)
                            & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) )).

fof(d15_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & v2_anproj_2(A)
        & v3_anproj_2(A)
        & l1_collsp(A) )
     => ( v8_anproj_2(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))
                                    & r1_collsp(A,B,D,G)
                                    & r1_collsp(A,C,E,H)
                                    & r1_collsp(A,F,G,H) ) ) ) ) ) ) ) ) ) )).

fof(t27_anproj_2,axiom,(
    $true )).

fof(t28_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
                                 => ~ ( r1_collsp(k6_anproj_1(A),B,C,D)
                                      & r1_collsp(k6_anproj_1(A),E,F,D)
                                      & r1_collsp(k6_anproj_1(A),B,E,G)
                                      & r1_collsp(k6_anproj_1(A),C,F,G)
                                      & r1_collsp(k6_anproj_1(A),B,F,H)
                                      & r1_collsp(k6_anproj_1(A),C,E,H)
                                      & r1_collsp(k6_anproj_1(A),G,D,H)
                                      & ~ r1_collsp(k6_anproj_1(A),B,C,F)
                                      & ~ r1_collsp(k6_anproj_1(A),B,C,E)
                                      & ~ r1_collsp(k6_anproj_1(A),B,E,F)
                                      & ~ r1_collsp(k6_anproj_1(A),C,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t29_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                   => ( E = np__0
                                      & F = np__0
                                      & G = np__0 ) ) ) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
                 => ~ ( B != C
                      & ! [D] :
                          ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                         => ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                             => ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                                  & r1_collsp(k6_anproj_1(A),B,C,F)
                                  & r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) ) ) ) ) )).

fof(t30_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ( ? [B] :
            ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
                & B != C
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                       => ? [F] :
                            ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                            & r1_collsp(k6_anproj_1(A),B,C,F)
                            & r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                       => ? [F] :
                            ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                            & r1_collsp(k6_anproj_1(A),B,C,F)
                            & r1_collsp(k6_anproj_1(A),D,E,F) ) ) ) ) ) ) ) )).

fof(t31_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                   => ( E = np__0
                                      & F = np__0
                                      & G = np__0 ) ) ) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & E = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)) ) ) ) ) ) ) )
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v2_collsp(B)
                & v3_collsp(B)
                & v4_collsp(B)
                & v2_anproj_2(B)
                & v3_anproj_2(B)
                & l1_collsp(B) )
             => ~ ( B = k6_anproj_1(A)
                  & v7_anproj_2(B) ) ) ) ) )).

fof(t32_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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))
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                           => ( F = np__0
                                              & G = np__0
                                              & H = np__0
                                              & I = np__0 ) ) ) ) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                     => ~ ( ~ r1_collsp(k6_anproj_1(A),B,C,D)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                             => ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                                 => ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
                                          & r1_collsp(k6_anproj_1(A),E,F,H)
                                          & r1_collsp(k6_anproj_1(A),C,D,G)
                                          & r1_collsp(k6_anproj_1(A),B,H,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t33_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_rlvect_1(A) )
     => ~ ( v4_collsp(k6_anproj_1(A))
          & v3_anproj_2(k6_anproj_1(A))
          & ? [B] :
              ( m1_subset_1(B,u1_struct_0(k6_anproj_1(A)))
              & ? [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_anproj_1(A)))
                  & ? [D] :
                      ( m1_subset_1(D,u1_struct_0(k6_anproj_1(A)))
                      & ~ r1_collsp(k6_anproj_1(A),B,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k6_anproj_1(A)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k6_anproj_1(A)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k6_anproj_1(A)))
                                  & ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(k6_anproj_1(A)))
                                      & r1_collsp(k6_anproj_1(A),E,F,H)
                                      & r1_collsp(k6_anproj_1(A),C,D,G)
                                      & r1_collsp(k6_anproj_1(A),B,H,G) ) ) ) ) ) ) )
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v2_collsp(B)
                & v3_collsp(B)
                & v4_collsp(B)
                & v2_anproj_2(B)
                & v3_anproj_2(B)
                & l1_collsp(B) )
             => ~ ( B = k6_anproj_1(A)
                  & v8_anproj_2(B) ) ) ) ) )).

fof(t34_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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))
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                           => ( F = np__0
                                              & G = np__0
                                              & H = np__0
                                              & I = np__0 ) ) ) ) ) ) ) ) ) )
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v2_collsp(B)
                & v3_collsp(B)
                & v4_collsp(B)
                & v2_anproj_2(B)
                & v3_anproj_2(B)
                & l1_collsp(B) )
             => ~ ( B = k6_anproj_1(A)
                  & v8_anproj_2(B) ) ) ) ) )).

fof(t35_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                           => ( F = np__0
                                              & G = np__0
                                              & H = np__0
                                              & I = np__0 ) ) ) ) ) ) ) ) ) )
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v2_collsp(B)
                & v3_collsp(B)
                & v4_collsp(B)
                & v2_anproj_2(B)
                & v3_anproj_2(B)
                & l1_collsp(B) )
             => ~ ( B = k6_anproj_1(A)
                  & ~ v7_anproj_2(B) ) ) ) ) )).

fof(t36_anproj_2,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)
        & ~ v3_realset2(A)
        & l2_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))
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ? [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & ? [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                          & ? [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                              & F = k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,J)) ) ) ) ) )
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlvect_1(A,k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,H)),k3_rlvect_1(A,E,I)) = k1_rlvect_1(A)
                                           => ( F = np__0
                                              & G = np__0
                                              & H = np__0
                                              & I = np__0 ) ) ) ) ) ) ) ) ) )
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v2_collsp(B)
                & v3_collsp(B)
                & v4_collsp(B)
                & v2_anproj_2(B)
                & v3_anproj_2(B)
                & l1_collsp(B) )
             => ~ ( B = k6_anproj_1(A)
                  & ~ v7_anproj_2(B)
                  & v8_anproj_2(B) ) ) ) ) )).

fof(t37_anproj_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( ( ~ v3_struct_0(A)
          & v2_collsp(A)
          & v3_collsp(A)
          & v4_collsp(A)
          & v2_anproj_2(A)
          & v3_anproj_2(A)
          & v7_anproj_2(A)
          & l1_collsp(A) )
      <=> ( ~ v3_struct_0(A)
          & v2_collsp(A)
          & v3_collsp(A)
          & v4_collsp(A)
          & v3_anproj_2(A)
          & l1_collsp(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))
                              & r1_collsp(A,B,C,F)
                              & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------