SET007 Axioms: SET007+254.ax


%------------------------------------------------------------------------------
% File     : SET007+254 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Desargues Theorem In Projective 3-Space
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : projdes1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   30 (   5 unit)
%            Number of atoms       :  518 (  26 equality)
%            Maximal formula depth :   47 (  17 average)
%            Number of connectives :  587 (  99 ~  ;  22  |; 292  &)
%                                         (   2 <=>; 172 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   15 (   1 propositional; 0-5 arity)
%            Number of functors    :    1 (   0 constant; 1-1 arity)
%            Number of variables   :  160 (   0 singleton; 159 !;   1 ?)
%            Maximal term depth    :    2 (   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(cc1_projdes1,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)
          & ~ v7_anproj_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_collsp(A)
          & v3_collsp(A)
          & v4_collsp(A)
          & v2_anproj_2(A)
          & v3_anproj_2(A)
          & v5_anproj_2(A)
          & ~ v7_anproj_2(A) ) ) ) )).

fof(t1_projdes1,axiom,(
    ! [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) )
     => ! [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,D)
                   => ( r1_collsp(A,C,D,B)
                      & r1_collsp(A,D,B,C)
                      & r1_collsp(A,C,B,D)
                      & r1_collsp(A,B,D,C)
                      & r1_collsp(A,D,C,B) ) ) ) ) ) ) )).

fof(t2_projdes1,axiom,(
    $true )).

fof(t3_projdes1,axiom,(
    $true )).

fof(t4_projdes1,axiom,(
    $true )).

fof(t5_projdes1,axiom,(
    ! [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) )
     => ! [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,D) ) ) ) ) )).

fof(t6_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( ~ r1_collsp(A,B,C,D)
                          & r1_collsp(A,B,C,E)
                          & B != E
                          & r1_collsp(A,B,E,D) ) ) ) ) ) ) )).

fof(t7_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_collsp(A,B,C,E)
                          & r1_collsp(A,B,D,E) )
                       => ( r1_collsp(A,B,C,D)
                          | B = E ) ) ) ) ) ) ) )).

fof(t8_projdes1,axiom,(
    ! [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) )
     => ! [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))
                             => ~ ( ~ r1_collsp(A,B,C,D)
                                  & r1_collsp(A,B,D,E)
                                  & r1_collsp(A,C,D,F)
                                  & D != E
                                  & r1_collsp(A,G,E,F)
                                  & r1_collsp(A,B,C,G)
                                  & B != G
                                  & F = D ) ) ) ) ) ) ) ) )).

fof(d1_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_projdes1(A,B,C,D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                            & r1_collsp(A,B,C,F)
                            & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) )).

fof(t9_projdes1,axiom,(
    $true )).

fof(t10_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ~ ( ~ r1_collsp(A,B,C,D)
                            & ~ r1_collsp(A,C,D,E)
                            & ~ r1_collsp(A,D,E,B)
                            & ~ r1_collsp(A,E,B,C) )
                       => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t11_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_projdes1(A,B,C,D,E)
                       => ( r1_projdes1(A,C,D,E,B)
                          & r1_projdes1(A,D,E,B,C)
                          & r1_projdes1(A,E,B,C,D)
                          & r1_projdes1(A,C,B,D,E)
                          & r1_projdes1(A,D,C,E,B)
                          & r1_projdes1(A,E,D,B,C)
                          & r1_projdes1(A,B,E,C,D)
                          & r1_projdes1(A,B,D,E,C)
                          & r1_projdes1(A,C,E,B,D)
                          & r1_projdes1(A,D,B,C,E)
                          & r1_projdes1(A,E,C,D,B)
                          & r1_projdes1(A,D,B,E,C)
                          & r1_projdes1(A,E,C,B,D)
                          & r1_projdes1(A,B,D,C,E)
                          & r1_projdes1(A,C,E,D,B)
                          & r1_projdes1(A,B,C,E,D)
                          & r1_projdes1(A,B,E,D,C)
                          & r1_projdes1(A,C,D,B,E)
                          & r1_projdes1(A,C,B,E,D)
                          & r1_projdes1(A,D,C,B,E)
                          & r1_projdes1(A,D,E,C,B)
                          & r1_projdes1(A,E,B,D,C)
                          & r1_projdes1(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t12_projdes1,axiom,(
    ! [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) )
     => ! [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_projdes1(A,B,C,D,E)
                                      & r1_projdes1(A,B,C,D,F)
                                      & r1_projdes1(A,B,C,D,G)
                                      & r1_projdes1(A,B,C,D,H) )
                                   => ( r1_collsp(A,B,C,D)
                                      | r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_projdes1,axiom,(
    ! [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) )
     => ! [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_projdes1(A,E,F,G,B)
                                      & r1_projdes1(A,E,F,G,D)
                                      & r1_projdes1(A,E,F,G,C)
                                      & r1_projdes1(A,B,C,D,H) )
                                   => ( r1_collsp(A,B,C,D)
                                      | r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_projdes1,axiom,(
    ! [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) )
     => ! [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))
                             => ( ( r1_collsp(A,B,C,D)
                                  & r1_projdes1(A,E,F,G,B)
                                  & r1_projdes1(A,E,F,G,C) )
                               => ( B = C
                                  | r1_projdes1(A,E,F,G,D) ) ) ) ) ) ) ) ) ) )).

fof(t15_projdes1,axiom,(
    ! [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) )
     => ! [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_projdes1(A,B,C,D,E)
                                      & r1_projdes1(A,B,C,D,F)
                                      & r1_projdes1(A,B,C,D,G)
                                      & r1_projdes1(A,B,C,D,H)
                                      & ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ~ ( r1_collsp(A,E,F,I)
                                              & r1_collsp(A,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_projdes1,axiom,(
    ! [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) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r1_projdes1(A,B,C,D,E) ) ) ) ) ) )).

fof(t17_projdes1,axiom,(
    ! [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) )
     => ! [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,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t18_projdes1,axiom,(
    ! [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) )
     => ! [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))
                     => ( ~ ( B != C
                            & B != D
                            & C != D
                            & B != E
                            & C != E
                            & E != D )
                       => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t19_projdes1,axiom,(
    ! [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) )
     => ! [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_projdes1(A,B,C,D,E)
                              & r1_collsp(A,E,B,F)
                              & B != F
                              & r1_projdes1(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t20_projdes1,axiom,(
    ! [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) )
     => ! [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))
                                         => ( ( r1_projdes1(A,B,C,D,H)
                                              & r1_projdes1(A,B,C,D,I)
                                              & r1_projdes1(A,B,C,D,J)
                                              & r1_projdes1(A,E,F,G,H)
                                              & r1_projdes1(A,E,F,G,I)
                                              & r1_projdes1(A,E,F,G,J) )
                                           => ( r1_collsp(A,B,C,D)
                                              | r1_collsp(A,E,F,G)
                                              | r1_projdes1(A,B,C,D,E)
                                              | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_projdes1,axiom,(
    ! [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) )
     => ! [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,D,B,C)
                                                  & r1_collsp(A,B,E,I)
                                                  & r1_collsp(A,C,G,I)
                                                  & r1_collsp(A,E,F,J)
                                                  & r1_collsp(A,G,H,J)
                                                  & r1_collsp(A,B,F,K)
                                                  & r1_collsp(A,C,H,K) )
                                               => ( B = C
                                                  | r1_projdes1(A,B,E,F,D)
                                                  | r1_collsp(A,C,G,H)
                                                  | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_projdes1,axiom,(
    ! [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) )
     => ! [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_projdes1(A,B,C,D,E)
                              & r1_projdes1(A,B,C,D,F)
                              & ~ r1_collsp(A,B,C,F)
                              & r1_projdes1(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(t23_projdes1,axiom,(
    ! [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) )
     => ! [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,E,B,F)
                                      & r1_collsp(A,E,C,G)
                                      & r1_collsp(A,E,D,H) )
                                   => ( r1_projdes1(A,B,C,D,E)
                                      | E = F
                                      | E = G
                                      | E = H
                                      | ( ~ r1_collsp(A,F,G,H)
                                        & ~ r1_projdes1(A,F,G,H,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_projdes1,axiom,(
    ! [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) )
     => ! [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))
                                             => ! [L] :
                                                  ( m1_subset_1(L,u1_struct_0(A))
                                                 => ! [M] :
                                                      ( m1_subset_1(M,u1_struct_0(A))
                                                     => ~ ( r1_projdes1(A,B,C,D,E)
                                                          & ~ r1_projdes1(A,B,C,D,F)
                                                          & ~ r1_projdes1(A,B,C,F,E)
                                                          & ~ r1_projdes1(A,C,D,F,E)
                                                          & ~ r1_projdes1(A,B,D,F,E)
                                                          & r1_collsp(A,E,F,G)
                                                          & r1_collsp(A,E,B,H)
                                                          & r1_collsp(A,E,C,I)
                                                          & r1_collsp(A,E,D,J)
                                                          & r1_collsp(A,B,F,K)
                                                          & r1_collsp(A,H,G,K)
                                                          & r1_collsp(A,C,F,L)
                                                          & r1_collsp(A,I,G,L)
                                                          & r1_collsp(A,D,F,M)
                                                          & E != H
                                                          & E != G
                                                          & F != G
                                                          & E != I
                                                          & r1_collsp(A,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_projdes1,axiom,(
    ! [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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_projdes1(A,B,C,D,E)
                      <=> ( ~ r1_collsp(A,C,D,E)
                          & ~ r1_collsp(A,B,C,D)
                          & ~ r1_collsp(A,B,D,E)
                          & ~ r1_collsp(A,B,E,C) ) ) ) ) ) ) ) )).

fof(t25_projdes1,axiom,(
    $true )).

fof(t26_projdes1,axiom,(
    ! [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) )
     => ! [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,F)
                                                  & r1_collsp(A,B,D,G)
                                                  & r1_collsp(A,B,E,H)
                                                  & r1_collsp(A,C,D,I)
                                                  & r1_collsp(A,F,G,I)
                                                  & r1_collsp(A,D,E,J)
                                                  & r1_collsp(A,G,H,J)
                                                  & r1_collsp(A,C,E,K)
                                                  & r1_collsp(A,F,H,K) )
                                               => ( r1_collsp(A,B,C,D)
                                                  | r1_collsp(A,B,D,E)
                                                  | r1_collsp(A,B,C,E)
                                                  | C = F
                                                  | D = G
                                                  | B = F
                                                  | B = G
                                                  | B = H
                                                  | r1_collsp(A,J,K,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_projdes1,axiom,(
    ! [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) )
     => v5_anproj_2(A) ) )).
%------------------------------------------------------------------------------