SET007 Axioms: SET007+268.ax


%------------------------------------------------------------------------------
% File     : SET007+268 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Incidence 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    : incproj [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (   6 unit)
%            Number of atoms       :  850 (  74 equality)
%            Maximal formula depth :   65 (  15 average)
%            Number of connectives :  912 ( 121 ~  ;  22  |; 470  &)
%                                         (  25 <=>; 274 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   1 propositional; 0-5 arity)
%            Number of functors    :   11 (   0 constant; 1-3 arity)
%            Number of variables   :  313 (   0 singleton; 277 !;  36 ?)
%            Maximal term depth    :    3 (   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(fc1_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ~ v1_xboole_0(k1_incproj(A)) ) )).

fof(fc2_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => v1_incsp_1(k3_incproj(A)) ) )).

fof(fc3_incproj,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) )
     => ( v1_incsp_1(k3_incproj(A))
        & v1_incproj(k3_incproj(A))
        & v2_incproj(k3_incproj(A))
        & v3_incproj(k3_incproj(A))
        & v4_incproj(k3_incproj(A))
        & v5_incproj(k3_incproj(A)) ) ) )).

fof(rc1_incproj,axiom,(
    ? [A] :
      ( l1_incsp_1(A)
      & v1_incsp_1(A)
      & v1_incproj(A)
      & v2_incproj(A)
      & v3_incproj(A)
      & v4_incproj(A)
      & v5_incproj(A) ) )).

fof(fc4_incproj,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) )
     => ( v1_incsp_1(k3_incproj(A))
        & v1_incproj(k3_incproj(A))
        & v2_incproj(k3_incproj(A))
        & v3_incproj(k3_incproj(A))
        & v4_incproj(k3_incproj(A))
        & v5_incproj(k3_incproj(A)) ) ) )).

fof(rc2_incproj,axiom,(
    ? [A] :
      ( l1_incsp_1(A)
      & v1_incproj(A)
      & v2_incproj(A)
      & v3_incproj(A)
      & v4_incproj(A)
      & v5_incproj(A)
      & ~ v6_incproj(A)
      & v7_incproj(A)
      & v9_incproj(A)
      & v10_incproj(A) ) )).

fof(rc3_incproj,axiom,(
    ? [A] :
      ( l1_incsp_1(A)
      & v1_incproj(A)
      & v2_incproj(A)
      & v3_incproj(A)
      & v4_incproj(A)
      & v5_incproj(A)
      & ~ v6_incproj(A)
      & v7_incproj(A)
      & v9_incproj(A)
      & v11_incproj(A) ) )).

fof(rc4_incproj,axiom,(
    ? [A] :
      ( l1_incsp_1(A)
      & v1_incproj(A)
      & v2_incproj(A)
      & v3_incproj(A)
      & v4_incproj(A)
      & v5_incproj(A)
      & v6_incproj(A)
      & v9_incproj(A)
      & v10_incproj(A) ) )).

fof(rc5_incproj,axiom,(
    ? [A] :
      ( l1_incsp_1(A)
      & v1_incproj(A)
      & v2_incproj(A)
      & v3_incproj(A)
      & v4_incproj(A)
      & v5_incproj(A)
      & v6_incproj(A)
      & v9_incproj(A)
      & v11_incproj(A) ) )).

fof(t1_incproj,axiom,(
    $true )).

fof(t2_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_incproj(B,A)
        <=> m1_subset_1(B,k1_incproj(A)) ) ) )).

fof(d2_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),k1_incproj(A))
         => ( B = k2_incproj(A)
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),B)
              <=> ( r2_hidden(C,u1_struct_0(A))
                  & r2_hidden(D,k1_incproj(A))
                  & ? [E] :
                      ( D = E
                      & r2_hidden(C,E) ) ) ) ) ) ) )).

fof(d3_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => k3_incproj(A) = g1_incsp_1(u1_struct_0(A),k1_incproj(A),k2_incproj(A)) ) )).

fof(t3_incproj,axiom,(
    $true )).

fof(t4_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ( u1_incsp_1(k3_incproj(A)) = u1_struct_0(A)
        & u2_incsp_1(k3_incproj(A)) = k1_incproj(A)
        & u3_incsp_1(k3_incproj(A)) = k2_incproj(A) ) ) )).

fof(t5_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
        <=> m1_subset_1(B,u1_incsp_1(k3_incproj(A))) ) ) )).

fof(t6_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_incproj(B,A)
        <=> m1_subset_1(B,u2_incsp_1(k3_incproj(A))) ) ) )).

fof(t7_incproj,axiom,(
    $true )).

fof(t8_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
             => ( r1_incsp_1(k3_incproj(A),B,C)
              <=> r2_hidden(k4_tarski(B,C),k2_incproj(A)) ) ) ) ) )).

fof(t9_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_incproj(E,A)
                     => ( ( B = D
                          & C = E )
                       => ( r1_incsp_1(k3_incproj(A),B,C)
                        <=> r2_hidden(D,E) ) ) ) ) ) ) ) )).

fof(t10_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(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))
                  & B != C
                  & C != D
                  & D != B ) ) ) ) )).

fof(t11_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) )).

fof(t12_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
             => ! [D] :
                  ( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u2_incsp_1(k3_incproj(A)))
                     => ~ ( r1_incsp_1(k3_incproj(A),B,D)
                          & r1_incsp_1(k3_incproj(A),C,D)
                          & r1_incsp_1(k3_incproj(A),B,E)
                          & r1_incsp_1(k3_incproj(A),C,E)
                          & B != C
                          & D != E ) ) ) ) ) ) )).

fof(t13_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
             => ? [D] :
                  ( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
                  & r1_incsp_1(k3_incproj(A),B,D)
                  & r1_incsp_1(k3_incproj(A),C,D) ) ) ) ) )).

fof(t14_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_incsp_1(k3_incproj(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))
                             => ( ( B = E
                                  & C = F
                                  & D = G )
                               => ( r1_collsp(A,E,F,G)
                                <=> ? [H] :
                                      ( m1_subset_1(H,u2_incsp_1(k3_incproj(A)))
                                      & r1_incsp_1(k3_incproj(A),B,H)
                                      & r1_incsp_1(k3_incproj(A),C,H)
                                      & r1_incsp_1(k3_incproj(A),D,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
               => r1_incsp_1(k3_incproj(A),B,C) ) ) ) )).

fof(t16_incproj,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) )
     => ! [B] :
          ( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
         => ? [C] :
              ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
              & ? [D] :
                  ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                  & ? [E] :
                      ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                      & C != D
                      & D != E
                      & E != C
                      & r1_incsp_1(k3_incproj(A),C,B)
                      & r1_incsp_1(k3_incproj(A),D,B)
                      & r1_incsp_1(k3_incproj(A),E,B) ) ) ) ) ) )).

fof(t17_incproj,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u2_incsp_1(k3_incproj(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u2_incsp_1(k3_incproj(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u2_incsp_1(k3_incproj(A)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u2_incsp_1(k3_incproj(A)))
                                         => ~ ( r1_incsp_1(k3_incproj(A),B,G)
                                              & r1_incsp_1(k3_incproj(A),C,G)
                                              & r1_incsp_1(k3_incproj(A),D,H)
                                              & r1_incsp_1(k3_incproj(A),E,H)
                                              & r1_incsp_1(k3_incproj(A),F,G)
                                              & r1_incsp_1(k3_incproj(A),F,H)
                                              & r1_incsp_1(k3_incproj(A),B,I)
                                              & r1_incsp_1(k3_incproj(A),D,I)
                                              & r1_incsp_1(k3_incproj(A),C,J)
                                              & r1_incsp_1(k3_incproj(A),E,J)
                                              & ~ r1_incsp_1(k3_incproj(A),F,I)
                                              & ~ r1_incsp_1(k3_incproj(A),F,J)
                                              & G != H
                                              & ! [K] :
                                                  ( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
                                                 => ~ ( r1_incsp_1(k3_incproj(A),K,I)
                                                      & r1_incsp_1(k3_incproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_incproj,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) )
     => ( ! [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) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
               => ? [D] :
                    ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                    & r1_incsp_1(k3_incproj(A),D,B)
                    & r1_incsp_1(k3_incproj(A),D,C) ) ) ) ) ) )).

fof(t19_incproj,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) )
     => ~ ( ? [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) ) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
             => ! [C] :
                  ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
                 => ? [D] :
                      ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                      & r1_incsp_1(k3_incproj(A),D,B)
                      & r1_incsp_1(k3_incproj(A),D,C) ) ) ) ) ) )).

fof(t20_incproj,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) )
     => ( ! [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) ) ) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
               => ! [D] :
                    ( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
                   => ? [E] :
                        ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                        & ? [F] :
                            ( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
                            & ? [G] :
                                ( m1_subset_1(G,u2_incsp_1(k3_incproj(A)))
                                & r1_incsp_1(k3_incproj(A),B,G)
                                & r1_incsp_1(k3_incproj(A),E,G)
                                & r1_incsp_1(k3_incproj(A),F,G)
                                & r1_incsp_1(k3_incproj(A),E,C)
                                & r1_incsp_1(k3_incproj(A),F,D) ) ) ) ) ) ) ) ) )).

fof(d4_incproj,axiom,(
    $true )).

fof(d5_incproj,axiom,(
    ! [A,B,C] :
      ( r1_incproj(A,B,C)
    <=> ( A != B
        & B != C
        & C != A ) ) )).

fof(d6_incproj,axiom,(
    ! [A,B,C,D] :
      ( r2_incproj(A,B,C,D)
    <=> ( A != B
        & B != C
        & C != A
        & D != A
        & D != B
        & D != C ) ) )).

fof(d7_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ( r3_incproj(A,B,C,D)
                  <=> ( r1_incsp_1(A,B,D)
                      & r1_incsp_1(A,C,D) ) ) ) ) ) ) )).

fof(d8_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ! [B] :
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ( r4_incproj(A,B,C,D,E)
                      <=> ( r1_incsp_1(A,B,D)
                          & r1_incsp_1(A,C,D)
                          & r1_incsp_1(A,E,D) ) ) ) ) ) ) ) )).

fof(t21_incproj,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) )
     => ( ! [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) ) ) ) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
                                   => ! [I] :
                                        ( m1_subset_1(I,u2_incsp_1(k3_incproj(A)))
                                       => ! [J] :
                                            ( m1_subset_1(J,u2_incsp_1(k3_incproj(A)))
                                           => ! [K] :
                                                ( m1_subset_1(K,u2_incsp_1(k3_incproj(A)))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
                                                               => ~ ( ~ r1_incsp_1(k3_incproj(A),C,I)
                                                                    & ~ r1_incsp_1(k3_incproj(A),D,I)
                                                                    & ~ r1_incsp_1(k3_incproj(A),B,J)
                                                                    & ~ r1_incsp_1(k3_incproj(A),E,J)
                                                                    & ~ r1_incsp_1(k3_incproj(A),B,K)
                                                                    & ~ r1_incsp_1(k3_incproj(A),D,K)
                                                                    & ~ r1_incsp_1(k3_incproj(A),C,L)
                                                                    & ~ r1_incsp_1(k3_incproj(A),E,L)
                                                                    & r4_incproj(k3_incproj(A),F,B,I,E)
                                                                    & r4_incproj(k3_incproj(A),F,C,J,D)
                                                                    & r4_incproj(k3_incproj(A),G,C,K,E)
                                                                    & r4_incproj(k3_incproj(A),G,B,L,D)
                                                                    & r4_incproj(k3_incproj(A),H,B,M,C)
                                                                    & r4_incproj(k3_incproj(A),H,D,N,E)
                                                                    & r3_incproj(k3_incproj(A),F,G,O)
                                                                    & r1_incsp_1(k3_incproj(A),H,O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_incproj,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) )
     => ( ! [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) ) ) ) ) ) ) ) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_incsp_1(k3_incproj(A)))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_incsp_1(k3_incproj(A)))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
                                                               => ! [P] :
                                                                    ( m1_subset_1(P,u2_incsp_1(k3_incproj(A)))
                                                                   => ! [Q] :
                                                                        ( m1_subset_1(Q,u2_incsp_1(k3_incproj(A)))
                                                                       => ! [R] :
                                                                            ( m1_subset_1(R,u2_incsp_1(k3_incproj(A)))
                                                                           => ! [S] :
                                                                                ( m1_subset_1(S,u2_incsp_1(k3_incproj(A)))
                                                                               => ! [T] :
                                                                                    ( m1_subset_1(T,u2_incsp_1(k3_incproj(A)))
                                                                                   => ~ ( r4_incproj(k3_incproj(A),B,C,L,D)
                                                                                        & r4_incproj(k3_incproj(A),B,F,M,E)
                                                                                        & r4_incproj(k3_incproj(A),B,H,N,G)
                                                                                        & r4_incproj(k3_incproj(A),H,F,O,K)
                                                                                        & r4_incproj(k3_incproj(A),H,I,P,D)
                                                                                        & r4_incproj(k3_incproj(A),F,J,Q,D)
                                                                                        & r4_incproj(k3_incproj(A),K,E,R,G)
                                                                                        & r4_incproj(k3_incproj(A),C,I,S,G)
                                                                                        & r4_incproj(k3_incproj(A),C,J,T,E)
                                                                                        & r1_incproj(L,M,N)
                                                                                        & B != D
                                                                                        & B != F
                                                                                        & B != H
                                                                                        & B != C
                                                                                        & B != E
                                                                                        & B != G
                                                                                        & D != C
                                                                                        & F != E
                                                                                        & H != G
                                                                                        & ! [U] :
                                                                                            ( m1_subset_1(U,u2_incsp_1(k3_incproj(A)))
                                                                                           => ~ r4_incproj(k3_incproj(A),I,J,U,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_incproj,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) )
     => ( ! [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) ) ) ) ) ) ) ) ) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_incsp_1(k3_incproj(A)))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_incsp_1(k3_incproj(A)))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
                                                               => ! [P] :
                                                                    ( m1_subset_1(P,u2_incsp_1(k3_incproj(A)))
                                                                   => ! [Q] :
                                                                        ( m1_subset_1(Q,u2_incsp_1(k3_incproj(A)))
                                                                       => ! [R] :
                                                                            ( m1_subset_1(R,u2_incsp_1(k3_incproj(A)))
                                                                           => ! [S] :
                                                                                ( m1_subset_1(S,u2_incsp_1(k3_incproj(A)))
                                                                               => ! [T] :
                                                                                    ( m1_subset_1(T,u2_incsp_1(k3_incproj(A)))
                                                                                   => ( ( r2_incproj(B,C,D,E)
                                                                                        & r2_incproj(B,F,G,H)
                                                                                        & r1_incsp_1(k3_incproj(A),B,N)
                                                                                        & r1_incsp_1(k3_incproj(A),B,Q)
                                                                                        & r4_incproj(k3_incproj(A),D,H,L,I)
                                                                                        & r4_incproj(k3_incproj(A),E,F,O,J)
                                                                                        & r4_incproj(k3_incproj(A),C,G,R,K)
                                                                                        & r4_incproj(k3_incproj(A),C,H,M,J)
                                                                                        & r4_incproj(k3_incproj(A),E,G,P,I)
                                                                                        & r4_incproj(k3_incproj(A),D,F,S,K)
                                                                                        & r4_incproj(k3_incproj(A),F,G,N,H)
                                                                                        & r4_incproj(k3_incproj(A),C,D,Q,E)
                                                                                        & r3_incproj(k3_incproj(A),I,J,T) )
                                                                                     => ( N = Q
                                                                                        | r1_incsp_1(k3_incproj(A),K,T) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ( v1_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u2_incsp_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u2_incsp_1(A))
                       => ~ ( r1_incsp_1(A,B,D)
                            & r1_incsp_1(A,C,D)
                            & r1_incsp_1(A,B,E)
                            & r1_incsp_1(A,C,E)
                            & B != C
                            & D != E ) ) ) ) ) ) ) )).

fof(d10_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ( v2_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ? [D] :
                    ( m1_subset_1(D,u2_incsp_1(A))
                    & r1_incsp_1(A,B,D)
                    & r1_incsp_1(A,C,D) ) ) ) ) ) )).

fof(d11_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ( v3_incproj(A)
      <=> ~ ! [B] :
              ( m1_subset_1(B,u1_incsp_1(A))
             => ! [C] :
                  ( m1_subset_1(C,u2_incsp_1(A))
                 => r1_incsp_1(A,B,C) ) ) ) ) )).

fof(d12_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ( v4_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u2_incsp_1(A))
           => ? [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                        & C != D
                        & D != E
                        & E != C
                        & r1_incsp_1(A,C,B)
                        & r1_incsp_1(A,D,B)
                        & r1_incsp_1(A,E,B) ) ) ) ) ) ) )).

fof(d13_incproj,axiom,(
    ! [A] :
      ( l1_incsp_1(A)
     => ( v5_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u2_incsp_1(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u2_incsp_1(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u2_incsp_1(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u2_incsp_1(A))
                                               => ~ ( r1_incsp_1(A,B,H)
                                                    & r1_incsp_1(A,C,H)
                                                    & r1_incsp_1(A,D,I)
                                                    & r1_incsp_1(A,E,I)
                                                    & r1_incsp_1(A,F,H)
                                                    & r1_incsp_1(A,F,I)
                                                    & r1_incsp_1(A,B,J)
                                                    & r1_incsp_1(A,D,J)
                                                    & r1_incsp_1(A,C,K)
                                                    & r1_incsp_1(A,E,K)
                                                    & ~ r1_incsp_1(A,F,J)
                                                    & ~ r1_incsp_1(A,F,K)
                                                    & H != I
                                                    & ! [L] :
                                                        ( m1_subset_1(L,u1_incsp_1(A))
                                                       => ~ ( r1_incsp_1(A,L,J)
                                                            & r1_incsp_1(A,L,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d14_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v6_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u2_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u2_incsp_1(A))
               => ? [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                    & r1_incsp_1(A,D,B)
                    & r1_incsp_1(A,D,C) ) ) ) ) ) )).

fof(d15_incproj,axiom,(
    $true )).

fof(d16_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v7_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u2_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u2_incsp_1(A))
                   => ? [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                        & ? [F] :
                            ( m1_subset_1(F,u1_incsp_1(A))
                            & ? [G] :
                                ( m1_subset_1(G,u2_incsp_1(A))
                                & r1_incsp_1(A,B,G)
                                & r1_incsp_1(A,E,G)
                                & r1_incsp_1(A,F,G)
                                & r1_incsp_1(A,E,C)
                                & r1_incsp_1(A,F,D) ) ) ) ) ) ) ) ) )).

fof(d17_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v8_incproj(A)
      <=> ( v7_incproj(A)
          & ~ v6_incproj(A) ) ) ) )).

fof(d18_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v9_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u2_incsp_1(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u2_incsp_1(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u2_incsp_1(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(A))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(A))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(A))
                                                               => ~ ( ~ r1_incsp_1(A,C,I)
                                                                    & ~ r1_incsp_1(A,D,I)
                                                                    & ~ r1_incsp_1(A,B,J)
                                                                    & ~ r1_incsp_1(A,E,J)
                                                                    & ~ r1_incsp_1(A,B,K)
                                                                    & ~ r1_incsp_1(A,D,K)
                                                                    & ~ r1_incsp_1(A,C,L)
                                                                    & ~ r1_incsp_1(A,E,L)
                                                                    & r4_incproj(A,F,B,I,E)
                                                                    & r4_incproj(A,F,C,J,D)
                                                                    & r4_incproj(A,G,C,K,E)
                                                                    & r4_incproj(A,G,B,L,D)
                                                                    & r4_incproj(A,H,B,M,C)
                                                                    & r4_incproj(A,H,D,N,E)
                                                                    & r3_incproj(A,F,G,O)
                                                                    & r1_incsp_1(A,H,O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d19_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v10_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_incsp_1(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_incsp_1(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_incsp_1(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(A))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(A))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(A))
                                                               => ! [P] :
                                                                    ( m1_subset_1(P,u2_incsp_1(A))
                                                                   => ! [Q] :
                                                                        ( m1_subset_1(Q,u2_incsp_1(A))
                                                                       => ! [R] :
                                                                            ( m1_subset_1(R,u2_incsp_1(A))
                                                                           => ! [S] :
                                                                                ( m1_subset_1(S,u2_incsp_1(A))
                                                                               => ! [T] :
                                                                                    ( m1_subset_1(T,u2_incsp_1(A))
                                                                                   => ~ ( r4_incproj(A,B,C,L,D)
                                                                                        & r4_incproj(A,B,F,M,E)
                                                                                        & r4_incproj(A,B,H,N,G)
                                                                                        & r4_incproj(A,H,F,O,K)
                                                                                        & r4_incproj(A,H,I,P,D)
                                                                                        & r4_incproj(A,F,J,Q,D)
                                                                                        & r4_incproj(A,K,E,R,G)
                                                                                        & r4_incproj(A,C,I,S,G)
                                                                                        & r4_incproj(A,C,J,T,E)
                                                                                        & r1_incproj(L,M,N)
                                                                                        & B != D
                                                                                        & B != F
                                                                                        & B != H
                                                                                        & B != C
                                                                                        & B != E
                                                                                        & B != G
                                                                                        & D != C
                                                                                        & F != E
                                                                                        & H != G
                                                                                        & ! [U] :
                                                                                            ( m1_subset_1(U,u2_incsp_1(A))
                                                                                           => ~ r4_incproj(A,I,J,U,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d20_incproj,axiom,(
    ! [A] :
      ( ( v1_incproj(A)
        & v2_incproj(A)
        & v3_incproj(A)
        & v4_incproj(A)
        & v5_incproj(A)
        & l1_incsp_1(A) )
     => ( v11_incproj(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_incsp_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_incsp_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_incsp_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_incsp_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_incsp_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_incsp_1(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_incsp_1(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_incsp_1(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_incsp_1(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_incsp_1(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u2_incsp_1(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u2_incsp_1(A))
                                                       => ! [N] :
                                                            ( m1_subset_1(N,u2_incsp_1(A))
                                                           => ! [O] :
                                                                ( m1_subset_1(O,u2_incsp_1(A))
                                                               => ! [P] :
                                                                    ( m1_subset_1(P,u2_incsp_1(A))
                                                                   => ! [Q] :
                                                                        ( m1_subset_1(Q,u2_incsp_1(A))
                                                                       => ! [R] :
                                                                            ( m1_subset_1(R,u2_incsp_1(A))
                                                                           => ! [S] :
                                                                                ( m1_subset_1(S,u2_incsp_1(A))
                                                                               => ! [T] :
                                                                                    ( m1_subset_1(T,u2_incsp_1(A))
                                                                                   => ( ( r2_incproj(B,C,D,E)
                                                                                        & r2_incproj(B,F,G,H)
                                                                                        & r1_incsp_1(A,B,N)
                                                                                        & r1_incsp_1(A,B,Q)
                                                                                        & r4_incproj(A,D,H,L,I)
                                                                                        & r4_incproj(A,E,F,O,J)
                                                                                        & r4_incproj(A,C,G,R,K)
                                                                                        & r4_incproj(A,C,H,M,J)
                                                                                        & r4_incproj(A,E,G,P,I)
                                                                                        & r4_incproj(A,D,F,S,K)
                                                                                        & r4_incproj(A,F,G,N,H)
                                                                                        & r4_incproj(A,C,D,Q,E)
                                                                                        & r3_incproj(A,I,J,T) )
                                                                                     => ( N = Q
                                                                                        | r1_incsp_1(A,K,T) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_m1_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_incproj(B,A)
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ? [B] : m1_incproj(B,A) ) )).

fof(redefinition_m1_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => ! [B] :
          ( m1_incproj(B,A)
        <=> m2_collsp(B,A) ) ) )).

fof(dt_k1_incproj,axiom,(
    $true )).

fof(dt_k2_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => m2_relset_1(k2_incproj(A),u1_struct_0(A),k1_incproj(A)) ) )).

fof(dt_k3_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => l1_incsp_1(k3_incproj(A)) ) )).

fof(d1_incproj,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & v4_collsp(A)
        & l1_collsp(A) )
     => k1_incproj(A) = a_1_0_incproj(A) ) )).

fof(fraenkel_a_1_0_incproj,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_collsp(B)
        & v3_collsp(B)
        & v4_collsp(B)
        & l1_collsp(B) )
     => ( r2_hidden(A,a_1_0_incproj(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & m1_incproj(C,B) ) ) ) )).
%------------------------------------------------------------------------------