SET007 Axioms: SET007+342.ax


%------------------------------------------------------------------------------
% File     : SET007+342 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Oriented Metric-Affine Plane - Part II
% 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    : dirort [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   31 (   2 unit)
%            Number of atoms       :  425 (  27 equality)
%            Maximal formula depth :   29 (  14 average)
%            Number of connectives :  477 (  83 ~  ;   7  |; 197  &)
%                                         (  11 <=>; 179 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-5 arity)
%            Number of functors    :    3 (   0 constant; 1-3 arity)
%            Number of variables   :  167 (   0 singleton; 154 !;  13 ?)
%            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(rc1_dirort,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_dirort(A) ) )).

fof(rc2_dirort,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_dirort(A)
      & v2_dirort(A)
      & v3_dirort(A)
      & v4_dirort(A)
      & v5_dirort(A) ) )).

fof(rc3_dirort,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_dirort(A)
      & v2_dirort(A)
      & v3_dirort(A)
      & v4_dirort(A)
      & v6_dirort(A) ) )).

fof(t1_dirort,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))
             => ( r1_analmetr(A,B,C)
               => ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k6_analort(A,B,C)))
                                     => ( r2_analoaf(k6_analort(A,B,C),D,D,F,H)
                                        & r2_analoaf(k6_analort(A,B,C),D,F,H,H)
                                        & ~ ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k6_analort(A,B,C),D,F,G,E)
                                            & D != F
                                            & E != G )
                                        & ~ ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k6_analort(A,B,C),D,F,E,H)
                                            & ~ r2_analoaf(k6_analort(A,B,C),D,F,G,H)
                                            & ~ r2_analoaf(k6_analort(A,B,C),D,F,H,G) )
                                        & ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
                                         => r2_analoaf(k6_analort(A,B,C),F,D,G,E) )
                                        & ( ( r2_analoaf(k6_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k6_analort(A,B,C),D,F,G,H) )
                                         => r2_analoaf(k6_analort(A,B,C),D,F,E,H) )
                                        & ~ ( r2_analoaf(k6_analort(A,B,C),D,E,F,G)
                                            & ~ r2_analoaf(k6_analort(A,B,C),F,G,D,E)
                                            & ~ r2_analoaf(k6_analort(A,B,C),F,G,E,D) ) ) ) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k6_analort(A,B,C),F,G,D,E) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k6_analort(A,B,C),D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t2_dirort,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))
             => ( r1_analmetr(A,B,C)
               => ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(k7_analort(A,B,C)))
                                     => ( r2_analoaf(k7_analort(A,B,C),D,D,F,H)
                                        & r2_analoaf(k7_analort(A,B,C),D,F,H,H)
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,G,E)
                                            & D != F
                                            & E != G )
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,E,H)
                                            & ~ r2_analoaf(k7_analort(A,B,C),D,F,G,H)
                                            & ~ r2_analoaf(k7_analort(A,B,C),D,F,H,G) )
                                        & ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                         => r2_analoaf(k7_analort(A,B,C),F,D,G,E) )
                                        & ( ( r2_analoaf(k7_analort(A,B,C),D,F,E,G)
                                            & r2_analoaf(k7_analort(A,B,C),D,F,G,H) )
                                         => r2_analoaf(k7_analort(A,B,C),D,F,E,H) )
                                        & ~ ( r2_analoaf(k7_analort(A,B,C),D,E,F,G)
                                            & ~ r2_analoaf(k7_analort(A,B,C),F,G,D,E)
                                            & ~ r2_analoaf(k7_analort(A,B,C),F,G,E,D) ) ) ) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k7_analort(A,B,C),F,G,D,E) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k7_analort(A,B,C)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k7_analort(A,B,C)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k7_analort(A,B,C)))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(k7_analort(A,B,C)))
                                  & F != G
                                  & r2_analoaf(k7_analort(A,B,C),D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(d1_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_dirort(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_analoaf(A,B,B,D,F)
                                & r2_analoaf(A,B,D,F,F)
                                & ~ ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,E,C)
                                    & B != D
                                    & C != E )
                                & ~ ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,C,F)
                                    & ~ r2_analoaf(A,B,D,E,F)
                                    & ~ r2_analoaf(A,B,D,F,E) )
                                & ( r2_analoaf(A,B,D,C,E)
                                 => r2_analoaf(A,D,B,E,C) )
                                & ( ( r2_analoaf(A,B,D,C,E)
                                    & r2_analoaf(A,B,D,E,F) )
                                 => r2_analoaf(A,B,D,C,F) )
                                & ~ ( r2_analoaf(A,B,C,D,E)
                                    & ~ r2_analoaf(A,D,E,B,C)
                                    & ~ r2_analoaf(A,D,E,C,B) ) ) ) ) ) ) )
          & ! [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))
                          & D != E
                          & r2_analoaf(A,D,E,B,C) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & D != E
                          & r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t3_dirort,axiom,(
    $true )).

fof(t4_dirort,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))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k7_analort(A,B,C))
                  & v1_dirort(k7_analort(A,B,C))
                  & l1_analoaf(k7_analort(A,B,C)) ) ) ) ) ) )).

fof(t5_dirort,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))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k6_analort(A,B,C))
                  & v1_dirort(k6_analort(A,B,C))
                  & l1_analoaf(k6_analort(A,B,C)) ) ) ) ) ) )).

fof(t6_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & r2_analoaf(A,E,D,B,C)
                      & E != D ) ) ) ) ) )).

fof(t7_dirort,axiom,(
    $true )).

fof(t8_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & B != E
                      & ( r2_analoaf(A,C,D,B,E)
                        | r2_analoaf(A,C,D,E,B) ) ) ) ) ) ) )).

fof(d2_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_dirort(A,B,C,D,E)
                      <=> ( r2_analoaf(A,B,C,D,E)
                          | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).

fof(d3_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_dirort(A,B,C,D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                            & ? [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                                & F != G
                                & r2_analoaf(A,F,G,B,C)
                                & r2_analoaf(A,F,G,D,E) ) ) ) ) ) ) ) ) )).

fof(d4_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v2_dirort(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))
                                       => ~ ( r2_analoaf(A,B,C,E,F)
                                            & r2_analoaf(A,H,I,E,F)
                                            & r2_analoaf(A,H,I,D,G)
                                            & H != I
                                            & E != F
                                            & ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v3_dirort(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))
                                       => ~ ( r2_analoaf(A,B,C,E,F)
                                            & r2_analoaf(A,E,F,H,I)
                                            & r2_analoaf(A,D,G,H,I)
                                            & H != I
                                            & E != F
                                            & ~ r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v4_dirort(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))
                                       => ~ ( r2_analoaf(A,B,C,E,F)
                                            & r2_analoaf(A,E,F,H,I)
                                            & r2_analoaf(A,B,C,D,G)
                                            & B != C
                                            & E != F
                                            & ~ r2_analoaf(A,D,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v5_dirort(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analoaf(A,B,C,D,E)
                         => r2_analoaf(A,D,E,C,B) ) ) ) ) ) ) ) )).

fof(d8_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v6_dirort(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analoaf(A,B,C,D,E)
                         => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) )).

fof(t9_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_dirort(A,B,C,D,D)
                    & r2_dirort(A,D,D,B,C) ) ) ) ) ) )).

fof(t10_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_dirort(A,B,C,D,E)
                       => r2_dirort(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t11_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_dirort(A,B,C,D,E)
                       => r2_dirort(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t12_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v4_dirort(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_dirort(A,B,C,F,G)
                                    & r2_analoaf(A,B,C,D,E) )
                                 => ( B = C
                                    | r2_analoaf(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v2_dirort(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( ( r2_analoaf(A,B,C,E,F)
                                    & r2_dirort(A,E,F,D,G) )
                                 => ( E = F
                                    | r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v2_dirort(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_dirort(A,B,C,D,E)
                                    & r2_dirort(A,D,E,F,G) )
                                 => ( D = E
                                    | r2_dirort(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_dirort,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] :
                  ( ( ~ v3_struct_0(D)
                    & v1_dirort(D)
                    & l1_analoaf(D) )
                 => ( ( r1_analmetr(A,B,C)
                      & D = k6_analort(A,B,C) )
                   => ( v5_dirort(D)
                      & v4_dirort(D)
                      & v3_dirort(D)
                      & v2_dirort(D) ) ) ) ) ) ) )).

fof(t16_dirort,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] :
                  ( ( ~ v3_struct_0(D)
                    & v1_dirort(D)
                    & l1_analoaf(D) )
                 => ( ( r1_analmetr(A,B,C)
                      & D = k7_analort(A,B,C) )
                   => ( v6_dirort(D)
                      & v4_dirort(D)
                      & v3_dirort(D)
                      & v2_dirort(D) ) ) ) ) ) ) )).

fof(t17_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v4_dirort(A)
       => v3_dirort(A) ) ) )).

fof(t18_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v4_dirort(A)
       => v2_dirort(A) ) ) )).

fof(t19_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v2_dirort(A)
       => ( v3_dirort(A)
        <=> ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => ( F = G
                                      | r2_dirort(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_dirort,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dirort(A)
        & l1_analoaf(A) )
     => ( v3_dirort(A)
       => ( ( ~ v5_dirort(A)
            & ~ v6_dirort(A) )
          | v4_dirort(A) ) ) ) )).
%------------------------------------------------------------------------------