SET007 Axioms: SET007+230.ax


%------------------------------------------------------------------------------
% File     : SET007+230 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Classical Configurations in Affine Planes
% 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    : aff_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   43 (  14 unit)
%            Number of atoms       :  548 (  47 equality)
%            Maximal formula depth :   38 (  13 average)
%            Number of connectives :  563 (  58 ~  ;  53  |; 258  &)
%                                         (  19 <=>; 175 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   28 (   1 propositional; 0-5 arity)
%            Number of functors    :    2 (   0 constant; 1-1 arity)
%            Number of variables   :  151 (   0 singleton; 151 !;   0 ?)
%            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(d1_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v1_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & v1_aff_1(C,A)
                                            & r2_hidden(D,B)
                                            & r2_hidden(E,B)
                                            & r2_hidden(F,B)
                                            & r2_hidden(G,C)
                                            & r2_hidden(H,C)
                                            & r2_hidden(I,C)
                                            & r2_analoaf(A,D,H,E,G)
                                            & r2_analoaf(A,E,I,F,H) )
                                         => r2_analoaf(A,D,I,F,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(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))
                                           => ( ( v1_aff_1(B,A)
                                                & v1_aff_1(C,A)
                                                & r2_hidden(D,B)
                                                & r2_hidden(D,C)
                                                & r2_hidden(E,B)
                                                & r2_hidden(F,B)
                                                & r2_hidden(G,B)
                                                & r2_hidden(H,C)
                                                & r2_hidden(I,C)
                                                & r2_hidden(J,C)
                                                & r2_analoaf(A,E,I,F,H)
                                                & r2_analoaf(A,F,J,G,I) )
                                             => ( B = C
                                                | D = E
                                                | D = H
                                                | D = F
                                                | D = I
                                                | D = G
                                                | D = J
                                                | r2_analoaf(A,E,J,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v3_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(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))
                                           => ( ( v1_aff_1(B,A)
                                                & v1_aff_1(C,A)
                                                & r2_hidden(D,B)
                                                & r2_hidden(D,C)
                                                & r2_hidden(E,B)
                                                & r2_hidden(F,B)
                                                & r2_hidden(G,B)
                                                & r2_hidden(I,C)
                                                & r2_hidden(J,C)
                                                & r2_analoaf(A,E,I,F,H)
                                                & r2_analoaf(A,F,J,G,I)
                                                & r2_analoaf(A,E,J,G,H) )
                                             => ( B = C
                                                | D = E
                                                | D = H
                                                | D = F
                                                | D = I
                                                | D = G
                                                | D = J
                                                | F = G
                                                | r2_hidden(H,C) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_hidden(E,B)
                                                    & r2_hidden(E,C)
                                                    & r2_hidden(E,D)
                                                    & r2_hidden(F,B)
                                                    & r2_hidden(I,B)
                                                    & r2_hidden(G,C)
                                                    & r2_hidden(J,C)
                                                    & r2_hidden(H,D)
                                                    & r2_hidden(K,D)
                                                    & v1_aff_1(B,A)
                                                    & v1_aff_1(C,A)
                                                    & v1_aff_1(D,A)
                                                    & r2_analoaf(A,F,G,I,J)
                                                    & r2_analoaf(A,F,H,I,K) )
                                                 => ( E = F
                                                    | E = G
                                                    | E = H
                                                    | B = C
                                                    | B = D
                                                    | r2_analoaf(A,G,H,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v5_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_hidden(E,B)
                                                    & r2_hidden(E,C)
                                                    & r2_hidden(F,B)
                                                    & r2_hidden(I,B)
                                                    & r2_hidden(G,C)
                                                    & r2_hidden(J,C)
                                                    & r2_hidden(H,D)
                                                    & r2_hidden(K,D)
                                                    & v1_aff_1(B,A)
                                                    & v1_aff_1(C,A)
                                                    & v1_aff_1(D,A)
                                                    & r2_analoaf(A,F,G,I,J)
                                                    & r2_analoaf(A,F,H,I,K)
                                                    & r2_analoaf(A,G,H,J,K) )
                                                 => ( E = F
                                                    | E = G
                                                    | E = H
                                                    | B = C
                                                    | B = D
                                                    | r1_aff_1(A,F,G,H)
                                                    | H = K
                                                    | r2_hidden(E,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_hidden(E,B)
                                                    & r2_hidden(E,C)
                                                    & r2_hidden(E,D)
                                                    & r2_hidden(F,B)
                                                    & r2_hidden(I,B)
                                                    & r2_hidden(G,C)
                                                    & r2_hidden(J,C)
                                                    & r2_hidden(H,D)
                                                    & v1_aff_1(B,A)
                                                    & v1_aff_1(C,A)
                                                    & v1_aff_1(D,A)
                                                    & r2_analoaf(A,F,G,I,J)
                                                    & r2_analoaf(A,F,H,I,K)
                                                    & r2_analoaf(A,G,H,J,K) )
                                                 => ( E = F
                                                    | E = G
                                                    | E = H
                                                    | B = C
                                                    | B = D
                                                    | r2_hidden(K,D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v7_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & r2_hidden(C,B)
                                            & r2_hidden(F,B)
                                            & r2_hidden(I,B)
                                            & r1_aff_1(A,C,D,G)
                                            & r1_aff_1(A,C,E,H)
                                            & r2_analoaf(A,D,E,G,H)
                                            & r2_analoaf(A,D,F,G,I)
                                            & r2_aff_1(A,D,E,B) )
                                         => ( r2_hidden(D,B)
                                            | C = F
                                            | D = E
                                            | r2_analoaf(A,E,F,H,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v8_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & r2_hidden(C,B)
                                            & r2_hidden(F,B)
                                            & r2_hidden(I,B)
                                            & r1_aff_1(A,C,D,G)
                                            & r2_analoaf(A,D,E,G,H)
                                            & r2_analoaf(A,E,F,H,I)
                                            & r2_analoaf(A,D,F,G,I)
                                            & r2_aff_1(A,D,E,B) )
                                         => ( r2_hidden(D,B)
                                            | C = F
                                            | D = E
                                            | r1_aff_1(A,C,E,H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v9_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & r2_hidden(C,B)
                                            & r2_hidden(F,B)
                                            & r2_hidden(I,B)
                                            & r1_aff_1(A,C,D,G)
                                            & r1_aff_1(A,C,E,H)
                                            & r2_analoaf(A,E,F,H,I)
                                            & r2_analoaf(A,D,F,G,I)
                                            & r2_aff_1(A,D,E,B) )
                                         => ( r2_hidden(D,B)
                                            | C = F
                                            | D = E
                                            | r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d10_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v10_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & r2_hidden(C,B)
                                            & r2_hidden(F,B)
                                            & r1_aff_1(A,C,D,G)
                                            & r1_aff_1(A,C,E,H)
                                            & r2_analoaf(A,D,E,G,H)
                                            & r2_analoaf(A,D,F,G,I)
                                            & r2_analoaf(A,E,F,H,I)
                                            & r2_aff_1(A,D,E,B) )
                                         => ( r2_hidden(D,B)
                                            | C = F
                                            | D = E
                                            | r2_hidden(I,B) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d11_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v11_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(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))
                                           => ( ( r4_aff_1(A,B,C)
                                                & r4_aff_1(A,B,D)
                                                & r2_hidden(E,B)
                                                & r2_hidden(H,B)
                                                & r2_hidden(F,C)
                                                & r2_hidden(I,C)
                                                & r2_hidden(G,D)
                                                & r2_hidden(J,D)
                                                & v1_aff_1(B,A)
                                                & v1_aff_1(C,A)
                                                & v1_aff_1(D,A)
                                                & r2_analoaf(A,E,F,H,I)
                                                & r2_analoaf(A,E,G,H,J) )
                                             => ( B = C
                                                | B = D
                                                | r2_analoaf(A,F,G,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v12_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(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))
                                           => ( ( r4_aff_1(A,B,C)
                                                & r2_hidden(E,B)
                                                & r2_hidden(H,B)
                                                & r2_hidden(F,C)
                                                & r2_hidden(I,C)
                                                & r2_hidden(G,D)
                                                & r2_hidden(J,D)
                                                & v1_aff_1(B,A)
                                                & v1_aff_1(C,A)
                                                & v1_aff_1(D,A)
                                                & r2_analoaf(A,E,F,H,I)
                                                & r2_analoaf(A,E,G,H,J)
                                                & r2_analoaf(A,F,G,I,J) )
                                             => ( B = C
                                                | B = D
                                                | r1_aff_1(A,E,F,G)
                                                | G = J
                                                | r4_aff_1(A,B,D) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d13_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v13_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & v1_aff_1(C,A)
                                            & r2_hidden(D,B)
                                            & r2_hidden(E,B)
                                            & r2_hidden(F,B)
                                            & r4_aff_1(A,B,C)
                                            & r2_hidden(G,C)
                                            & r2_hidden(H,C)
                                            & r2_hidden(I,C)
                                            & r2_analoaf(A,D,H,E,G)
                                            & r2_analoaf(A,E,I,F,H) )
                                         => ( B = C
                                            | r2_analoaf(A,D,I,F,G) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d14_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v14_aff_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(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))
                                       => ( ( v1_aff_1(B,A)
                                            & v1_aff_1(C,A)
                                            & r2_hidden(D,B)
                                            & r2_hidden(E,B)
                                            & r2_hidden(F,B)
                                            & r4_aff_1(A,B,C)
                                            & r2_hidden(G,C)
                                            & r2_hidden(H,C)
                                            & r2_analoaf(A,D,H,E,G)
                                            & r2_analoaf(A,E,I,F,H)
                                            & r2_analoaf(A,D,I,F,G) )
                                         => ( B = C
                                            | G = H
                                            | r2_hidden(I,C) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_aff_2,axiom,(
    $true )).

fof(t2_aff_2,axiom,(
    $true )).

fof(t3_aff_2,axiom,(
    $true )).

fof(t4_aff_2,axiom,(
    $true )).

fof(t5_aff_2,axiom,(
    $true )).

fof(t6_aff_2,axiom,(
    $true )).

fof(t7_aff_2,axiom,(
    $true )).

fof(t8_aff_2,axiom,(
    $true )).

fof(t9_aff_2,axiom,(
    $true )).

fof(t10_aff_2,axiom,(
    $true )).

fof(t11_aff_2,axiom,(
    $true )).

fof(t12_aff_2,axiom,(
    $true )).

fof(t13_aff_2,axiom,(
    $true )).

fof(t14_aff_2,axiom,(
    $true )).

fof(t15_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
      <=> v3_aff_2(A) ) ) )).

fof(t16_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
      <=> v5_aff_2(A) ) ) )).

fof(t17_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v7_aff_2(A)
       => v8_aff_2(A) ) ) )).

fof(t18_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v8_aff_2(A)
       => v9_aff_2(A) ) ) )).

fof(t19_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v9_aff_2(A)
       => v10_aff_2(A) ) ) )).

fof(t20_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v10_aff_2(A)
       => v7_aff_2(A) ) ) )).

fof(t21_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v11_aff_2(A)
      <=> v12_aff_2(A) ) ) )).

fof(t22_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v13_aff_2(A)
      <=> v14_aff_2(A) ) ) )).

fof(t23_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
       => v13_aff_2(A) ) ) )).

fof(t24_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v1_aff_2(A)
      <=> ( v2_aff_2(A)
          & v13_aff_2(A) ) ) ) )).

fof(t25_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
       => v4_aff_2(A) ) ) )).

fof(t26_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
       => v7_aff_2(A) ) ) )).

fof(t27_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v8_aff_2(A)
       => v12_aff_2(A) ) ) )).

fof(t28_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v7_aff_2(A)
       => v11_aff_2(A) ) ) )).

fof(t29_aff_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v11_aff_2(A)
       => v13_aff_2(A) ) ) )).
%------------------------------------------------------------------------------