SET007 Axioms: SET007+286.ax


%------------------------------------------------------------------------------
% File     : SET007+286 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Fanoian, Pappian and Desarguesian Affine 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    : papdesaf [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (  15 unit)
%            Number of atoms       :  426 (  23 equality)
%            Maximal formula depth :   26 (   8 average)
%            Number of connectives :  468 (  92 ~  ;   8  |; 246  &)
%                                         (  10 <=>; 112 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-5 arity)
%            Number of functors    :   12 (   2 constant; 0-3 arity)
%            Number of variables   :   97 (   0 singleton;  92 !;   5 ?)
%            Maximal term depth    :    5 (   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_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A)) ) ) )).

fof(fc2_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v3_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v2_diraf(k2_diraf(A)) ) ) )).

fof(rc1_papdesaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v2_analoaf(A)
      & v1_papdesaf(A)
      & v2_papdesaf(A)
      & v3_papdesaf(A)
      & v4_papdesaf(A) ) )).

fof(rc2_papdesaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v1_diraf(A)
      & v2_diraf(A)
      & v2_aff_2(A)
      & v4_aff_2(A)
      & v7_aff_2(A)
      & v11_aff_2(A)
      & v1_translac(A) ) )).

fof(rc3_papdesaf,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v1_diraf(A)
      & v2_aff_2(A)
      & v4_aff_2(A)
      & v7_aff_2(A)
      & v11_aff_2(A)
      & v1_translac(A) ) )).

fof(fc3_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v1_translac(k2_diraf(A)) ) ) )).

fof(fc4_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v1_papdesaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v2_aff_2(k2_diraf(A))
        & v1_translac(k2_diraf(A)) ) ) )).

fof(fc5_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v2_papdesaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v4_aff_2(k2_diraf(A))
        & v1_translac(k2_diraf(A)) ) ) )).

fof(fc6_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v3_papdesaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v7_aff_2(k2_diraf(A))
        & v1_translac(k2_diraf(A)) ) ) )).

fof(fc7_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & v4_papdesaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & v11_aff_2(k2_diraf(A))
        & v1_translac(k2_diraf(A)) ) ) )).

fof(t1_papdesaf,axiom,(
    $true )).

fof(t2_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( m1_subset_1(B,u1_struct_0(A))
           => m1_subset_1(B,u1_struct_0(k2_diraf(A))) )
          & ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
           => m1_subset_1(B,u1_struct_0(A)) )
          & ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_diraf(A)))) )
          & ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_diraf(A))))
           => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t3_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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(k2_diraf(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k2_diraf(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_diraf(A)))
                             => ( ( B = E
                                  & C = F
                                  & D = G )
                               => ( r3_diraf(A,B,C,D)
                                <=> r1_aff_1(k2_diraf(A),E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t4_papdesaf,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(k2_analoaf(A)))
        <=> m1_subset_1(B,u1_struct_0(A)) ) ) )).

fof(t5_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [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))
                                           => ( ( C = G
                                                & D = H
                                                & E = I
                                                & F = J )
                                             => ( r2_diraf(B,C,D,E,F)
                                              <=> r1_geomtrap(A,G,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ~ ( B = k2_analoaf(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] :
                          ( m1_subset_1(E,k1_numbers)
                          & ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & k4_rlvect_1(A,k3_rlvect_1(A,C,E),k3_rlvect_1(A,D,F)) = k1_rlvect_1(A)
                              & ~ ( E = np__0
                                  & F = np__0 ) ) ) ) ) ) ) ) )).

fof(d1_papdesaf,axiom,(
    $true )).

fof(d2_papdesaf,axiom,(
    $true )).

fof(d3_papdesaf,axiom,(
    $true )).

fof(d4_papdesaf,axiom,(
    $true )).

fof(d5_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v1_translac(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,B,D,C,E)
                            & r2_analoaf(A,B,E,C,D) )
                         => r2_analoaf(A,B,C,B,D) ) ) ) ) ) ) ) )).

fof(d6_papdesaf,axiom,(
    $true )).

fof(d7_papdesaf,axiom,(
    $true )).

fof(d8_papdesaf,axiom,(
    $true )).

fof(d9_papdesaf,axiom,(
    $true )).

fof(d10_papdesaf,axiom,(
    $true )).

fof(d11_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v1_papdesaf(A)
      <=> v2_aff_2(k2_diraf(A)) ) ) )).

fof(d12_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v2_papdesaf(A)
      <=> v4_aff_2(k2_diraf(A)) ) ) )).

fof(d13_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v3_papdesaf(A)
      <=> v7_aff_2(k2_diraf(A)) ) ) )).

fof(d14_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v4_papdesaf(A)
      <=> v11_aff_2(k2_diraf(A)) ) ) )).

fof(d15_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v5_papdesaf(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))
                                   => ( ( r2_analoaf(A,B,C,B,F)
                                        & r2_analoaf(A,B,D,B,G)
                                        & r2_analoaf(A,B,E,B,H)
                                        & r2_analoaf(A,C,D,F,G)
                                        & r2_analoaf(A,C,E,F,H) )
                                     => ( r3_diraf(A,B,C,D)
                                        | r3_diraf(A,B,C,E)
                                        | r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d16_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v6_papdesaf(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))
                                   => ( ( r2_analoaf(A,C,B,B,F)
                                        & r2_analoaf(A,D,B,B,G)
                                        & r2_analoaf(A,E,B,B,H)
                                        & r2_analoaf(A,C,D,G,F)
                                        & r2_analoaf(A,C,E,H,F) )
                                     => ( r3_diraf(A,B,C,D)
                                        | r3_diraf(A,B,C,E)
                                        | r2_analoaf(A,D,E,H,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_papdesaf,axiom,(
    $true )).

fof(t8_papdesaf,axiom,(
    $true )).

fof(t9_papdesaf,axiom,(
    $true )).

fof(t10_papdesaf,axiom,(
    $true )).

fof(t11_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v6_papdesaf(A)
       => v5_papdesaf(A) ) ) )).

fof(t12_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,C,B,B,E)
                              & r3_diraf(A,B,D,F)
                              & r2_diraf(A,C,D,E,F) )
                           => ( r3_diraf(A,B,C,D)
                              | ( r2_analoaf(A,D,B,B,F)
                                & r2_analoaf(A,C,D,F,E) ) ) ) ) ) ) ) ) ) )).

fof(t13_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,B,E)
                              & r3_diraf(A,B,D,F)
                              & r2_diraf(A,C,D,E,F) )
                           => ( r3_diraf(A,B,C,D)
                              | ( r2_analoaf(A,B,D,B,F)
                                & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t14_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v6_papdesaf(A)
       => v4_aff_2(k2_diraf(A)) ) ) )).

fof(t15_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ( ( k6_rlvect_1(A,B,C) = k3_rlvect_1(A,k6_rlvect_1(A,E,B),G)
                                  & r1_geomtrap(A,B,D,B,F)
                                  & r1_geomtrap(A,C,D,E,F) )
                               => ( G = np__0
                                  | r1_geomtrap(A,B,C,B,D)
                                  | ( F = k4_rlvect_1(A,E,k3_rlvect_1(A,k6_rlvect_1(A,D,C),k2_real_1(k1_real_1(G))))
                                    & F = k4_rlvect_1(A,B,k3_rlvect_1(A,k6_rlvect_1(A,D,B),k2_real_1(k1_real_1(G))))
                                    & k6_rlvect_1(A,D,C) = k3_rlvect_1(A,k6_rlvect_1(A,F,E),k1_real_1(G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_papdesaf,axiom,(
    $true )).

fof(t17_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => v6_papdesaf(B) ) ) ) )).

fof(t18_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => ( v6_papdesaf(B)
              & v5_papdesaf(B) ) ) ) ) )).

fof(t19_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => v2_aff_2(k2_diraf(B)) ) ) ) )).

fof(t20_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => v4_aff_2(k2_diraf(B)) ) ) ) )).

fof(t21_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
       => v7_aff_2(A) ) ) )).

fof(t22_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => v7_aff_2(k2_diraf(B)) ) ) ) )).

fof(t23_papdesaf,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] :
          ( ( ~ v3_struct_0(B)
            & ~ v3_realset2(B)
            & v2_analoaf(B)
            & l1_analoaf(B) )
         => ( B = k2_analoaf(A)
           => v11_aff_2(k2_diraf(B)) ) ) ) )).

fof(t24_papdesaf,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v1_translac(k2_diraf(A)) ) )).
%------------------------------------------------------------------------------