SET007 Axioms: SET007+222.ax


%------------------------------------------------------------------------------
% File     : SET007+222 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Fano-Desargues Parallelity 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    : parsp_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   74 (  11 unit)
%            Number of atoms       :  872 (  59 equality)
%            Maximal formula depth :   36 (  13 average)
%            Number of connectives :  953 ( 155 ~  ;  20  |; 389  &)
%                                         (   5 <=>; 384 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-5 arity)
%            Number of functors    :   13 (   0 constant; 1-8 arity)
%            Number of variables   :  348 (   0 singleton; 342 !;   6 ?)
%            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(rc1_parsp_2,axiom,(
    ? [A] :
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A)
      & v1_parsp_1(A)
      & v2_parsp_1(A)
      & v1_parsp_2(A) ) )).

fof(t1_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k9_parsp_1(A))
        & v2_parsp_1(k9_parsp_1(A))
        & l1_parsp_1(k9_parsp_1(A)) ) ) )).

fof(t2_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                     => ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
                      <=> ? [F] :
                            ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                            & ? [G] :
                                ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                & ? [H] :
                                    ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                    & ? [I] :
                                        ( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                        & k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k4_mcart_1(F,G,H,I)
                                        & ~ ( ! [J] :
                                                ( m1_subset_1(J,u1_struct_0(A))
                                               => ~ ( k10_group_1(A,J,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))
                                                    & k10_group_1(A,J,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))
                                                    & k10_group_1(A,J,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)) ) )
                                            & ~ ( k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A)
                                                & k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A)
                                                & k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t3_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                     => ! [F] :
                          ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                             => ( k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,B,D) = k4_mcart_1(E,F,E,G)
                               => ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
                                  | ( E != F
                                    & E != G
                                    & F != G ) ) ) ) ) ) ) ) ) ) )).

fof(t4_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                     => ! [F] :
                          ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( ( k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,B,D) = k4_mcart_1(E,F,E,G)
                                          & k10_group_1(A,H,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))
                                          & k10_group_1(A,H,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))
                                          & k10_group_1(A,H,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) )
                                       => ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
                                          | ( H = k1_rlvect_1(A)
                                            & I = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                     => ! [F] :
                          ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                         => ! [G] :
                              ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                     => ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
                                          & r1_parsp_1(k9_parsp_1(A),B,D,C,E)
                                          & k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k4_mcart_1(F,G,H,I) )
                                       => ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
                                          | ( k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))
                                            & k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))
                                            & k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ~ ! [B] :
            ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                   => r1_parsp_1(k9_parsp_1(A),B,C,B,D) ) ) ) ) )).

fof(t7_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                     => ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
                          & r1_parsp_1(k9_parsp_1(A),D,B,C,E)
                          & r1_parsp_1(k9_parsp_1(A),D,C,B,E) )
                       => ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) = k1_rlvect_1(A)
                          | r1_parsp_1(k9_parsp_1(A),D,B,D,C) ) ) ) ) ) ) ) )).

fof(t8_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k9_parsp_1(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k9_parsp_1(A)))
                             => ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,F)
                                  & r1_parsp_1(k9_parsp_1(A),B,C,E,G)
                                  & r1_parsp_1(k9_parsp_1(A),B,D,C,F)
                                  & r1_parsp_1(k9_parsp_1(A),B,E,C,G) )
                               => ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
                                  | r1_parsp_1(k9_parsp_1(A),B,C,B,E)
                                  | r1_parsp_1(k9_parsp_1(A),D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(d1_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & l1_parsp_1(A) )
     => ( v1_parsp_2(A)
      <=> ( ~ ! [B] :
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => r1_parsp_1(A,B,C,B,D) ) ) )
          & ! [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_parsp_1(A,C,D,B,E)
                              & r1_parsp_1(A,B,C,D,E)
                              & r1_parsp_1(A,B,D,C,E) )
                           => r1_parsp_1(A,B,C,B,D) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r1_parsp_1(A,B,E,C,F)
                                      & r1_parsp_1(A,B,E,D,G)
                                      & r1_parsp_1(A,B,C,E,F)
                                      & r1_parsp_1(A,B,D,E,G) )
                                   => ( r1_parsp_1(A,B,E,B,C)
                                      | r1_parsp_1(A,B,E,B,D)
                                      | r1_parsp_1(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_parsp_2,axiom,(
    $true )).

fof(t10_parsp_2,axiom,(
    $true )).

fof(t11_parsp_2,axiom,(
    $true )).

fof(t12_parsp_2,axiom,(
    $true )).

fof(t13_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r1_parsp_1(A,B,C,B,D) ) ) ) ) ) )).

fof(d2_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ( r1_parsp_2(A,B,C,D)
                  <=> r1_parsp_1(A,B,C,B,D) ) ) ) ) ) )).

fof(t14_parsp_2,axiom,(
    $true )).

fof(t15_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ( r1_parsp_2(A,B,C,D)
                   => ( r1_parsp_2(A,B,D,C)
                      & r1_parsp_2(A,D,C,B)
                      & r1_parsp_2(A,C,B,D)
                      & r1_parsp_2(A,C,D,B)
                      & r1_parsp_2(A,D,B,C) ) ) ) ) ) ) )).

fof(t16_parsp_2,axiom,(
    $true )).

fof(t17_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ~ ( ~ r1_parsp_2(A,B,C,D)
                                  & r1_parsp_1(A,B,C,E,F)
                                  & r1_parsp_1(A,B,D,E,G)
                                  & E != F
                                  & E != G
                                  & r1_parsp_2(A,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t18_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ( ~ ( B != C
                        & C != D
                        & D != B )
                   => r1_parsp_2(A,B,C,D) ) ) ) ) ) )).

fof(t19_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ( ( r1_parsp_2(A,B,C,D)
                              & r1_parsp_2(A,B,C,E)
                              & r1_parsp_2(A,B,C,F) )
                           => ( B = C
                              | r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t20_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r1_parsp_2(A,B,C,D) ) ) ) ) ) )).

fof(t21_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( ( r1_parsp_2(A,B,C,D)
                          & r1_parsp_2(A,B,C,E) )
                       => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t22_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ~ ( ~ r1_parsp_2(A,B,C,D)
                          & r1_parsp_1(A,B,C,D,E)
                          & r1_parsp_2(A,B,C,E) ) ) ) ) ) ) )).

fof(t23_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ~ ( ~ r1_parsp_2(A,B,C,D)
                              & r1_parsp_1(A,B,C,D,E)
                              & D != E
                              & r1_parsp_2(A,B,C,F)
                              & r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) )).

fof(t24_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ~ ( ~ r1_parsp_2(A,B,C,D)
                          & r1_parsp_2(A,B,C,E)
                          & r1_parsp_2(A,B,D,E)
                          & B != E ) ) ) ) ) ) )).

fof(t25_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ( ( r1_parsp_2(A,B,C,D)
                              & r1_parsp_2(A,B,C,E)
                              & r1_parsp_2(A,B,D,F) )
                           => ( B = C
                              | B = D
                              | r1_parsp_1(A,C,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t26_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r1_parsp_2(A,B,C,F)
                                  & r1_parsp_2(A,B,C,G)
                                  & r1_parsp_2(A,D,E,F)
                                  & r1_parsp_2(A,D,E,G) )
                               => ( r1_parsp_1(A,B,C,D,E)
                                  | F = G ) ) ) ) ) ) ) ) ) )).

fof(t27_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( ( r1_parsp_2(A,B,C,D)
                          & r1_parsp_1(A,B,C,D,E) )
                       => ( B = C
                          | r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) ) )).

fof(t28_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( ( r1_parsp_2(A,B,C,D)
                          & r1_parsp_1(A,B,C,D,E) )
                       => ( B = C
                          | r1_parsp_1(A,D,C,D,E) ) ) ) ) ) ) ) )).

fof(t29_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r1_parsp_2(A,B,C,E)
                                  & r1_parsp_2(A,B,D,F)
                                  & r1_parsp_2(A,B,D,G)
                                  & r1_parsp_1(A,C,D,E,F)
                                  & r1_parsp_1(A,C,D,E,G) )
                               => ( r1_parsp_2(A,B,C,D)
                                  | F = G ) ) ) ) ) ) ) ) ) )).

fof(t30_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( ( r1_parsp_2(A,B,C,D)
                          & r1_parsp_2(A,B,C,E) )
                       => ( B = C
                          | r1_parsp_2(A,B,D,E) ) ) ) ) ) ) ) )).

fof(t31_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( ( r1_parsp_2(A,B,C,D)
                          & r1_parsp_2(A,B,D,E) )
                       => ( B = D
                          | r1_parsp_2(A,C,D,E) ) ) ) ) ) ) ) )).

fof(d3_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                      <=> ( ~ r1_parsp_2(A,B,C,D)
                          & r1_parsp_1(A,B,C,D,E)
                          & r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) ) )).

fof(t32_parsp_2,axiom,(
    $true )).

fof(t33_parsp_2,axiom,(
    $true )).

fof(t34_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => ( B != C
                          & C != D
                          & D != B
                          & B != E
                          & C != E
                          & D != E ) ) ) ) ) ) ) )).

fof(t35_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => ( ~ r1_parsp_2(A,B,C,D)
                          & ~ r1_parsp_2(A,C,B,E)
                          & ~ r1_parsp_2(A,D,E,B)
                          & ~ r1_parsp_2(A,E,D,C) ) ) ) ) ) ) ) )).

fof(t36_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => ( ~ r1_parsp_2(A,B,C,D)
                          & ~ r1_parsp_2(A,C,B,E)
                          & ~ r1_parsp_2(A,D,E,B)
                          & ~ r1_parsp_2(A,E,D,C)
                          & ~ r1_parsp_2(A,B,D,C)
                          & ~ r1_parsp_2(A,C,B,D)
                          & ~ r1_parsp_2(A,C,D,B)
                          & ~ r1_parsp_2(A,D,B,C)
                          & ~ r1_parsp_2(A,D,C,B)
                          & ~ r1_parsp_2(A,C,E,B)
                          & ~ r1_parsp_2(A,B,C,E)
                          & ~ r1_parsp_2(A,B,E,C)
                          & ~ r1_parsp_2(A,E,B,C)
                          & ~ r1_parsp_2(A,E,C,B)
                          & ~ r1_parsp_2(A,D,B,E)
                          & ~ r1_parsp_2(A,B,D,E)
                          & ~ r1_parsp_2(A,B,E,D)
                          & ~ r1_parsp_2(A,E,B,D)
                          & ~ r1_parsp_2(A,E,D,B)
                          & ~ r1_parsp_2(A,E,C,D)
                          & ~ r1_parsp_2(A,C,D,E)
                          & ~ r1_parsp_2(A,C,E,D)
                          & ~ r1_parsp_2(A,D,C,E)
                          & ~ r1_parsp_2(A,D,E,C) ) ) ) ) ) ) ) )).

fof(t37_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ~ ( r2_parsp_2(A,B,C,D,E)
                              & r1_parsp_2(A,B,C,F)
                              & r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) )).

fof(t38_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => r2_parsp_2(A,B,D,C,E) ) ) ) ) ) ) )).

fof(t39_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => r2_parsp_2(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t40_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => r2_parsp_2(A,C,B,E,D) ) ) ) ) ) ) )).

fof(t41_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => ( r2_parsp_2(A,B,D,C,E)
                          & r2_parsp_2(A,D,E,B,C)
                          & r2_parsp_2(A,C,B,E,D)
                          & r2_parsp_2(A,D,B,E,C)
                          & r2_parsp_2(A,E,C,D,B)
                          & r2_parsp_2(A,C,E,B,D)
                          & r2_parsp_2(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t42_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ~ ( ~ r1_parsp_2(A,B,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t43_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ( ( r2_parsp_2(A,B,C,D,E)
                              & r2_parsp_2(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) )).

fof(t44_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ~ ( r2_parsp_2(A,B,C,D,E)
                          & r1_parsp_1(A,B,E,C,D) ) ) ) ) ) ) )).

fof(t45_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ~ ( r2_parsp_2(A,B,C,D,E)
                          & r2_parsp_2(A,B,C,E,D) ) ) ) ) ) ) )).

fof(t46_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r1_parsp_2(A,B,C,D)
                          & D != B
                          & D != C ) ) ) ) ) ) )).

fof(t47_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r2_parsp_2(A,B,C,D,E)
                                  & r2_parsp_2(A,B,C,F,G) )
                               => r1_parsp_1(A,D,F,E,G) ) ) ) ) ) ) ) ) )).

fof(t48_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r2_parsp_2(A,E,F,B,C)
                                  & r2_parsp_2(A,E,F,D,G) )
                               => ( r1_parsp_2(A,B,C,D)
                                  | r2_parsp_2(A,B,C,D,G) ) ) ) ) ) ) ) ) ) )).

fof(t49_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r1_parsp_2(A,B,C,D)
                                  & r2_parsp_2(A,B,E,C,F)
                                  & r2_parsp_2(A,B,E,D,G) )
                               => ( C = D
                                  | r2_parsp_2(A,C,F,D,G) ) ) ) ) ) ) ) ) ) )).

fof(t50_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( ( r2_parsp_2(A,B,C,D,E)
                                          & r2_parsp_2(A,B,C,F,G)
                                          & r2_parsp_2(A,D,E,H,I) )
                                       => r1_parsp_1(A,F,H,G,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t51_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t52_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != C
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ r2_parsp_2(A,B,D,E,C) ) ) ) ) ) ) )).

fof(d4_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                      <=> ~ ( ~ ( B = C
                                & D = E )
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ~ ( r2_parsp_2(A,F,G,B,C)
                                        & r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t53_parsp_2,axiom,(
    $true )).

fof(t54_parsp_2,axiom,(
    $true )).

fof(t55_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ( r3_parsp_2(A,B,B,C,D)
                   => C = D ) ) ) ) ) )).

fof(t56_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                 => ( r3_parsp_2(A,B,C,D,D)
                   => B = C ) ) ) ) ) )).

fof(t57_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_parsp_2(A,B,C,C,B)
               => B = C ) ) ) ) )).

fof(t58_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                       => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t59_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                       => r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) )).

fof(t60_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                       => ( r1_parsp_2(A,B,C,D)
                          | r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t61_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r2_parsp_2(A,B,C,D,E)
                       => r3_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t62_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r3_parsp_2(A,B,C,D,E)
                                  & r1_parsp_2(A,B,C,D)
                                  & r2_parsp_2(A,F,G,B,C) )
                               => r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) )).

fof(t63_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                         => ( ( r3_parsp_2(A,B,C,D,E)
                              & r3_parsp_2(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) )).

fof(t64_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                      & r3_parsp_2(A,B,C,D,E) ) ) ) ) ) )).

fof(t65_parsp_2,axiom,(
    $true )).

fof(t66_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r3_parsp_2(A,B,C,B,C) ) ) ) )).

fof(t67_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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,u1_struct_0(A))
                             => ( ( r3_parsp_2(A,B,C,D,E)
                                  & r3_parsp_2(A,B,C,F,G) )
                               => r3_parsp_2(A,D,E,F,G) ) ) ) ) ) ) ) ) )).

fof(t68_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                       => r3_parsp_2(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t69_parsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & v1_parsp_2(A)
        & l1_parsp_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))
                     => ( r3_parsp_2(A,B,C,D,E)
                       => r3_parsp_2(A,C,B,E,D) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------