SET007 Axioms: SET007+214.ax


%------------------------------------------------------------------------------
% File     : SET007+214 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   91 (  24 unit)
%            Number of atoms       :  925 (  60 equality)
%            Maximal formula depth :   33 (  11 average)
%            Number of connectives :  985 ( 151 ~  ;   4  |; 576  &)
%                                         (  11 <=>; 243 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-5 arity)
%            Number of functors    :   27 (   0 constant; 1-8 arity)
%            Number of variables   :  260 (   0 singleton; 235 !;  25 ?)
%            Maximal term depth    :    6 (   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_1,axiom,(
    ? [A] :
      ( l1_parsp_1(A)
      & v1_parsp_1(A) ) )).

fof(rc2_parsp_1,axiom,(
    ? [A] :
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A) ) )).

fof(fc1_parsp_1,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) )
     => ~ v1_xboole_0(k5_parsp_1(A)) ) )).

fof(fc2_parsp_1,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) )
     => ~ v1_xboole_0(k6_parsp_1(A)) ) )).

fof(fc3_parsp_1,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))
        & v1_parsp_1(k9_parsp_1(A)) ) ) )).

fof(rc3_parsp_1,axiom,(
    ? [A] :
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A)
      & v1_parsp_1(A)
      & v2_parsp_1(A) ) )).

fof(d1_parsp_1,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
            & m2_relset_1(B,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
         => ( B = k1_parsp_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                   => k2_binop_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),B,C,D) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D)),k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D)),k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D))) ) ) ) ) ) )).

fof(d2_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
             => k2_parsp_1(A,B,C) = k2_binop_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k1_parsp_1(A),B,C) ) ) ) )).

fof(t1_parsp_1,axiom,(
    $true )).

fof(t2_parsp_1,axiom,(
    $true )).

fof(t3_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
             => k2_parsp_1(A,B,C) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C))) ) ) ) )).

fof(t4_parsp_1,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(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))
                             => k2_parsp_1(A,k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D),k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,F,G)) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,B,E),k4_rlvect_1(A,C,F),k4_rlvect_1(A,D,G)) ) ) ) ) ) ) ) )).

fof(d3_parsp_1,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
            & m2_relset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
         => ( B = k3_parsp_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
               => k8_funct_2(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),B,C) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k5_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k5_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k5_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C))) ) ) ) ) )).

fof(d4_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
         => k4_parsp_1(A,B) = k8_funct_2(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_parsp_1(A),B) ) ) )).

fof(t5_parsp_1,axiom,(
    $true )).

fof(t6_parsp_1,axiom,(
    $true )).

fof(t7_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
         => k4_parsp_1(A,B) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k5_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B)),k5_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B)),k5_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B))) ) ) )).

fof(d5_parsp_1,axiom,(
    ! [A,B] :
      ( m1_parsp_1(B,A)
    <=> r1_tarski(B,k4_zfmisc_1(A,A,A,A)) ) )).

fof(d6_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_1(A,B,C,D,E)
                      <=> r2_hidden(k5_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D,E),u1_parsp_1(A)) ) ) ) ) ) ) )).

fof(d7_parsp_1,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) )
     => k5_parsp_1(A) = k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(d8_parsp_1,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) )
     => k6_parsp_1(A) = k4_zfmisc_1(k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A)) ) )).

fof(d9_parsp_1,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] :
          ( B = k7_parsp_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ( r2_hidden(C,k6_parsp_1(A))
                & ? [D] :
                    ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(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)))
                                & C = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),D,E,F,G)
                                & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_1(A,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,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A)
                                & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_1(A,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,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A)
                                & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_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)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) )).

fof(t8_parsp_1,axiom,(
    $true )).

fof(t9_parsp_1,axiom,(
    $true )).

fof(t10_parsp_1,axiom,(
    $true )).

fof(t11_parsp_1,axiom,(
    $true )).

fof(t12_parsp_1,axiom,(
    $true )).

fof(t13_parsp_1,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) )
     => r1_tarski(k7_parsp_1(A),k4_zfmisc_1(k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A))) ) )).

fof(d10_parsp_1,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) )
     => k8_parsp_1(A) = k7_parsp_1(A) ) )).

fof(d11_parsp_1,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) )
     => k9_parsp_1(A) = g1_parsp_1(k5_parsp_1(A),k8_parsp_1(A)) ) )).

fof(t14_parsp_1,axiom,(
    $true )).

fof(t15_parsp_1,axiom,(
    $true )).

fof(t16_parsp_1,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) )
     => u1_struct_0(k9_parsp_1(A)) = k5_parsp_1(A) ) )).

fof(t17_parsp_1,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) )
     => u1_parsp_1(k9_parsp_1(A)) = k8_parsp_1(A) ) )).

fof(t18_parsp_1,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)
                      <=> r2_hidden(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),k8_parsp_1(A)) ) ) ) ) ) ) )).

fof(t19_parsp_1,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)))
                     => ( r2_hidden(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),k8_parsp_1(A))
                      <=> ( r2_hidden(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),k6_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)))
                                          & 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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
                                          & k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
                                          & k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t20_parsp_1,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)
                      <=> ( r2_hidden(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),k6_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)))
                                          & 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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
                                          & k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
                                          & k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t21_parsp_1,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) )
     => u1_struct_0(k9_parsp_1(A)) = k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(t22_parsp_1,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)))
                     => r2_hidden(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),k6_parsp_1(A)) ) ) ) ) ) )).

fof(t23_parsp_1,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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
                                        & k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
                                        & k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t24_parsp_1,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)))
             => r1_parsp_1(k9_parsp_1(A),B,C,C,B) ) ) ) )).

fof(t25_parsp_1,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,D,D) ) ) ) ) )).

fof(t26_parsp_1,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,E)
                                  & r1_parsp_1(k9_parsp_1(A),B,C,F,G)
                                  & ~ r1_parsp_1(k9_parsp_1(A),D,E,F,G)
                                  & B != C ) ) ) ) ) ) ) ) )).

fof(t27_parsp_1,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)
                   => r1_parsp_1(k9_parsp_1(A),C,B,C,D) ) ) ) ) ) )).

fof(t28_parsp_1,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),B,D,C,E) ) ) ) ) ) )).

fof(d12_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_parsp_1(A) )
     => ( v2_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))
                                       => ( r1_parsp_1(A,B,C,C,B)
                                          & r1_parsp_1(A,B,C,D,D)
                                          & ~ ( r1_parsp_1(A,B,C,F,G)
                                              & r1_parsp_1(A,B,C,H,I)
                                              & ~ r1_parsp_1(A,F,G,H,I)
                                              & B != C )
                                          & ( r1_parsp_1(A,B,C,B,D)
                                           => r1_parsp_1(A,C,B,C,D) )
                                          & ? [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                              & r1_parsp_1(A,B,C,D,J)
                                              & r1_parsp_1(A,B,D,C,J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_parsp_1,axiom,(
    $true )).

fof(t30_parsp_1,axiom,(
    $true )).

fof(t31_parsp_1,axiom,(
    $true )).

fof(t32_parsp_1,axiom,(
    $true )).

fof(t33_parsp_1,axiom,(
    $true )).

fof(t34_parsp_1,axiom,(
    $true )).

fof(t35_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(A)
        & l1_parsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_parsp_1(A,B,C,B,C) ) ) ) )).

fof(t36_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,D,E)
                       => r1_parsp_1(A,D,E,B,C) ) ) ) ) ) ) )).

fof(t37_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,B,C,D) ) ) ) ) )).

fof(t38_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,D,E)
                       => r1_parsp_1(A,C,B,D,E) ) ) ) ) ) ) )).

fof(t39_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,D,E)
                       => r1_parsp_1(A,B,C,E,D) ) ) ) ) ) ) )).

fof(t40_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,D,E)
                       => ( r1_parsp_1(A,C,B,D,E)
                          & r1_parsp_1(A,B,C,E,D)
                          & r1_parsp_1(A,C,B,E,D)
                          & r1_parsp_1(A,D,E,B,C)
                          & r1_parsp_1(A,E,D,B,C)
                          & r1_parsp_1(A,D,E,C,B)
                          & r1_parsp_1(A,E,D,C,B) ) ) ) ) ) ) ) )).

fof(t41_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                   => ( r1_parsp_1(A,B,D,B,C)
                      & r1_parsp_1(A,C,B,B,D)
                      & r1_parsp_1(A,B,C,D,B)
                      & r1_parsp_1(A,B,D,C,B)
                      & r1_parsp_1(A,C,B,D,B)
                      & r1_parsp_1(A,D,B,B,C)
                      & r1_parsp_1(A,D,B,C,B)
                      & r1_parsp_1(A,C,B,C,D)
                      & r1_parsp_1(A,B,C,C,D)
                      & r1_parsp_1(A,C,B,D,C)
                      & r1_parsp_1(A,C,D,C,B)
                      & r1_parsp_1(A,B,C,D,C)
                      & r1_parsp_1(A,D,C,C,B)
                      & r1_parsp_1(A,C,D,B,C)
                      & r1_parsp_1(A,D,C,B,C)
                      & r1_parsp_1(A,D,B,D,C)
                      & r1_parsp_1(A,B,D,D,C)
                      & r1_parsp_1(A,D,B,C,D)
                      & r1_parsp_1(A,B,D,C,D)
                      & r1_parsp_1(A,D,C,D,B)
                      & r1_parsp_1(A,C,D,D,B)
                      & r1_parsp_1(A,D,C,B,D)
                      & r1_parsp_1(A,C,D,B,D) ) ) ) ) ) ) )).

fof(t42_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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))
                     => ( ~ ( B != C
                            & D != E
                            & ~ ( B = D
                                & C = E )
                            & ~ ( B = E
                                & C = D ) )
                       => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t43_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,D,E,B,C)
                                  & r1_parsp_1(A,B,C,F,G) )
                               => ( B = C
                                  | r1_parsp_1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t44_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                   => ( B != C
                      & C != D
                      & D != B ) ) ) ) ) ) )).

fof(t45_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,D,E)
                       => ( B != C
                          & D != E ) ) ) ) ) ) ) )).

fof(t46_parsp_1,axiom,(
    $true )).

fof(t47_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                   => ( ~ r1_parsp_1(A,B,D,B,C)
                      & ~ r1_parsp_1(A,C,B,B,D)
                      & ~ r1_parsp_1(A,B,C,D,B)
                      & ~ r1_parsp_1(A,B,D,C,B)
                      & ~ r1_parsp_1(A,C,B,D,B)
                      & ~ r1_parsp_1(A,D,B,B,C)
                      & ~ r1_parsp_1(A,D,B,C,B)
                      & ~ r1_parsp_1(A,C,B,C,D)
                      & ~ r1_parsp_1(A,B,C,C,D)
                      & ~ r1_parsp_1(A,C,B,D,C)
                      & ~ r1_parsp_1(A,C,D,C,B)
                      & ~ r1_parsp_1(A,C,B,D,C)
                      & ~ r1_parsp_1(A,D,C,C,B)
                      & ~ r1_parsp_1(A,C,D,B,C)
                      & ~ r1_parsp_1(A,D,C,B,C)
                      & ~ r1_parsp_1(A,D,B,D,C)
                      & ~ r1_parsp_1(A,B,D,D,C)
                      & ~ r1_parsp_1(A,D,B,C,D)
                      & ~ r1_parsp_1(A,B,D,C,D)
                      & ~ r1_parsp_1(A,D,C,D,B)
                      & ~ r1_parsp_1(A,C,D,D,B)
                      & ~ r1_parsp_1(A,D,C,B,D)
                      & ~ r1_parsp_1(A,C,D,B,D) ) ) ) ) ) ) )).

fof(t48_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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))
                                     => ~ ( ~ r1_parsp_1(A,B,C,D,E)
                                          & r1_parsp_1(A,B,C,F,G)
                                          & r1_parsp_1(A,D,E,H,I)
                                          & F != G
                                          & H != I
                                          & r1_parsp_1(A,F,G,H,I) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                                  & r1_parsp_1(A,B,C,E,F)
                                  & r1_parsp_1(A,B,D,E,G)
                                  & r1_parsp_1(A,C,D,F,G)
                                  & E != F
                                  & r1_parsp_1(A,E,F,E,G) ) ) ) ) ) ) ) ) )).

fof(t50_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,D,E,F)
                              & r1_parsp_1(A,C,D,E,F) )
                           => ( r1_parsp_1(A,B,C,B,D)
                              | E = F ) ) ) ) ) ) ) ) )).

fof(t51_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,D,B,E)
                          & r1_parsp_1(A,C,D,C,E) )
                       => ( r1_parsp_1(A,B,C,B,D)
                          | D = E ) ) ) ) ) ) ) )).

fof(t52_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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))
                                 => ( ( r1_parsp_1(A,B,C,E,F)
                                      & r1_parsp_1(A,B,D,E,G)
                                      & r1_parsp_1(A,B,D,E,H)
                                      & r1_parsp_1(A,C,D,F,G)
                                      & r1_parsp_1(A,C,D,F,H) )
                                   => ( r1_parsp_1(A,B,C,B,D)
                                      | G = H ) ) ) ) ) ) ) ) ) ) )).

fof(t53_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                          & r1_parsp_1(A,B,C,B,E) )
                       => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t54_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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 ) )
       => ! [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,B,C,D,E) ) ) ) ) ) ) )).

fof(t55_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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) ) ) )
       => ! [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,B,C,D,E) ) ) ) ) ) ) )).

fof(t56_parsp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_parsp_1(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_1(A,B,C,B,D)
                              & E != F
                              & r1_parsp_1(A,E,F,E,B)
                              & r1_parsp_1(A,E,F,E,C)
                              & r1_parsp_1(A,E,F,E,D) ) ) ) ) ) ) ) )).

fof(dt_m1_parsp_1,axiom,(
    $true )).

fof(existence_m1_parsp_1,axiom,(
    ! [A] :
    ? [B] : m1_parsp_1(B,A) )).

fof(dt_l1_parsp_1,axiom,(
    ! [A] :
      ( l1_parsp_1(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_parsp_1,axiom,(
    ? [A] : l1_parsp_1(A) )).

fof(abstractness_v1_parsp_1,axiom,(
    ! [A] :
      ( l1_parsp_1(A)
     => ( v1_parsp_1(A)
       => A = g1_parsp_1(u1_struct_0(A),u1_parsp_1(A)) ) ) )).

fof(dt_k1_parsp_1,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) )
     => ( v1_funct_1(k1_parsp_1(A))
        & v1_funct_2(k1_parsp_1(A),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
        & m2_relset_1(k1_parsp_1(A),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ) )).

fof(dt_k2_parsp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
        & m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
     => m1_subset_1(k2_parsp_1(A,B,C),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_k3_parsp_1,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) )
     => ( v1_funct_1(k3_parsp_1(A))
        & v1_funct_2(k3_parsp_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
        & m2_relset_1(k3_parsp_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ) )).

fof(dt_k4_parsp_1,axiom,(
    ! [A,B] :
      ( ( ~ 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)
        & m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
     => m1_subset_1(k4_parsp_1(A,B),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_k5_parsp_1,axiom,(
    $true )).

fof(dt_k6_parsp_1,axiom,(
    $true )).

fof(dt_k7_parsp_1,axiom,(
    $true )).

fof(dt_k8_parsp_1,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) )
     => m1_parsp_1(k8_parsp_1(A),k5_parsp_1(A)) ) )).

fof(dt_k9_parsp_1,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) )
     => l1_parsp_1(k9_parsp_1(A)) ) )).

fof(dt_u1_parsp_1,axiom,(
    ! [A] :
      ( l1_parsp_1(A)
     => m1_parsp_1(u1_parsp_1(A),u1_struct_0(A)) ) )).

fof(dt_g1_parsp_1,axiom,(
    ! [A,B] :
      ( m1_parsp_1(B,A)
     => ( v1_parsp_1(g1_parsp_1(A,B))
        & l1_parsp_1(g1_parsp_1(A,B)) ) ) )).

fof(free_g1_parsp_1,axiom,(
    ! [A,B] :
      ( m1_parsp_1(B,A)
     => ! [C,D] :
          ( g1_parsp_1(A,B) = g1_parsp_1(C,D)
         => ( A = C
            & B = D ) ) ) )).
%------------------------------------------------------------------------------