SET007 Axioms: SET007+367.ax


%------------------------------------------------------------------------------
% File     : SET007+367 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Product of Families of Groups and Vector 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    : prvect_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   91 (  10 unit)
%            Number of atoms       :  780 (  48 equality)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :  790 ( 101 ~  ;   0  |; 502  &)
%                                         (  14 <=>; 173 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-3 arity)
%            Number of functors    :   54 (   3 constant; 0-6 arity)
%            Number of variables   :  225 (   0 singleton; 220 !;   5 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_prvect_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v3_struct_0(k5_prvect_1(A,B))
        & v1_rlvect_1(k5_prvect_1(A,B))
        & v3_rlvect_1(k5_prvect_1(A,B))
        & v4_rlvect_1(k5_prvect_1(A,B))
        & v5_rlvect_1(k5_prvect_1(A,B))
        & v6_rlvect_1(k5_prvect_1(A,B)) ) ) )).

fof(fc2_prvect_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,k5_numbers) )
     => ( ~ v3_struct_0(k7_prvect_1(A,B))
        & v11_vectsp_1(k7_prvect_1(A,B),A) ) ) )).

fof(fc3_prvect_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,k5_numbers) )
     => ( ~ v3_struct_0(k7_prvect_1(A,B))
        & v11_vectsp_1(k7_prvect_1(A,B),A)
        & v12_vectsp_1(k7_prvect_1(A,B),A) ) ) )).

fof(rc1_prvect_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) )).

fof(fc4_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) )).

fof(fc5_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_relat_1(A)) )
     => ~ v1_xboole_0(k1_funct_1(A,B)) ) )).

fof(cc1_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => v1_finseq_1(B) ) ) )).

fof(cc2_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_prvect_1(B,A)
         => v1_finseq_1(B) ) ) )).

fof(rc2_prvect_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_prvect_1(A) ) )).

fof(t1_prvect_1,axiom,(
    $true )).

fof(t2_prvect_1,axiom,(
    $true )).

fof(t3_prvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A)) ) )).

fof(t4_prvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => r1_finseqop(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) ) )).

fof(t5_prvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
          & r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A))
          & r1_finseqop(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) )
       => ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & l1_rlvect_1(A) ) ) ) )).

fof(t6_prvect_1,axiom,(
    $true )).

fof(t7_prvect_1,axiom,(
    $true )).

fof(t8_prvect_1,axiom,(
    $true )).

fof(t9_prvect_1,axiom,(
    $true )).

fof(t10_prvect_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) )
     => r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A)) ) )).

fof(t11_prvect_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) )
     => r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)) ) )).

fof(d1_prvect_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A))
                    & m2_relset_1(D,k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A)) )
                 => ( D = k2_prvect_1(A,B,C)
                  <=> ! [E] :
                        ( m2_finseq_2(E,A,k4_finseq_2(C,A))
                       => ! [F] :
                            ( m2_finseq_2(F,A,k4_finseq_2(C,A))
                           => k2_binop_1(k4_finseq_2(C,A),k4_finseq_2(C,A),k4_finseq_2(C,A),D,E,F) = k1_prvect_1(A,C,B,E,F) ) ) ) ) ) ) ) )).

fof(d2_prvect_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k4_finseq_2(C,A),k4_finseq_2(C,A))
                    & m2_relset_1(D,k4_finseq_2(C,A),k4_finseq_2(C,A)) )
                 => ( D = k3_prvect_1(A,B,C)
                  <=> ! [E] :
                        ( m2_finseq_2(E,A,k4_finseq_2(C,A))
                       => k8_funct_2(k4_finseq_2(C,A),k4_finseq_2(C,A),D,E) = k5_finseqop(A,A,E,B) ) ) ) ) ) ) )).

fof(t12_prvect_1,axiom,(
    $true )).

fof(t13_prvect_1,axiom,(
    $true )).

fof(t14_prvect_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( v1_binop_1(C,B)
               => v1_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) )).

fof(t15_prvect_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( v2_binop_1(C,B)
               => v2_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) )).

fof(t16_prvect_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ( r3_binop_1(B,C,D)
                   => r3_binop_1(k4_finseq_2(A,B),k4_prvect_1(B,A,C),k2_prvect_1(B,D,A)) ) ) ) ) ) )).

fof(t17_prvect_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,B)
                    & m2_relset_1(D,B,B) )
                 => ( ( v1_setwiseo(C,B)
                      & v2_binop_1(C,B)
                      & r1_finseqop(B,D,C) )
                   => r1_finseqop(k4_finseq_2(A,B),k3_prvect_1(B,D,A),k2_prvect_1(B,C,A)) ) ) ) ) ) )).

fof(d3_prvect_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( v3_rlvect_1(A)
              & v4_rlvect_1(A)
              & v5_rlvect_1(A)
              & v6_rlvect_1(A) )
           => k5_prvect_1(A,B) = g1_rlvect_1(k4_finseq_2(B,u1_struct_0(A)),k2_prvect_1(u1_struct_0(A),u1_rlvect_1(A),B),k4_prvect_1(u1_struct_0(A),B,u2_struct_0(A))) ) ) ) )).

fof(d4_prvect_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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A)))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A))) )
             => ( C = k6_prvect_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A)))
                       => k2_binop_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A)),k4_finseq_2(B,u1_struct_0(A)),C,D,E) = k3_finseqop(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),D,E) ) ) ) ) ) ) )).

fof(d5_prvect_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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v11_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( C = k7_prvect_1(A,B)
              <=> ( g1_rlvect_1(u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C)) = k5_prvect_1(A,B)
                  & u2_vectsp_1(A,C) = k6_prvect_1(A,B) ) ) ) ) ) )).

fof(t18_prvect_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m2_finseq_2(F,B,k4_finseq_2(A,B))
                         => ! [G] :
                              ( m2_finseq_2(G,B,k4_finseq_2(A,B))
                             => ( r6_binop_1(B,C,D)
                               => k3_finseqop(B,B,B,C,E,k1_prvect_1(B,A,D,F,G)) = k1_finseqop(B,B,B,D,k3_finseqop(B,B,B,C,E,F),k3_finseqop(B,B,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d6_prvect_1,axiom,(
    $true )).

fof(d7_prvect_1,axiom,(
    $true )).

fof(d8_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( m1_prvect_1(B,A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_relat_1(A))
                 => ( v1_funct_1(k1_funct_1(B,C))
                    & v1_funct_2(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
                    & m2_relset_1(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) ) ) ) ) )).

fof(d9_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( m2_prvect_1(B,A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_relat_1(A))
                 => ( v1_funct_1(k1_funct_1(B,C))
                    & v1_funct_2(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C))
                    & m2_relset_1(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) ) ) ) ) )).

fof(t19_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( m1_prvect_1(B,A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
                 => ( v1_funct_1(k1_funct_1(B,C))
                    & v1_funct_2(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
                    & m2_relset_1(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) ) ) ) ) )).

fof(t20_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( m2_prvect_1(B,A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
                 => ( v1_funct_1(k1_funct_1(B,C))
                    & v1_funct_2(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C))
                    & m2_relset_1(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) ) ) ) ) )).

fof(t21_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_card_3(A),k4_card_3(A))
            & m2_relset_1(B,k4_card_3(A),k4_card_3(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_card_3(A),k4_card_3(A))
                & m2_relset_1(C,k4_card_3(A),k4_card_3(A)) )
             => ( ! [D] :
                    ( m1_subset_1(D,k4_card_3(A))
                   => ! [E] :
                        ( m2_subset_1(E,k5_numbers,k4_finseq_1(A))
                       => k9_prvect_1(A,k12_prvect_1(k4_card_3(A),B,D),E) = k9_prvect_1(A,k12_prvect_1(k4_card_3(A),C,D),E) ) )
               => B = C ) ) ) ) )).

fof(t22_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_prvect_1(B,A)
         => ( k2_funct_6(B) = A
            & r1_tarski(k4_card_3(k3_funct_6(B)),k4_card_3(A)) ) ) ) )).

fof(t23_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m2_prvect_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(A))
             => ! [D] :
                  ( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
                 => k9_prvect_1(A,k12_prvect_1(k4_card_3(A),k13_prvect_1(A,B),C),D) = k8_funct_2(k1_funct_1(A,D),k1_funct_1(A,D),k11_prvect_1(A,B,D),k9_prvect_1(A,C,D)) ) ) ) ) )).

fof(t24_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
            & m2_relset_1(B,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
                & m2_relset_1(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
             => ( ! [D] :
                    ( m1_subset_1(D,k4_card_3(A))
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(A))
                       => ! [F] :
                            ( m2_subset_1(F,k5_numbers,k4_finseq_1(A))
                           => k9_prvect_1(A,k14_prvect_1(k4_card_3(A),B,D,E),F) = k9_prvect_1(A,k14_prvect_1(k4_card_3(A),C,D,E),F) ) ) )
               => B = C ) ) ) ) )).

fof(d10_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
                & m2_relset_1(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
             => ( C = k15_prvect_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(A))
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(A))
                       => ! [F] :
                            ( m2_subset_1(F,k5_numbers,k4_finseq_1(A))
                           => k9_prvect_1(A,k14_prvect_1(k4_card_3(A),C,D,E),F) = k2_binop_1(k1_funct_1(A,F),k1_funct_1(A,F),k1_funct_1(A,F),k10_prvect_1(A,B,F),k9_prvect_1(A,D,F),k9_prvect_1(A,E,F)) ) ) ) ) ) ) ) )).

fof(t25_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ( ! [C] :
                ( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
               => v1_binop_1(k10_prvect_1(A,B,C),k1_funct_1(A,C)) )
           => v1_binop_1(k15_prvect_1(A,B),k4_card_3(A)) ) ) ) )).

fof(t26_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ( ! [C] :
                ( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
               => v2_binop_1(k10_prvect_1(A,B,C),k1_funct_1(A,C)) )
           => v2_binop_1(k15_prvect_1(A,B),k4_card_3(A)) ) ) ) )).

fof(t27_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(A))
             => ( ! [D] :
                    ( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
                   => r3_binop_1(k1_funct_1(A,D),k9_prvect_1(A,C,D),k10_prvect_1(A,B,D)) )
               => r3_binop_1(k4_card_3(A),C,k15_prvect_1(A,B)) ) ) ) ) )).

fof(t28_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ! [C] :
              ( m2_prvect_1(C,A)
             => ( ! [D] :
                    ( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
                   => ( r1_finseqop(k1_funct_1(A,D),k11_prvect_1(A,C,D),k10_prvect_1(A,B,D))
                      & v1_setwiseo(k10_prvect_1(A,B,D),k1_funct_1(A,D)) ) )
               => r1_finseqop(k4_card_3(A),k13_prvect_1(A,C),k15_prvect_1(A,B)) ) ) ) ) )).

fof(d11_prvect_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_prvect_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k2_relat_1(A))
           => ( ~ v3_struct_0(B)
              & v3_rlvect_1(B)
              & v4_rlvect_1(B)
              & v5_rlvect_1(B)
              & v6_rlvect_1(B)
              & l1_rlvect_1(B) ) ) ) ) )).

fof(d12_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B)
            & ~ v1_xboole_0(B)
            & v1_finseq_1(B) )
         => ( B = k17_prvect_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] :
                  ( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
                 => k1_funct_1(B,C) = u1_struct_0(k16_prvect_1(A,C)) ) ) ) ) ) )).

fof(d13_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ! [B] :
          ( m1_prvect_1(B,k17_prvect_1(A))
         => ( B = k19_prvect_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(k17_prvect_1(A))
              & ! [C] :
                  ( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
                 => k10_prvect_1(k17_prvect_1(A),B,C) = u1_rlvect_1(k18_prvect_1(A,C)) ) ) ) ) ) )).

fof(d14_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ! [B] :
          ( m2_prvect_1(B,k17_prvect_1(A))
         => ( B = k20_prvect_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(k17_prvect_1(A))
              & ! [C] :
                  ( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
                 => k11_prvect_1(k17_prvect_1(A),B,C) = k7_vectsp_1(k18_prvect_1(A,C)) ) ) ) ) ) )).

fof(d15_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k17_prvect_1(A)))
         => ( B = k21_prvect_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
               => k9_prvect_1(k17_prvect_1(A),B,C) = u2_struct_0(k18_prvect_1(A,C)) ) ) ) ) )).

fof(d16_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => k22_prvect_1(A) = g1_rlvect_1(k4_card_3(k17_prvect_1(A)),k15_prvect_1(k17_prvect_1(A),k19_prvect_1(A)),k21_prvect_1(A)) ) )).

fof(s1_prvect_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finseq_1(A)
      & k3_finseq_1(A) = k3_finseq_1(f1_s1_prvect_1)
      & ! [B] :
          ( m2_subset_1(B,k5_numbers,k4_finseq_1(f1_s1_prvect_1))
         => k1_funct_1(A,B) = f2_s1_prvect_1(B) ) ) )).

fof(dt_m1_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ! [B] :
          ( m1_prvect_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) )).

fof(existence_m1_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ? [B] : m1_prvect_1(B,A) ) )).

fof(dt_m2_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ! [B] :
          ( m2_prvect_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) )).

fof(existence_m2_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A) )
     => ? [B] : m2_prvect_1(B,A) ) )).

fof(dt_k1_prvect_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,k4_finseq_2(B,A))
        & m1_subset_1(E,k4_finseq_2(B,A)) )
     => m2_finseq_2(k1_prvect_1(A,B,C,D,E),A,k4_finseq_2(B,A)) ) )).

fof(redefinition_k1_prvect_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,k4_finseq_2(B,A))
        & m1_subset_1(E,k4_finseq_2(B,A)) )
     => k1_prvect_1(A,B,C,D,E) = k3_funcop_1(C,D,E) ) )).

fof(dt_k2_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k2_prvect_1(A,B,C))
        & v1_funct_2(k2_prvect_1(A,B,C),k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A))
        & m2_relset_1(k2_prvect_1(A,B,C),k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A)) ) ) )).

fof(dt_k3_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k3_prvect_1(A,B,C))
        & v1_funct_2(k3_prvect_1(A,B,C),k4_finseq_2(C,A),k4_finseq_2(C,A))
        & m2_relset_1(k3_prvect_1(A,B,C),k4_finseq_2(C,A),k4_finseq_2(C,A)) ) ) )).

fof(dt_k4_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => m2_finseq_2(k4_prvect_1(A,B,C),A,k4_finseq_2(B,A)) ) )).

fof(redefinition_k4_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => k4_prvect_1(A,B,C) = k2_finseq_2(B,C) ) )).

fof(dt_k5_prvect_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v3_struct_0(k5_prvect_1(A,B))
        & v1_rlvect_1(k5_prvect_1(A,B))
        & v3_rlvect_1(k5_prvect_1(A,B))
        & v4_rlvect_1(k5_prvect_1(A,B))
        & v5_rlvect_1(k5_prvect_1(A,B))
        & v6_rlvect_1(k5_prvect_1(A,B))
        & l1_rlvect_1(k5_prvect_1(A,B)) ) ) )).

fof(dt_k6_prvect_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,k5_numbers) )
     => ( v1_funct_1(k6_prvect_1(A,B))
        & v1_funct_2(k6_prvect_1(A,B),k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A)))
        & m2_relset_1(k6_prvect_1(A,B),k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A))) ) ) )).

fof(dt_k7_prvect_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,k5_numbers) )
     => ( v11_vectsp_1(k7_prvect_1(A,B),A)
        & l4_vectsp_1(k7_prvect_1(A,B),A) ) ) )).

fof(dt_k8_prvect_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,k4_finseq_2(B,A)) )
     => m2_finseq_2(k8_prvect_1(A,B,C,D,E),A,k4_finseq_2(B,A)) ) )).

fof(redefinition_k8_prvect_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,k4_finseq_2(B,A)) )
     => k8_prvect_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) )).

fof(dt_k9_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & m1_subset_1(B,k4_card_3(A))
        & m1_subset_1(C,k1_relat_1(A)) )
     => m1_subset_1(k9_prvect_1(A,B,C),k1_funct_1(A,C)) ) )).

fof(redefinition_k9_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & m1_subset_1(B,k4_card_3(A))
        & m1_subset_1(C,k1_relat_1(A)) )
     => k9_prvect_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k10_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m1_prvect_1(B,A)
        & m1_subset_1(C,k4_finseq_1(A)) )
     => ( v1_funct_1(k10_prvect_1(A,B,C))
        & v1_funct_2(k10_prvect_1(A,B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
        & m2_relset_1(k10_prvect_1(A,B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) )).

fof(redefinition_k10_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m1_prvect_1(B,A)
        & m1_subset_1(C,k4_finseq_1(A)) )
     => k10_prvect_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k11_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m2_prvect_1(B,A)
        & m1_subset_1(C,k4_finseq_1(A)) )
     => ( v1_funct_1(k11_prvect_1(A,B,C))
        & v1_funct_2(k11_prvect_1(A,B,C),k1_funct_1(A,C),k1_funct_1(A,C))
        & m2_relset_1(k11_prvect_1(A,B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) )).

fof(redefinition_k11_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m2_prvect_1(B,A)
        & m1_subset_1(C,k4_finseq_1(A)) )
     => k11_prvect_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k12_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k12_prvect_1(A,B,C),A) ) )).

fof(redefinition_k12_prvect_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,A) )
     => k12_prvect_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k13_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m2_prvect_1(B,A) )
     => ( v1_funct_1(k13_prvect_1(A,B))
        & v1_funct_2(k13_prvect_1(A,B),k4_card_3(A),k4_card_3(A))
        & m2_relset_1(k13_prvect_1(A,B),k4_card_3(A),k4_card_3(A)) ) ) )).

fof(redefinition_k13_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m2_prvect_1(B,A) )
     => k13_prvect_1(A,B) = k7_funct_6(B) ) )).

fof(dt_k14_prvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => m1_subset_1(k14_prvect_1(A,B,C,D),A) ) )).

fof(redefinition_k14_prvect_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => k14_prvect_1(A,B,C,D) = k1_binop_1(B,C,D) ) )).

fof(dt_k15_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & m1_prvect_1(B,A) )
     => ( v1_funct_1(k15_prvect_1(A,B))
        & v1_funct_2(k15_prvect_1(A,B),k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
        & m2_relset_1(k15_prvect_1(A,B),k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) ) ) )).

fof(dt_k16_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A)
        & m1_subset_1(B,k4_finseq_1(A)) )
     => ( ~ v3_struct_0(k16_prvect_1(A,B))
        & v3_rlvect_1(k16_prvect_1(A,B))
        & v4_rlvect_1(k16_prvect_1(A,B))
        & v5_rlvect_1(k16_prvect_1(A,B))
        & v6_rlvect_1(k16_prvect_1(A,B))
        & l1_rlvect_1(k16_prvect_1(A,B)) ) ) )).

fof(redefinition_k16_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A)
        & m1_subset_1(B,k4_finseq_1(A)) )
     => k16_prvect_1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k17_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ( v1_relat_1(k17_prvect_1(A))
        & v2_relat_1(k17_prvect_1(A))
        & v1_funct_1(k17_prvect_1(A))
        & ~ v1_xboole_0(k17_prvect_1(A))
        & v1_finseq_1(k17_prvect_1(A)) ) ) )).

fof(dt_k18_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A)
        & m1_subset_1(B,k4_finseq_1(k17_prvect_1(A))) )
     => ( ~ v3_struct_0(k18_prvect_1(A,B))
        & v3_rlvect_1(k18_prvect_1(A,B))
        & v4_rlvect_1(k18_prvect_1(A,B))
        & v5_rlvect_1(k18_prvect_1(A,B))
        & v6_rlvect_1(k18_prvect_1(A,B))
        & l1_rlvect_1(k18_prvect_1(A,B)) ) ) )).

fof(redefinition_k18_prvect_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A)
        & m1_subset_1(B,k4_finseq_1(k17_prvect_1(A))) )
     => k18_prvect_1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k19_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => m1_prvect_1(k19_prvect_1(A),k17_prvect_1(A)) ) )).

fof(dt_k20_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => m2_prvect_1(k20_prvect_1(A),k17_prvect_1(A)) ) )).

fof(dt_k21_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => m1_subset_1(k21_prvect_1(A),k4_card_3(k17_prvect_1(A))) ) )).

fof(dt_k22_prvect_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & ~ v1_xboole_0(A)
        & v1_finseq_1(A)
        & v1_prvect_1(A) )
     => ( ~ v3_struct_0(k22_prvect_1(A))
        & v1_rlvect_1(k22_prvect_1(A))
        & v3_rlvect_1(k22_prvect_1(A))
        & v4_rlvect_1(k22_prvect_1(A))
        & v5_rlvect_1(k22_prvect_1(A))
        & v6_rlvect_1(k22_prvect_1(A))
        & l1_rlvect_1(k22_prvect_1(A)) ) ) )).
%------------------------------------------------------------------------------