SET007 Axioms: SET007+361.ax


%------------------------------------------------------------------------------
% File     : SET007+361 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Sum and Product of Finite Sequences of Elements of a Field
% 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    : fvsum_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  145 (  12 unit)
%            Number of atoms       :  984 ( 136 equality)
%            Maximal formula depth :   18 (   8 average)
%            Number of connectives :  974 ( 135 ~  ;   1  |; 434  &)
%                                         (   1 <=>; 403 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   1 propositional; 0-3 arity)
%            Number of functors    :   54 (   4 constant; 0-6 arity)
%            Number of variables   :  430 (   0 singleton; 429 !;   1 ?)
%            Maximal term depth    :    6 (   2 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(cc1_fvsum_1,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v5_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_algstr_1(A) ) ) ) )).

fof(t1_fvsum_1,axiom,(
    $true )).

fof(t2_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A) )
     => v1_binop_1(u1_rlvect_1(A),u1_struct_0(A)) ) )).

fof(t3_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => v2_binop_1(u1_rlvect_1(A),u1_struct_0(A)) ) )).

fof(t4_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => v1_binop_1(u1_group_1(A),u1_struct_0(A)) ) )).

fof(t5_fvsum_1,axiom,(
    $true )).

fof(t6_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)) ) )).

fof(t7_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_group_1(A) ) )).

fof(t8_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => r3_binop_1(u1_struct_0(A),k1_rlvect_1(A),u1_rlvect_1(A)) ) )).

fof(t9_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => k3_binop_1(u1_struct_0(A),u1_rlvect_1(A)) = k1_rlvect_1(A) ) )).

fof(t10_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) ) )).

fof(t11_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => v1_setwiseo(u1_group_1(A),u1_struct_0(A)) ) )).

fof(t12_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => r6_binop_1(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A)) ) )).

fof(d1_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_fvsum_1(A,B) = k8_funcop_1(u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,k6_partfun1(u1_struct_0(A))) ) ) )).

fof(d2_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => k2_fvsum_1(A) = k8_finseqop(u1_struct_0(A),u1_rlvect_1(A),k6_partfun1(u1_struct_0(A)),k7_vectsp_1(A)) ) )).

fof(t13_fvsum_1,axiom,(
    $true )).

fof(t14_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k2_fvsum_1(A),B,C) = k6_rlvect_1(A,B,C) ) ) ) )).

fof(t15_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r7_binop_1(u1_struct_0(A),k1_fvsum_1(A,B),u1_rlvect_1(A)) ) ) )).

fof(t16_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => r1_finseqop(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) ) )).

fof(t17_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => v1_finseqop(u1_rlvect_1(A),u1_struct_0(A)) ) )).

fof(t18_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_algstr_1(A)
        & l1_rlvect_1(A) )
     => k6_finseqop(u1_struct_0(A),u1_rlvect_1(A)) = k7_vectsp_1(A) ) )).

fof(t19_fvsum_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) )
     => r7_binop_1(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) ) )).

fof(d3_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k3_fvsum_1(A,B,C) = k1_finseqop(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) )).

fof(t20_fvsum_1,axiom,(
    $true )).

fof(t21_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_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] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(F,k3_setwop_2(k3_fvsum_1(A,B,C)))
                              & D = k1_funct_1(B,F)
                              & E = k1_funct_1(C,F) )
                           => k1_funct_1(k3_fvsum_1(A,B,C),F) = k2_rlvect_1(A,D,E) ) ) ) ) ) ) ) )).

fof(t22_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C)))
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C)))
                             => ( ( r2_hidden(B,k2_setwop_2(A))
                                  & D = k1_funct_1(F,B)
                                  & E = k1_funct_1(G,B) )
                               => k1_funct_1(k4_fvsum_1(A,C,F,G),B) = k2_rlvect_1(C,D,E) ) ) ) ) ) ) ) ) )).

fof(t23_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( k3_fvsum_1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A))
            & k3_fvsum_1(A,B,k6_finseq_1(u1_struct_0(A))) = k6_finseq_1(u1_struct_0(A)) ) ) ) )).

fof(t24_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_fvsum_1(np__1,A,k4_matrix_2(u1_struct_0(A),B),k4_matrix_2(u1_struct_0(A),C)) = k4_matrix_2(u1_struct_0(A),k2_rlvect_1(A,B,C)) ) ) ) )).

fof(t25_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k4_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C),k4_finseqop(u1_struct_0(B),A,D)) = k4_finseqop(u1_struct_0(B),A,k2_rlvect_1(B,C,D)) ) ) ) ) )).

fof(t26_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k4_fvsum_1(A,B,C,D) = k4_fvsum_1(A,B,D,C) ) ) ) ) )).

fof(t27_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k4_fvsum_1(A,B,C,k4_fvsum_1(A,B,D,E)) = k4_fvsum_1(A,B,k4_fvsum_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t28_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v5_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ( k4_fvsum_1(A,B,C,k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))) = C
                & C = k4_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B)),C) ) ) ) ) )).

fof(d4_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => k5_fvsum_1(A,B) = k5_finseqop(u1_struct_0(A),u1_struct_0(A),B,k7_vectsp_1(A)) ) ) )).

fof(t29_fvsum_1,axiom,(
    $true )).

fof(t30_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ( ( r2_hidden(A,k3_setwop_2(k5_fvsum_1(B,D)))
                      & C = k1_funct_1(D,A) )
                   => k1_funct_1(k5_fvsum_1(B,D),A) = k5_rlvect_1(B,C) ) ) ) ) ) )).

fof(t31_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                     => ( ( r2_hidden(A,k2_setwop_2(B))
                          & D = k1_funct_1(E,A) )
                       => k1_funct_1(k6_fvsum_1(B,C,E),A) = k5_rlvect_1(C,D) ) ) ) ) ) ) )).

fof(t32_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => k5_fvsum_1(A,k6_finseq_1(u1_struct_0(A))) = k6_finseq_1(u1_struct_0(A)) ) )).

fof(t33_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_fvsum_1(np__1,A,k4_matrix_2(u1_struct_0(A),B)) = k4_matrix_2(u1_struct_0(A),k5_rlvect_1(A,B)) ) ) )).

fof(t34_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k6_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C)) = k4_finseqop(u1_struct_0(B),A,k5_rlvect_1(B,C)) ) ) ) )).

fof(t35_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ( k4_fvsum_1(A,B,C,k6_fvsum_1(A,B,C)) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))
                & k4_fvsum_1(A,B,k6_fvsum_1(A,B,C),C) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B)) ) ) ) ) )).

fof(t36_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ( k4_fvsum_1(A,B,C,D) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))
                   => ( C = k6_fvsum_1(A,B,D)
                      & D = k6_fvsum_1(A,B,C) ) ) ) ) ) ) )).

fof(t37_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k6_fvsum_1(A,B,k6_fvsum_1(A,B,C)) = C ) ) ) )).

fof(t38_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ( k6_fvsum_1(A,B,C) = k6_fvsum_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t39_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => ( ( k4_fvsum_1(A,B,D,C) = k4_fvsum_1(A,B,E,C)
                          | k4_fvsum_1(A,B,D,C) = k4_fvsum_1(A,B,C,E) )
                       => D = E ) ) ) ) ) ) )).

fof(t40_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k6_fvsum_1(A,B,k4_fvsum_1(A,B,C,D)) = k4_fvsum_1(A,B,k6_fvsum_1(A,B,C),k6_fvsum_1(A,B,D)) ) ) ) ) )).

fof(d5_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k7_fvsum_1(A,B,C) = k1_finseqop(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k2_fvsum_1(A),B,C) ) ) ) )).

fof(t41_fvsum_1,axiom,(
    $true )).

fof(t42_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m2_finseq_1(F,u1_struct_0(B))
                         => ( ( r2_hidden(A,k3_setwop_2(k7_fvsum_1(B,E,F)))
                              & C = k1_funct_1(E,A)
                              & D = k1_funct_1(F,A) )
                           => k1_funct_1(k7_fvsum_1(B,E,F),A) = k6_rlvect_1(B,C,D) ) ) ) ) ) ) ) )).

fof(t43_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                             => ( ( r2_hidden(A,k2_setwop_2(B))
                                  & D = k1_funct_1(F,A)
                                  & E = k1_funct_1(G,A) )
                               => k1_funct_1(k8_fvsum_1(B,C,F,G),A) = k6_rlvect_1(C,D,E) ) ) ) ) ) ) ) ) )).

fof(t44_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( k7_fvsum_1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A))
            & k7_fvsum_1(A,B,k6_finseq_1(u1_struct_0(A))) = k6_finseq_1(u1_struct_0(A)) ) ) ) )).

fof(t45_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_fvsum_1(np__1,A,k4_matrix_2(u1_struct_0(A),B),k4_matrix_2(u1_struct_0(A),C)) = k4_matrix_2(u1_struct_0(A),k6_rlvect_1(A,B,C)) ) ) ) )).

fof(t46_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k8_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C),k4_finseqop(u1_struct_0(B),A,D)) = k4_finseqop(u1_struct_0(B),A,k6_rlvect_1(B,C,D)) ) ) ) ) )).

fof(t47_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k8_fvsum_1(A,B,C,D) = k4_fvsum_1(A,B,C,k6_fvsum_1(A,B,D)) ) ) ) ) )).

fof(t48_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k8_fvsum_1(A,B,C,k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))) = C ) ) ) )).

fof(t49_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v5_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k8_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B)),C) = k6_fvsum_1(A,B,C) ) ) ) )).

fof(t50_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_algstr_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k8_fvsum_1(A,B,C,k6_fvsum_1(A,B,D)) = k4_fvsum_1(A,B,C,D) ) ) ) ) )).

fof(t51_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k6_fvsum_1(A,B,k8_fvsum_1(A,B,C,D)) = k8_fvsum_1(A,B,D,C) ) ) ) ) )).

fof(t52_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k6_fvsum_1(A,B,k8_fvsum_1(A,B,C,D)) = k4_fvsum_1(A,B,k6_fvsum_1(A,B,C),D) ) ) ) ) )).

fof(t53_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k8_fvsum_1(A,B,C,C) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B)) ) ) ) )).

fof(t54_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ( k8_fvsum_1(A,B,C,D) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))
                   => C = D ) ) ) ) ) )).

fof(t55_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k8_fvsum_1(A,B,k8_fvsum_1(A,B,C,D),E) = k8_fvsum_1(A,B,C,k4_fvsum_1(A,B,D,E)) ) ) ) ) ) )).

fof(t56_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k4_fvsum_1(A,B,C,k8_fvsum_1(A,B,D,E)) = k8_fvsum_1(A,B,k4_fvsum_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t57_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k8_fvsum_1(A,B,C,k8_fvsum_1(A,B,D,E)) = k4_fvsum_1(A,B,k8_fvsum_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t58_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => C = k8_fvsum_1(A,B,k4_fvsum_1(A,B,C,D),D) ) ) ) ) )).

fof(t59_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => C = k4_fvsum_1(A,B,k8_fvsum_1(A,B,C,D),D) ) ) ) ) )).

fof(t60_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k8_funcop_1(u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,k6_partfun1(u1_struct_0(A))),C) = k1_group_1(A,B,C) ) ) ) )).

fof(t61_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k1_fvsum_1(A,B),C) = k1_group_1(A,B,C) ) ) ) )).

fof(d6_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_fvsum_1(A,B,C) = k5_finseqop(u1_struct_0(A),u1_struct_0(A),B,k1_fvsum_1(A,C)) ) ) ) )).

fof(t62_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ( ( r2_hidden(A,k3_setwop_2(k9_fvsum_1(B,E,C)))
                          & D = k1_funct_1(E,A) )
                       => k1_funct_1(k9_fvsum_1(B,E,C),A) = k1_group_1(B,C,D) ) ) ) ) ) ) )).

fof(t63_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                         => ( ( r2_hidden(A,k2_setwop_2(B))
                              & D = k1_funct_1(F,A) )
                           => k1_funct_1(k10_fvsum_1(B,C,F,E),A) = k1_group_1(C,E,D) ) ) ) ) ) ) ) )).

fof(t64_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k9_fvsum_1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) )).

fof(t65_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k10_fvsum_1(np__1,A,k4_matrix_2(u1_struct_0(A),C),B) = k4_matrix_2(u1_struct_0(A),k1_group_1(A,B,C)) ) ) ) )).

fof(t66_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k10_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,D),C) = k4_finseqop(u1_struct_0(B),A,k1_group_1(B,C,D)) ) ) ) ) )).

fof(t67_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k10_fvsum_1(A,B,E,k1_group_1(B,C,D)) = k10_fvsum_1(A,B,k10_fvsum_1(A,B,E,D),C) ) ) ) ) ) )).

fof(t68_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k10_fvsum_1(A,B,E,k2_rlvect_1(B,C,D)) = k4_fvsum_1(A,B,k10_fvsum_1(A,B,E,C),k10_fvsum_1(A,B,E,D)) ) ) ) ) ) )).

fof(t69_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k10_fvsum_1(A,B,k4_fvsum_1(A,B,D,E),C) = k4_fvsum_1(A,B,k10_fvsum_1(A,B,D,C),k10_fvsum_1(A,B,E,C)) ) ) ) ) ) )).

fof(t70_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k10_fvsum_1(A,B,C,k2_group_1(B)) = C ) ) ) )).

fof(t71_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k10_fvsum_1(A,B,C,k1_rlvect_1(B)) = k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B)) ) ) ) )).

fof(t72_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => k10_fvsum_1(A,B,C,k5_rlvect_1(B,k2_group_1(B))) = k6_fvsum_1(A,B,C) ) ) ) )).

fof(d7_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k11_fvsum_1(A,B,C) = k1_finseqop(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) ) ) ) )).

fof(t73_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m2_finseq_1(F,u1_struct_0(B))
                         => ( ( r2_hidden(A,k3_setwop_2(k11_fvsum_1(B,E,F)))
                              & C = k1_funct_1(E,A)
                              & D = k1_funct_1(F,A) )
                           => k1_funct_1(k11_fvsum_1(B,E,F),A) = k1_group_1(B,C,D) ) ) ) ) ) ) ) )).

fof(t74_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C)))
                             => ( ( r2_hidden(A,k2_setwop_2(B))
                                  & D = k1_funct_1(F,A)
                                  & E = k1_funct_1(G,A) )
                               => k1_funct_1(k12_fvsum_1(B,C,F,G),A) = k1_group_1(C,D,E) ) ) ) ) ) ) ) ) )).

fof(t75_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ( k11_fvsum_1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A))
            & k11_fvsum_1(A,B,k6_finseq_1(u1_struct_0(A))) = k6_finseq_1(u1_struct_0(A)) ) ) ) )).

fof(t76_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_fvsum_1(np__1,A,k4_matrix_2(u1_struct_0(A),B),k4_matrix_2(u1_struct_0(A),C)) = k4_matrix_2(u1_struct_0(A),k1_group_1(A,B,C)) ) ) ) )).

fof(t77_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k12_fvsum_1(A,B,C,D) = k12_fvsum_1(A,B,D,C) ) ) ) ) )).

fof(t78_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k11_fvsum_1(A,B,C) = k11_fvsum_1(A,C,B) ) ) ) )).

fof(t79_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k12_fvsum_1(A,B,C,k12_fvsum_1(A,B,D,E)) = k12_fvsum_1(A,B,k12_fvsum_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t80_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ( k12_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C),D) = k10_fvsum_1(A,B,D,C)
                    & k12_fvsum_1(A,B,D,k4_finseqop(u1_struct_0(B),A,C)) = k10_fvsum_1(A,B,D,C) ) ) ) ) ) )).

fof(t81_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k12_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C),k4_finseqop(u1_struct_0(B),A,D)) = k4_finseqop(u1_struct_0(B),A,k10_group_1(B,C,D)) ) ) ) ) )).

fof(t82_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => k10_fvsum_1(A,B,k12_fvsum_1(A,B,D,E),C) = k12_fvsum_1(A,B,k10_fvsum_1(A,B,D,C),E) ) ) ) ) ) )).

fof(t83_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                     => ( k10_fvsum_1(A,B,k12_fvsum_1(A,B,D,E),C) = k12_fvsum_1(A,B,k10_fvsum_1(A,B,D,C),E)
                        & k10_fvsum_1(A,B,k12_fvsum_1(A,B,D,E),C) = k12_fvsum_1(A,B,D,k10_fvsum_1(A,B,E,C)) ) ) ) ) ) ) )).

fof(t84_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k10_fvsum_1(A,B,D,C) = k12_fvsum_1(A,B,k4_finseqop(u1_struct_0(B),A,C),D) ) ) ) ) )).

fof(d8_fvsum_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) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,B) = k2_finsop_1(u1_struct_0(A),B,u1_rlvect_1(A)) ) ) )).

fof(t85_fvsum_1,axiom,(
    $true )).

fof(t86_fvsum_1,axiom,(
    $true )).

fof(t87_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),C,k4_matrix_2(u1_struct_0(A),B))) = k2_rlvect_1(A,k9_rlvect_1(A,C),B) ) ) ) )).

fof(t88_fvsum_1,axiom,(
    $true )).

fof(t89_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),k4_matrix_2(u1_struct_0(A),B),C)) = k2_rlvect_1(A,B,k9_rlvect_1(A,C)) ) ) ) )).

fof(t90_fvsum_1,axiom,(
    $true )).

fof(t91_fvsum_1,axiom,(
    $true )).

fof(t92_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k9_rlvect_1(A,k9_fvsum_1(A,C,B)) = k1_group_1(A,B,k9_rlvect_1(A,C)) ) ) ) )).

fof(t93_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k4_finseq_2(np__0,u1_struct_0(A)))
         => k9_rlvect_1(A,B) = k1_rlvect_1(A) ) ) )).

fof(t94_fvsum_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) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => k9_rlvect_1(A,k5_fvsum_1(A,B)) = k5_rlvect_1(A,k9_rlvect_1(A,B)) ) ) )).

fof(t95_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k9_rlvect_1(B,k4_fvsum_1(A,B,C,D)) = k4_rlvect_1(B,k9_rlvect_1(B,C),k9_rlvect_1(B,D)) ) ) ) ) )).

fof(t96_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k9_rlvect_1(B,k8_fvsum_1(A,B,C,D)) = k6_rlvect_1(B,k9_rlvect_1(B,C),k9_rlvect_1(B,D)) ) ) ) ) )).

fof(d9_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => k13_fvsum_1(A,B) = k2_finsop_1(u1_struct_0(A),B,u1_group_1(A)) ) ) )).

fof(t97_fvsum_1,axiom,(
    $true )).

fof(t98_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => k13_fvsum_1(A,k6_finseq_1(u1_struct_0(A))) = k2_group_1(A) ) )).

fof(t99_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k13_fvsum_1(A,k4_matrix_2(u1_struct_0(A),B)) = B ) ) )).

fof(t100_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k13_fvsum_1(A,k8_finseq_1(u1_struct_0(A),C,k4_matrix_2(u1_struct_0(A),B))) = k10_group_1(A,k13_fvsum_1(A,C),B) ) ) ) )).

fof(t101_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k13_fvsum_1(A,k8_finseq_1(u1_struct_0(A),B,C)) = k10_group_1(A,k13_fvsum_1(A,B),k13_fvsum_1(A,C)) ) ) ) )).

fof(t102_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k13_fvsum_1(A,k8_finseq_1(u1_struct_0(A),k4_matrix_2(u1_struct_0(A),B),C)) = k10_group_1(A,B,k13_fvsum_1(A,C)) ) ) ) )).

fof(t103_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_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))
             => k13_fvsum_1(A,k7_rlvect_1(A,B,C)) = k10_group_1(A,B,C) ) ) ) )).

fof(t104_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_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))
                 => k13_fvsum_1(A,k8_rlvect_1(A,B,C,D)) = k10_group_1(A,k10_group_1(A,B,C),D) ) ) ) ) )).

fof(t105_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k4_finseq_2(np__0,u1_struct_0(A)))
         => k13_fvsum_1(A,B) = k2_group_1(A) ) ) )).

fof(t106_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => k13_fvsum_1(B,k4_finseqop(u1_struct_0(B),A,k2_group_1(B))) = k2_group_1(B) ) ) )).

fof(t107_fvsum_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_finseq_1(B,u1_struct_0(A))
         => ( ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & r2_hidden(C,k3_setwop_2(B))
                & k1_funct_1(B,C) = k1_rlvect_1(A) )
          <=> k13_fvsum_1(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(t108_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v8_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),k1_nat_1(A,B),D)) = k10_group_1(C,k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),A,D)),k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),B,D))) ) ) ) ) )).

fof(t109_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v8_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),k2_nat_1(A,B),D)) = k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),B,k13_fvsum_1(C,k4_finseqop(u1_struct_0(C),A,D)))) ) ) ) ) )).

fof(t110_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k13_fvsum_1(B,k4_finseqop(u1_struct_0(B),A,k10_group_1(B,C,D))) = k10_group_1(B,k13_fvsum_1(B,k4_finseqop(u1_struct_0(B),A,C)),k13_fvsum_1(B,k4_finseqop(u1_struct_0(B),A,D))) ) ) ) ) )).

fof(t111_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k13_fvsum_1(B,k12_fvsum_1(A,B,C,D)) = k10_group_1(B,k13_fvsum_1(B,C),k13_fvsum_1(B,D)) ) ) ) ) )).

fof(t112_fvsum_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & v8_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B)))
                 => k13_fvsum_1(B,k10_fvsum_1(A,B,D,C)) = k10_group_1(B,k13_fvsum_1(B,k4_finseqop(u1_struct_0(B),A,C)),k13_fvsum_1(B,D)) ) ) ) ) )).

fof(d10_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k14_fvsum_1(A,B,C) = k9_rlvect_1(A,k11_fvsum_1(A,B,C)) ) ) ) )).

fof(t113_fvsum_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)
        & v8_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))
             => k14_fvsum_1(A,k4_matrix_2(u1_struct_0(A),B),k4_matrix_2(u1_struct_0(A),C)) = k10_group_1(A,B,C) ) ) ) )).

fof(t114_fvsum_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)
        & v8_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))
                     => k14_fvsum_1(A,k7_rlvect_1(A,B,C),k7_rlvect_1(A,D,E)) = k4_rlvect_1(A,k10_group_1(A,B,D),k10_group_1(A,C,E)) ) ) ) ) ) )).

fof(t115_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k14_fvsum_1(A,B,C) = k14_fvsum_1(A,C,B) ) ) ) )).

fof(dt_k1_fvsum_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k1_fvsum_1(A,B))
        & v1_funct_2(k1_fvsum_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k1_fvsum_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k2_fvsum_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_funct_1(k2_fvsum_1(A))
        & v1_funct_2(k2_fvsum_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(k2_fvsum_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_k3_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k3_fvsum_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k4_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => m2_finseq_2(k4_fvsum_1(A,B,C,D),u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) ) )).

fof(redefinition_k4_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => k4_fvsum_1(A,B,C,D) = k3_fvsum_1(B,C,D) ) )).

fof(dt_k5_fvsum_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,u1_struct_0(A)) )
     => m2_finseq_1(k5_fvsum_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k6_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B))) )
     => m2_finseq_2(k6_fvsum_1(A,B,C),u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) ) )).

fof(redefinition_k6_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B))) )
     => k6_fvsum_1(A,B,C) = k5_fvsum_1(B,C) ) )).

fof(dt_k7_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k7_fvsum_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k8_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => m2_finseq_2(k8_fvsum_1(A,B,C,D),u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) ) )).

fof(redefinition_k8_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => k8_fvsum_1(A,B,C,D) = k7_fvsum_1(B,C,D) ) )).

fof(dt_k9_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k9_fvsum_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k10_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m2_finseq_2(k10_fvsum_1(A,B,C,D),u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) ) )).

fof(redefinition_k10_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k10_fvsum_1(A,B,C,D) = k9_fvsum_1(B,C,D) ) )).

fof(dt_k11_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k11_fvsum_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k12_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => m2_finseq_2(k12_fvsum_1(A,B,C,D),u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) ) )).

fof(redefinition_k12_fvsum_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k4_finseq_2(A,u1_struct_0(B)))
        & m1_subset_1(D,k4_finseq_2(A,u1_struct_0(B))) )
     => k12_fvsum_1(A,B,C,D) = k11_fvsum_1(B,C,D) ) )).

fof(dt_k13_fvsum_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_finseq_1(B,u1_struct_0(A)) )
     => m1_subset_1(k13_fvsum_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k14_fvsum_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l3_vectsp_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_struct_0(A)) )
     => m1_subset_1(k14_fvsum_1(A,B,C),u1_struct_0(A)) ) )).
%------------------------------------------------------------------------------