SET007 Axioms: SET007+788.ax


%------------------------------------------------------------------------------
% File     : SET007+788 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Calculation of Matrices of Field Elements. Part I
% 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    : matrix_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   66 (   0 unit)
%            Number of atoms       : 1417 ( 252 equality)
%            Maximal formula depth :   20 (  15 average)
%            Number of connectives : 1491 ( 140 ~  ;  56  |; 997  &)
%                                         (   1 <=>; 297 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   0 propositional; 1-4 arity)
%            Number of functors    :   20 (   3 constant; 0-3 arity)
%            Number of variables   :  235 (   0 singleton; 235 !;   0 ?)
%            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(d1_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => k1_matrix_4(A,B,C) = k3_matrix_3(A,B,k2_matrix_3(A,C)) ) ) ) )).

fof(t1_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
           => k2_matrix_3(A,k2_matrix_3(A,B)) = B ) ) ) )).

fof(t2_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
           => k3_matrix_3(A,B,k2_matrix_3(A,B)) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) ) ) ) )).

fof(t3_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
           => k1_matrix_4(A,B,B) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) ) ) ) )).

fof(t4_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k3_matrix_3(A,B,D) = k3_matrix_3(A,C,D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t5_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ~ r1_xreal_0(k3_finseq_1(C),np__0)
               => k1_matrix_4(A,B,k2_matrix_3(A,C)) = k3_matrix_3(A,B,C) ) ) ) ) )).

fof(t6_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C)
                  & B = k3_matrix_3(A,B,C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | C = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) ) ) ) ) ) )).

fof(t7_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C)
                  & k1_matrix_4(A,B,C) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = C ) ) ) ) ) )).

fof(t8_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C)
                  & k3_matrix_3(A,B,C) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | C = k2_matrix_3(A,B) ) ) ) ) ) )).

fof(t9_matrix_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & v7_vectsp_1(C)
                & v8_vectsp_1(C)
                & v9_vectsp_1(C)
                & ~ v10_vectsp_1(C)
                & l3_vectsp_1(C) )
             => ( ~ r1_xreal_0(A,np__0)
               => k2_matrix_3(C,k1_matrix_3(C,A,B)) = k1_matrix_3(C,A,B) ) ) ) ) )).

fof(t10_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C)
                  & k1_matrix_4(A,C,B) = C )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) ) ) ) ) ) )).

fof(t11_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k1_matrix_4(A,B,k1_matrix_4(A,C,C)) ) ) ) ) ) )).

fof(t12_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k2_matrix_3(A,k3_matrix_3(A,B,C)) = k3_matrix_3(A,k2_matrix_3(A,B),k2_matrix_3(A,C)) ) ) ) ) ) )).

fof(t13_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k1_matrix_4(A,B,k1_matrix_4(A,B,C)) = C ) ) ) ) ) )).

fof(t14_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k1_matrix_4(A,B,D) = k1_matrix_4(A,C,D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t15_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k1_matrix_4(A,D,B) = k1_matrix_4(A,D,C) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t16_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,B,C),D) = k1_matrix_4(A,k1_matrix_4(A,B,D),C) ) ) ) ) ) ) )).

fof(t17_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,D) = k1_matrix_4(A,k1_matrix_4(A,B,C),k1_matrix_4(A,D,C)) ) ) ) ) ) ) )).

fof(t18_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,D,B),k1_matrix_4(A,D,C)) = k1_matrix_4(A,C,B) ) ) ) ) ) ) )).

fof(t19_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) )
                     => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                          & k3_finseq_1(C) = k3_finseq_1(D)
                          & k3_finseq_1(D) = k3_finseq_1(E)
                          & k1_matrix_1(B) = k1_matrix_1(C)
                          & k1_matrix_1(C) = k1_matrix_1(D)
                          & k1_matrix_1(D) = k1_matrix_1(E)
                          & k1_matrix_4(A,B,C) = k1_matrix_4(A,D,E) )
                       => ( r1_xreal_0(k3_finseq_1(B),np__0)
                          | k1_matrix_4(A,B,D) = k1_matrix_4(A,C,E) ) ) ) ) ) ) ) )).

fof(t20_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k3_matrix_3(A,B,k1_matrix_4(A,C,C)) ) ) ) ) ) )).

fof(t21_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k1_matrix_4(A,k3_matrix_3(A,B,C),C) ) ) ) ) ) )).

fof(t22_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k3_matrix_3(A,k1_matrix_4(A,B,C),C) ) ) ) ) ) )).

fof(t23_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k3_matrix_3(A,B,D) = k3_matrix_3(A,k3_matrix_3(A,B,C),k1_matrix_4(A,D,C)) ) ) ) ) ) ) )).

fof(t24_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k3_matrix_3(A,B,C),D) = k3_matrix_3(A,k1_matrix_4(A,B,D),C) ) ) ) ) ) ) )).

fof(t25_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k3_matrix_3(A,k1_matrix_4(A,B,C),D) = k3_matrix_3(A,k1_matrix_4(A,D,C),B) ) ) ) ) ) ) )).

fof(t26_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k3_matrix_3(A,B,D) = k1_matrix_4(A,k3_matrix_3(A,B,C),k1_matrix_4(A,C,D)) ) ) ) ) ) ) )).

fof(t27_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,D) = k1_matrix_4(A,k3_matrix_3(A,B,C),k3_matrix_3(A,D,C)) ) ) ) ) ) ) )).

fof(t28_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) )
                     => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                          & k3_finseq_1(C) = k3_finseq_1(D)
                          & k3_finseq_1(D) = k3_finseq_1(E)
                          & k1_matrix_1(B) = k1_matrix_1(C)
                          & k1_matrix_1(C) = k1_matrix_1(D)
                          & k1_matrix_1(D) = k1_matrix_1(E)
                          & k3_matrix_3(A,B,C) = k3_matrix_3(A,D,E) )
                       => ( r1_xreal_0(k3_finseq_1(B),np__0)
                          | k1_matrix_4(A,B,D) = k1_matrix_4(A,E,C) ) ) ) ) ) ) ) )).

fof(t29_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) )
                     => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                          & k3_finseq_1(C) = k3_finseq_1(D)
                          & k3_finseq_1(D) = k3_finseq_1(E)
                          & k1_matrix_1(B) = k1_matrix_1(C)
                          & k1_matrix_1(C) = k1_matrix_1(D)
                          & k1_matrix_1(D) = k1_matrix_1(E)
                          & k1_matrix_4(A,B,D) = k1_matrix_4(A,E,C) )
                       => ( r1_xreal_0(k3_finseq_1(B),np__0)
                          | k3_matrix_3(A,B,C) = k3_matrix_3(A,D,E) ) ) ) ) ) ) ) )).

fof(t30_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) )
                     => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                          & k3_finseq_1(C) = k3_finseq_1(D)
                          & k3_finseq_1(D) = k3_finseq_1(E)
                          & k1_matrix_1(B) = k1_matrix_1(C)
                          & k1_matrix_1(C) = k1_matrix_1(D)
                          & k1_matrix_1(D) = k1_matrix_1(E)
                          & k3_matrix_3(A,B,C) = k1_matrix_4(A,D,E) )
                       => ( r1_xreal_0(k3_finseq_1(B),np__0)
                          | k3_matrix_3(A,B,E) = k1_matrix_4(A,D,C) ) ) ) ) ) ) ) )).

fof(t31_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,k3_matrix_3(A,C,D)) = k1_matrix_4(A,k1_matrix_4(A,B,C),D) ) ) ) ) ) ) )).

fof(t32_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,k1_matrix_4(A,C,D)) = k3_matrix_3(A,k1_matrix_4(A,B,C),D) ) ) ) ) ) ) )).

fof(t33_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,k1_matrix_4(A,C,D)) = k3_matrix_3(A,B,k1_matrix_4(A,D,C)) ) ) ) ) ) ) )).

fof(t34_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,B,D) = k3_matrix_3(A,k1_matrix_4(A,B,C),k1_matrix_4(A,C,D)) ) ) ) ) ) ) )).

fof(t35_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k2_matrix_3(A,B) = k2_matrix_3(A,C) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t36_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ( k2_matrix_3(A,B) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B))
           => ( r1_xreal_0(k3_finseq_1(B),np__0)
              | B = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) ) ) ) ) )).

fof(t37_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C)
                  & k3_matrix_3(A,B,k2_matrix_3(A,C)) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = C ) ) ) ) ) )).

fof(t38_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k3_matrix_3(A,k3_matrix_3(A,B,C),k2_matrix_3(A,C)) ) ) ) ) ) )).

fof(t39_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k3_matrix_3(A,B,k3_matrix_3(A,C,k2_matrix_3(A,C))) ) ) ) ) ) )).

fof(t40_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k3_matrix_3(A,k3_matrix_3(A,k2_matrix_3(A,C),B),C) ) ) ) ) ) )).

fof(t41_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k2_matrix_3(A,k3_matrix_3(A,k2_matrix_3(A,B),C)) = k3_matrix_3(A,B,k2_matrix_3(A,C)) ) ) ) ) ) )).

fof(t42_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k3_matrix_3(A,B,C) = k2_matrix_3(A,k3_matrix_3(A,k2_matrix_3(A,B),k2_matrix_3(A,C))) ) ) ) ) ) )).

fof(t43_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k2_matrix_3(A,k1_matrix_4(A,B,C)) = k1_matrix_4(A,C,B) ) ) ) ) ) )).

fof(t44_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k1_matrix_4(A,k2_matrix_3(A,B),C) = k1_matrix_4(A,k2_matrix_3(A,C),B) ) ) ) ) ) )).

fof(t45_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k1_matrix_4(A,k2_matrix_3(A,C),k1_matrix_4(A,k2_matrix_3(A,B),C)) ) ) ) ) ) )).

fof(t46_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,B),C),D) = k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,B),D),C) ) ) ) ) ) ) )).

fof(t47_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,B),C),D) = k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,C),D),B) ) ) ) ) ) ) )).

fof(t48_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,B),C),D) = k1_matrix_4(A,k1_matrix_4(A,k2_matrix_3(A,D),C),B) ) ) ) ) ) ) )).

fof(t49_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | k1_matrix_4(A,k1_matrix_4(A,D,B),k1_matrix_4(A,D,C)) = k2_matrix_3(A,k1_matrix_4(A,B,C)) ) ) ) ) ) ) )).

fof(t50_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
           => k1_matrix_4(A,k1_matrix_3(A,k3_finseq_1(B),k1_matrix_1(B)),B) = k2_matrix_3(A,B) ) ) ) )).

fof(t51_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | k3_matrix_3(A,B,C) = k1_matrix_4(A,B,k2_matrix_3(A,C)) ) ) ) ) ) )).

fof(t52_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => ( r1_xreal_0(k3_finseq_1(B),np__0)
                  | B = k1_matrix_4(A,B,k3_matrix_3(A,C,k2_matrix_3(A,C))) ) ) ) ) ) )).

fof(t53_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k1_matrix_4(A,B,D) = k3_matrix_3(A,C,k2_matrix_3(A,D)) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t54_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(B) = k1_matrix_1(C)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k1_matrix_4(A,D,B) = k3_matrix_3(A,D,k2_matrix_3(A,C)) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | B = C ) ) ) ) ) ) )).

fof(t55_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                  & k1_matrix_1(B) = k1_matrix_1(C) )
               => k2_matrix_1(B) = k2_matrix_1(C) ) ) ) ) )).

fof(t56_matrix_4,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_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D) )
                   => k11_fvsum_1(A,k3_fvsum_1(A,B,C),D) = k3_fvsum_1(A,k11_fvsum_1(A,B,D),k11_fvsum_1(A,C,D)) ) ) ) ) ) )).

fof(t57_matrix_4,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_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( ( k3_finseq_1(B) = k3_finseq_1(C)
                      & k3_finseq_1(C) = k3_finseq_1(D) )
                   => k11_fvsum_1(A,D,k3_fvsum_1(A,B,C)) = k3_fvsum_1(A,k11_fvsum_1(A,D,B),k11_fvsum_1(A,D,C)) ) ) ) ) ) )).

fof(t58_matrix_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(A)) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( m1_matrix_1(B,A,C,k1_matrix_1(B))
                <=> C = k3_finseq_1(B) ) ) ) ) ) )).

fof(t59_matrix_4,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)
            & v4_group_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & v8_vectsp_1(B)
            & v9_vectsp_1(B)
            & ~ v10_vectsp_1(B)
            & l3_vectsp_1(B) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) )
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) )
                     => ( ( k3_finseq_1(D) = k3_finseq_1(E)
                          & k1_matrix_1(D) = k1_matrix_1(E) )
                       => ( ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ r2_hidden(k4_tarski(A,F),k2_matrix_1(D)) )
                          | k7_matrix_1(u1_struct_0(B),k3_matrix_3(B,D,E),A) = k3_fvsum_1(B,k7_matrix_1(u1_struct_0(B),D,A),k7_matrix_1(u1_struct_0(B),E,A)) ) ) ) ) ) ) ) )).

fof(t60_matrix_4,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_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(C) = k1_matrix_1(D) )
                   => ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ r2_hidden(k4_tarski(E,B),k2_matrix_1(C)) )
                      | k8_matrix_1(u1_struct_0(A),k3_matrix_3(A,C,D),B) = k3_fvsum_1(A,k8_matrix_1(u1_struct_0(A),C,B),k8_matrix_1(u1_struct_0(A),D,B)) ) ) ) ) ) ) )).

fof(t61_matrix_4,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_finseq_1(C,u1_struct_0(A))
             => ( k3_finseq_1(B) = k3_finseq_1(C)
               => k9_rlvect_1(A,k3_fvsum_1(A,B,C)) = k4_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) ) ) ) ) )).

fof(t62_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k1_matrix_1(B) = k3_finseq_1(C) )
                   => ( r1_xreal_0(k3_finseq_1(B),np__0)
                      | r1_xreal_0(k3_finseq_1(C),np__0)
                      | k4_matrix_3(A,B,k3_matrix_3(A,C,D)) = k3_matrix_3(A,k4_matrix_3(A,B,C),k4_matrix_3(A,B,D)) ) ) ) ) ) ) )).

fof(t63_matrix_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_matrix_1(B)
            & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
                 => ( ( k3_finseq_1(C) = k3_finseq_1(D)
                      & k1_matrix_1(C) = k1_matrix_1(D)
                      & k3_finseq_1(B) = k1_matrix_1(C) )
                   => ( r1_xreal_0(k3_finseq_1(C),np__0)
                      | r1_xreal_0(k3_finseq_1(B),np__0)
                      | k4_matrix_3(A,k3_matrix_3(A,C,D),B) = k3_matrix_3(A,k4_matrix_3(A,C,B),k4_matrix_3(A,D,B)) ) ) ) ) ) ) )).

fof(t64_matrix_4,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m1_matrix_1(E,u1_struct_0(A),B,C)
                     => ! [F] :
                          ( m1_matrix_1(F,u1_struct_0(A),C,D)
                         => ( k1_matrix_1(E) = k3_finseq_1(F)
                           => ( r1_xreal_0(k3_finseq_1(E),np__0)
                              | r1_xreal_0(k3_finseq_1(F),np__0)
                              | m1_matrix_1(k4_matrix_3(A,E,F),u1_struct_0(A),B,D) ) ) ) ) ) ) ) ) )).

fof(dt_k1_matrix_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & v1_matrix_1(B)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
        & v1_matrix_1(C)
        & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) )
     => ( v1_matrix_1(k1_matrix_4(A,B,C))
        & m2_finseq_1(k1_matrix_4(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
%------------------------------------------------------------------------------