SET007 Axioms: SET007+436.ax


%------------------------------------------------------------------------------
% File     : SET007+436 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Associated Matrix of Linear Map
% 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    : matrlin [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   3 unit)
%            Number of atoms       : 1672 ( 107 equality)
%            Maximal formula depth :   40 (  15 average)
%            Number of connectives : 1783 ( 193 ~  ;   7  |;1215  &)
%                                         (   9 <=>; 359 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   47 (   1 propositional; 0-4 arity)
%            Number of functors    :   67 (   5 constant; 0-6 arity)
%            Number of variables   :  379 (   0 singleton; 369 !;  10 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_matrlin,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_matrlin(A) ) )).

fof(rc2_matrlin,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] :
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A)
          & v12_vectsp_1(B,A)
          & v2_matrlin(B,A) ) ) )).

fof(cc1_matrlin,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_finseq_1(B,k3_finseq_2(A))
         => ( v1_matrix_1(B)
           => ( v1_matrix_1(B)
              & v1_matrlin(B) ) ) ) ) )).

fof(t1_matrlin,axiom,(
    $true )).

fof(t2_matrlin,axiom,(
    $true )).

fof(t3_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k3_finseq_1(B) = k1_nat_1(A,np__1)
           => k3_finseq_1(k2_finseq_3(k1_nat_1(A,np__1),B)) = A ) ) ) )).

fof(t4_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_matrix_1(D,C,k1_nat_1(A,np__1),B)
                 => ! [E] :
                      ( ( v1_matrix_1(E)
                        & m2_finseq_1(E,k3_finseq_2(C)) )
                     => ( ( ~ r1_xreal_0(A,np__0)
                         => k1_matrix_1(D) = k1_matrix_1(k2_matrlin(C,k1_nat_1(A,np__1),D)) )
                        & ( E = k9_finseq_1(k1_funct_1(D,k1_nat_1(A,np__1)))
                         => k1_matrix_1(D) = k1_matrix_1(E) ) ) ) ) ) ) ) )).

fof(t5_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_matrix_1(D,C,k1_nat_1(A,np__1),B)
                 => m1_matrix_1(k2_matrlin(C,k1_nat_1(A,np__1),D),C,A,B) ) ) ) ) )).

fof(t6_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k3_finseq_1(B) = k1_nat_1(A,np__1)
           => B = k7_finseq_1(k2_finseq_3(k3_finseq_1(B),B),k9_finseq_1(k1_funct_1(B,k3_finseq_1(B)))) ) ) ) )).

fof(t7_matrlin,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_funct_1(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))))
        & v1_funct_2(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B))
        & v3_funct_2(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B))
        & m2_relset_1(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B)) ) ) )).

fof(t8_matrlin,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k2_relat_1(A)))
         => ~ ( v2_funct_1(A)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k1_relat_1(A),k1_relat_1(A))
                    & v3_funct_2(C,k1_relat_1(A),k1_relat_1(A))
                    & m2_relset_1(C,k1_relat_1(A),k1_relat_1(A)) )
                 => k7_finseq_1(k1_finseq_3(A,k3_subset_1(k2_relat_1(A),B)),k1_finseq_3(A,B)) != k5_relat_1(C,A) ) ) ) ) )).

fof(d1_matrlin,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_matrlin(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B))
              & v1_finseq_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(d2_matrlin,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_matrlin(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_matrlin(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_matrlin(C) )
             => ( C = k4_matrlin(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(C))
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ! [F] :
                              ( ( v1_relat_1(F)
                                & v1_funct_1(F)
                                & v1_finseq_1(F) )
                             => ( ( E = k1_funct_1(A,D)
                                  & F = k1_funct_1(B,D) )
                               => k1_funct_1(C,D) = k7_finseq_1(E,F) ) ) ) ) ) ) ) ) ) )).

fof(t9_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_6(C,A,B)
             => ! [D] :
                  ( m1_vectsp_6(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v1_vectsp_7(E,A,B)
                          & r1_tarski(k1_vectsp_6(A,B,C),E)
                          & r1_tarski(k1_vectsp_6(A,B,D),E)
                          & k4_vectsp_6(A,B,C) = k4_vectsp_6(A,B,D) )
                       => r1_vectsp_6(A,B,C,D) ) ) ) ) ) ) )).

fof(t10_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_vectsp_6(C,A,B)
             => ! [D] :
                  ( m1_vectsp_6(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_6(E,A,B)
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( v1_vectsp_7(F,A,B)
                              & r1_tarski(k1_vectsp_6(A,B,C),F)
                              & r1_tarski(k1_vectsp_6(A,B,D),F)
                              & r1_tarski(k1_vectsp_6(A,B,E),F)
                              & k4_vectsp_6(A,B,C) = k4_rlvect_1(B,k4_vectsp_6(A,B,D),k4_vectsp_6(A,B,E)) )
                           => r1_vectsp_6(A,B,C,k5_vectsp_6(A,B,D,E)) ) ) ) ) ) ) ) )).

fof(t11_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_vectsp_6(D,A,B)
                 => ! [E] :
                      ( m1_vectsp_6(E,A,B)
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( v1_vectsp_7(F,A,B)
                              & r1_tarski(k1_vectsp_6(A,B,D),F)
                              & r1_tarski(k1_vectsp_6(A,B,E),F)
                              & k4_vectsp_6(A,B,D) = k6_vectsp_1(A,B,C,k4_vectsp_6(A,B,E)) )
                           => ( C = k1_rlvect_1(A)
                              | r1_vectsp_6(A,B,D,k6_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(t12_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_7(D,A,B)
                 => ? [E] :
                      ( m1_vectsp_6(E,A,B)
                      & C = k4_vectsp_6(A,B,E)
                      & r1_tarski(k1_vectsp_6(A,B,E),D) ) ) ) ) ) )).

fof(d3_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ( v2_matrlin(B,A)
          <=> ? [C] :
                ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
                & m1_vectsp_7(C,A,B) ) ) ) ) )).

fof(d4_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ( m1_matrlin(C,A,B)
              <=> ( v2_funct_1(C)
                  & m1_vectsp_7(k2_relat_1(C),A,B) ) ) ) ) ) )).

fof(d5_matrlin,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_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
                         => ( F = k5_matrlin(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => k8_funct_2(u1_struct_0(B),u1_struct_0(C),F,G) = k4_rlvect_1(C,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,G)) ) ) ) ) ) ) ) ) )).

fof(d6_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
                         => ( F = k6_matrlin(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => k8_funct_2(u1_struct_0(B),u1_struct_0(C),F,G) = k6_vectsp_1(A,C,E,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,G)) ) ) ) ) ) ) ) ) )).

fof(t13_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(A))
                     => ( ( k3_finseq_1(D) = k3_finseq_1(E)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_hidden(F,k1_relat_1(D))
                                      & G = k1_funct_1(E,F) )
                                   => k1_funct_1(D,F) = k6_vectsp_1(A,B,G,C) ) ) ) )
                       => k9_rlvect_1(B,D) = k6_vectsp_1(A,B,k9_rlvect_1(A,E),C) ) ) ) ) ) ) )).

fof(t14_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ( ( k3_finseq_1(D) = k3_finseq_1(E)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k1_relat_1(D))
                               => k1_funct_1(E,F) = k6_vectsp_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),D,F),C) ) ) )
                       => k9_rlvect_1(B,E) = k6_vectsp_1(A,B,k9_rlvect_1(A,D),C) ) ) ) ) ) ) )).

fof(t15_matrlin,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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))
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k1_relat_1(B))
                 => k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) = k1_rlvect_1(A) ) )
           => k9_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) )).

fof(d7_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => k7_matrlin(A,B,C,D) = k1_finseqop(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) ) ) ) ) )).

fof(t16_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( k1_relat_1(D) = k1_relat_1(C)
                   => k1_relat_1(k7_matrlin(A,B,D,C)) = k1_relat_1(D) ) ) ) ) ) )).

fof(d8_matrlin,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( C = k8_matrlin(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(B)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k1_relat_1(C))
                       => k4_finseq_4(k5_numbers,u1_struct_0(A),C,D) = k9_rlvect_1(A,k1_matrlin(u1_struct_0(A),k5_numbers,k3_finseq_2(u1_struct_0(A)),B,D)) ) ) ) ) ) ) ) )).

fof(t17_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
             => ( k3_finseq_1(C) = np__0
               => k9_rlvect_1(B,k8_matrlin(B,C)) = k1_rlvect_1(B) ) ) ) ) )).

fof(t18_matrlin,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] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,B)
                & v2_matrlin(C,B)
                & l4_vectsp_1(C,B) )
             => ! [D] :
                  ( m1_matrix_1(D,u1_struct_0(C),k1_nat_1(A,np__1),np__0)
                 => k9_rlvect_1(C,k8_matrlin(C,D)) = k1_rlvect_1(C) ) ) ) ) )).

fof(t19_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_matrlin(u1_struct_0(B),k4_matrix_2(u1_struct_0(B),C)) = k4_matrix_1(u1_struct_0(B),k3_matrlin(u1_struct_0(B),k4_matrix_2(u1_struct_0(B),C))) ) ) ) )).

fof(t20_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(C))
                     => ( v1_mod_2(D,A,C,B)
                       => k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,E)) = k9_rlvect_1(B,k5_finseqop(u1_struct_0(C),u1_struct_0(B),E,D)) ) ) ) ) ) ) )).

fof(t21_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m2_finseq_1(F,u1_struct_0(C))
                         => ( ( k3_finseq_1(F) = k3_finseq_1(E)
                              & v1_mod_2(D,A,C,B) )
                           => k5_finseqop(u1_struct_0(C),u1_struct_0(B),k7_matrlin(A,C,E,F),D) = k7_matrlin(A,B,E,k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,D)) ) ) ) ) ) ) ) )).

fof(t22_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_matrlin(E,A,C)
                     => ! [F] :
                          ( m2_finseq_1(F,u1_struct_0(A))
                         => ( ( k3_finseq_1(F) = k3_finseq_1(E)
                              & v1_mod_2(D,A,C,B) )
                           => k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,k7_matrlin(A,C,F,E))) = k9_rlvect_1(B,k7_matrlin(A,B,F,k5_finseqop(u1_struct_0(C),u1_struct_0(B),E,D))) ) ) ) ) ) ) ) )).

fof(t23_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_vectsp_6(E,A,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k1_relat_1(C),k1_relat_1(C))
                            & v3_funct_2(F,k1_relat_1(C),k1_relat_1(C))
                            & m2_relset_1(F,k1_relat_1(C),k1_relat_1(C)) )
                         => ( D = k1_partfun1(k1_relat_1(C),k1_relat_1(C),k5_numbers,u1_struct_0(B),F,C)
                           => k3_vectsp_6(A,B,D,E) = k1_partfun1(k1_relat_1(C),k1_relat_1(C),k5_numbers,u1_struct_0(B),F,k3_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t24_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_vectsp_6(D,A,B)
                 => ( ( v2_funct_1(C)
                      & r1_tarski(k1_vectsp_6(A,B,D),k2_relat_1(C)) )
                   => k9_rlvect_1(B,k3_vectsp_6(A,B,C,D)) = k4_vectsp_6(A,B,D) ) ) ) ) ) )).

fof(t25_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
                     => ! [F,G] :
                          ( m2_finseq_1(G,u1_struct_0(C))
                         => ( ( r1_tarski(k2_relat_1(G),F)
                              & v1_mod_2(D,A,C,B)
                              & v1_mod_2(E,A,C,B)
                              & ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ( r2_hidden(H,F)
                                   => k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,H) = k8_funct_2(u1_struct_0(C),u1_struct_0(B),E,H) ) ) )
                           => k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,G)) = k8_funct_2(u1_struct_0(C),u1_struct_0(B),E,k9_rlvect_1(C,G)) ) ) ) ) ) ) ) )).

fof(t26_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
                     => ( ( v1_mod_2(D,A,C,B)
                          & v1_mod_2(E,A,C,B) )
                       => ! [F] :
                            ( m1_matrlin(F,A,C)
                           => ( k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,D) = k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,E)
                             => ( r1_xreal_0(k3_finseq_1(F),np__0)
                                | D = E ) ) ) ) ) ) ) ) ) )).

fof(t27_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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] :
                      ( ~ v1_xboole_0(E)
                     => ! [F] :
                          ( m1_matrix_1(F,E,A,B)
                         => ! [G] :
                              ( m1_matrix_1(G,E,C,B)
                             => ( r2_hidden(D,k1_relat_1(F))
                               => k7_matrix_1(E,k10_matrlin(E,A,C,B,F,G),D) = k7_matrix_1(E,F,D) ) ) ) ) ) ) ) ) )).

fof(t28_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m1_matrix_1(E,D,A,B)
                     => ! [F] :
                          ( m1_matrix_1(F,D,C,B)
                         => ( k1_matrix_1(E) = k1_matrix_1(F)
                           => k1_matrix_1(k10_matrlin(D,A,C,B,E,F)) = k1_matrix_1(E) ) ) ) ) ) ) ) )).

fof(t29_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ~ v1_xboole_0(F)
                         => ! [G] :
                              ( m1_matrix_1(G,F,A,B)
                             => ! [H] :
                                  ( m1_matrix_1(H,F,C,B)
                                 => ( ( r2_hidden(D,k1_relat_1(H))
                                      & E = k1_nat_1(k3_finseq_1(G),D) )
                                   => k7_matrix_1(F,k10_matrlin(F,A,C,B,G,H),E) = k7_matrix_1(F,H,D) ) ) ) ) ) ) ) ) ) )).

fof(t30_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m1_matrix_1(E,D,A,B)
                     => ! [F] :
                          ( m1_matrix_1(F,D,C,B)
                         => ( k1_matrix_1(E) = k1_matrix_1(F)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( r2_hidden(G,k2_finseq_1(k1_matrix_1(E)))
                                 => k8_matrix_1(D,k10_matrlin(D,A,C,B,E,F),G) = k8_finseq_1(D,k8_matrix_1(D,E,G),k8_matrix_1(D,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t31_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v4_group_1(D)
                    & v7_group_1(D)
                    & v7_vectsp_1(D)
                    & v8_vectsp_1(D)
                    & v9_vectsp_1(D)
                    & ~ v10_vectsp_1(D)
                    & l3_vectsp_1(D) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v3_rlvect_1(E)
                        & v4_rlvect_1(E)
                        & v5_rlvect_1(E)
                        & v6_rlvect_1(E)
                        & v12_vectsp_1(E,D)
                        & l4_vectsp_1(E,D) )
                     => ! [F] :
                          ( m1_matrix_1(F,u1_struct_0(E),A,B)
                         => ! [G] :
                              ( m1_matrix_1(G,u1_struct_0(E),C,B)
                             => k8_matrlin(E,k10_matrlin(u1_struct_0(E),A,C,B,F,G)) = k8_finseq_1(u1_struct_0(E),k8_matrlin(E,F),k8_matrlin(E,G)) ) ) ) ) ) ) ) )).

fof(t32_matrlin,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m1_matrix_1(E,D,A,B)
                     => ! [F] :
                          ( m1_matrix_1(F,D,C,B)
                         => ( k1_matrix_1(E) = k1_matrix_1(F)
                           => k4_matrix_1(D,k10_matrlin(D,A,C,B,E,F)) = k9_matrlin(D,k4_matrix_1(D,E),k4_matrix_1(D,F)) ) ) ) ) ) ) ) )).

fof(t33_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) )
                 => k1_finseqop(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_rlvect_1(B),k8_matrlin(B,C),k8_matrlin(B,D)) = k8_matrlin(B,k9_matrlin(u1_struct_0(B),C,D)) ) ) ) ) )).

fof(t34_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(B))
                 => ( k3_finseq_1(C) = k3_finseq_1(D)
                   => k9_rlvect_1(B,k11_matrlin(u1_struct_0(B),u1_rlvect_1(B),C,D)) = k4_rlvect_1(B,k9_rlvect_1(B,C),k9_rlvect_1(B,D)) ) ) ) ) ) )).

fof(t35_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
             => ! [D] :
                  ( ( v1_matrix_1(D)
                    & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) )
                 => ( k3_finseq_1(C) = k3_finseq_1(D)
                   => k4_rlvect_1(B,k9_rlvect_1(B,k8_matrlin(B,C)),k9_rlvect_1(B,k8_matrlin(B,D))) = k9_rlvect_1(B,k8_matrlin(B,k9_matrlin(u1_struct_0(B),C,D))) ) ) ) ) ) )).

fof(t36_matrlin,axiom,(
    $true )).

fof(t37_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( v1_matrix_1(C)
                & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
             => k9_rlvect_1(B,k8_matrlin(B,C)) = k9_rlvect_1(B,k8_matrlin(B,k4_matrix_1(u1_struct_0(B),C))) ) ) ) )).

fof(t38_matrlin,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) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,C)
                    & v2_matrlin(D,C)
                    & l4_vectsp_1(D,C) )
                 => ! [E] :
                      ( m1_matrix_1(E,u1_struct_0(C),A,B)
                     => ~ ( ~ r1_xreal_0(A,np__0)
                          & ~ r1_xreal_0(B,np__0)
                          & ? [F] :
                              ( m2_finseq_1(F,u1_struct_0(C))
                              & ? [G] :
                                  ( m2_finseq_1(G,u1_struct_0(C))
                                  & k3_finseq_1(F) = A
                                  & k3_finseq_1(G) = B
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( r2_hidden(H,k1_relat_1(G))
                                       => k4_finseq_4(k5_numbers,u1_struct_0(C),G,H) = k9_rlvect_1(C,k11_fvsum_1(C,F,k8_matrix_1(u1_struct_0(C),E,H))) ) )
                                  & ? [H] :
                                      ( m2_finseq_1(H,u1_struct_0(D))
                                      & ? [I] :
                                          ( m2_finseq_1(I,u1_struct_0(D))
                                          & k3_finseq_1(H) = B
                                          & k3_finseq_1(I) = A
                                          & ! [J] :
                                              ( m2_subset_1(J,k1_numbers,k5_numbers)
                                             => ( r2_hidden(J,k1_relat_1(I))
                                               => k4_finseq_4(k5_numbers,u1_struct_0(D),I,J) = k9_rlvect_1(D,k7_matrlin(C,D,k7_matrix_1(u1_struct_0(C),E,J),H)) ) )
                                          & k9_rlvect_1(D,k7_matrlin(C,D,F,I)) != k9_rlvect_1(D,k7_matrlin(C,D,G,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_matrlin(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(A))
                     => ( E = k12_matrlin(A,B,C,D)
                      <=> ( k3_finseq_1(E) = k3_finseq_1(C)
                          & ? [F] :
                              ( m1_vectsp_6(F,A,B)
                              & D = k4_vectsp_6(A,B,F)
                              & r1_tarski(k1_vectsp_6(A,B,F),k2_relat_1(C))
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( r1_xreal_0(np__1,G)
                                      & r1_xreal_0(G,k3_finseq_1(E)) )
                                   => k4_finseq_4(k5_numbers,u1_struct_0(A),E,G) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,k4_finseq_4(k5_numbers,u1_struct_0(B),C,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_matrlin(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( k12_matrlin(A,B,C,D) = k12_matrlin(A,B,C,E)
                       => D = E ) ) ) ) ) ) )).

fof(t40_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_matrlin(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => D = k9_rlvect_1(B,k7_matrlin(A,B,k12_matrlin(A,B,C,D),C)) ) ) ) ) )).

fof(t41_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( m1_matrlin(C,A,B)
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( k3_finseq_1(D) = k3_finseq_1(C)
                   => D = k12_matrlin(A,B,C,k9_rlvect_1(B,k7_matrlin(A,B,D,C))) ) ) ) ) ) )).

fof(t42_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_matrlin(E,A,B)
                     => ! [F] :
                          ( m1_matrlin(F,A,C)
                         => ! [G] :
                              ( m2_finseq_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m2_finseq_1(H,u1_struct_0(A))
                                 => ( k3_finseq_1(G) = k3_finseq_1(E)
                                   => ! [I] :
                                        ( m2_subset_1(I,k1_numbers,k5_numbers)
                                       => ( ( r2_hidden(I,k1_relat_1(F))
                                            & k3_finseq_1(H) = k3_finseq_1(E)
                                            & ! [J] :
                                                ( m2_subset_1(J,k1_numbers,k5_numbers)
                                               => ( r2_hidden(J,k1_relat_1(E))
                                                 => k1_funct_1(H,J) = k4_finseq_4(k5_numbers,u1_struct_0(A),k12_matrlin(A,C,F,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_finseq_4(k5_numbers,u1_struct_0(B),E,J))),I) ) ) )
                                         => ( r1_xreal_0(k3_finseq_1(E),np__0)
                                            | k4_finseq_4(k5_numbers,u1_struct_0(A),k12_matrlin(A,C,F,k9_rlvect_1(C,k7_matrlin(A,C,G,k5_finseqop(u1_struct_0(B),u1_struct_0(C),E,D)))),I) = k9_rlvect_1(A,k11_fvsum_1(A,G,H)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d10_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_matrlin(F,A,C)
                         => ! [G] :
                              ( ( v1_matrix_1(G)
                                & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) )
                             => ( G = k13_matrlin(A,B,C,D,E,F)
                              <=> ( k3_finseq_1(G) = k3_finseq_1(E)
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( r2_hidden(H,k1_relat_1(E))
                                       => k1_matrlin(u1_struct_0(A),k5_numbers,k3_finseq_2(u1_struct_0(A)),G,H) = k12_matrlin(A,C,F,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_finseq_4(k5_numbers,u1_struct_0(B),E,H))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t43_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_matrlin(E,A,B)
                     => ! [F] :
                          ( m1_matrlin(F,A,C)
                         => ( k3_finseq_1(E) = np__0
                           => k13_matrlin(A,B,C,D,E,F) = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t44_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_matrlin(E,A,B)
                     => ! [F] :
                          ( m1_matrlin(F,A,C)
                         => ( ~ r1_xreal_0(k3_finseq_1(E),np__0)
                           => k1_matrix_1(k13_matrlin(A,B,C,D,E,F)) = k3_finseq_1(F) ) ) ) ) ) ) ) )).

fof(t45_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ! [F] :
                          ( m1_matrlin(F,A,B)
                         => ! [G] :
                              ( m1_matrlin(G,A,C)
                             => ( ( v1_mod_2(D,A,B,C)
                                  & v1_mod_2(E,A,B,C)
                                  & k13_matrlin(A,B,C,D,F,G) = k13_matrlin(A,B,C,E,F,G) )
                               => ( r1_xreal_0(k3_finseq_1(F),np__0)
                                  | D = E ) ) ) ) ) ) ) ) ) )).

fof(t46_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & v2_matrlin(D,A)
                    & l4_vectsp_1(D,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => ! [G] :
                              ( m1_matrlin(G,A,B)
                             => ! [H] :
                                  ( m1_matrlin(H,A,C)
                                 => ! [I] :
                                      ( m1_matrlin(I,A,D)
                                     => ( ( v1_mod_2(E,A,B,C)
                                          & v1_mod_2(F,A,C,D) )
                                       => ( r1_xreal_0(k3_finseq_1(G),np__0)
                                          | r1_xreal_0(k3_finseq_1(H),np__0)
                                          | r1_xreal_0(k3_finseq_1(I),np__0)
                                          | k13_matrlin(A,B,D,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F),G,I) = k4_matrix_3(A,k13_matrlin(A,B,C,E,G,H),k13_matrlin(A,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_matrlin,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & v2_matrlin(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ! [F] :
                          ( m1_matrlin(F,A,B)
                         => ! [G] :
                              ( m1_matrlin(G,A,C)
                             => k13_matrlin(A,B,C,k5_matrlin(A,B,C,D,E),F,G) = k3_matrix_3(A,k13_matrlin(A,B,C,D,F,G),k13_matrlin(A,B,C,E,F,G)) ) ) ) ) ) ) ) )).

fof(t48_matrlin,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v12_vectsp_1(C,A)
                & v2_matrlin(C,A)
                & l4_vectsp_1(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_rlvect_1(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & v12_vectsp_1(D,A)
                    & v2_matrlin(D,A)
                    & l4_vectsp_1(D,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
                     => ! [F] :
                          ( m1_matrlin(F,A,C)
                         => ! [G] :
                              ( m1_matrlin(G,A,D)
                             => ( B != k1_rlvect_1(A)
                               => k13_matrlin(A,C,D,k6_matrlin(A,C,D,E,B),F,G) = k6_matrix_3(A,k13_matrlin(A,C,D,E,F,G),B) ) ) ) ) ) ) ) ) )).

fof(dt_m1_matrlin,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A) )
     => ! [C] :
          ( m1_matrlin(C,A,B)
         => m2_finseq_1(C,u1_struct_0(B)) ) ) )).

fof(existence_m1_matrlin,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A) )
     => ? [C] : m1_matrlin(C,A,B) ) )).

fof(dt_k1_matrlin,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(C)
        & m1_finseq_2(C,A)
        & v1_funct_1(D)
        & m1_relset_1(D,B,C) )
     => m2_finseq_2(k1_matrlin(A,B,C,D,E),A,C) ) )).

fof(redefinition_k1_matrlin,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(C)
        & m1_finseq_2(C,A)
        & v1_funct_1(D)
        & m1_relset_1(D,B,C) )
     => k1_matrlin(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) )).

fof(dt_k2_matrlin,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_matrix_1(C)
        & m1_finseq_1(C,k3_finseq_2(A)) )
     => ( v1_matrix_1(k2_matrlin(A,B,C))
        & m2_finseq_1(k2_matrlin(A,B,C),k3_finseq_2(A)) ) ) )).

fof(redefinition_k2_matrlin,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & v1_matrix_1(C)
        & m1_finseq_1(C,k3_finseq_2(A)) )
     => k2_matrlin(A,B,C) = k2_finseq_3(B,C) ) )).

fof(dt_k3_matrlin,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => m1_matrix_1(k3_matrlin(A,B),A,np__1,k3_finseq_1(B)) ) )).

fof(redefinition_k3_matrlin,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A) )
     => k3_matrlin(A,B) = k5_finseq_1(B) ) )).

fof(dt_k4_matrlin,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_matrlin(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_matrlin(B) )
     => ( v1_relat_1(k4_matrlin(A,B))
        & v1_funct_1(k4_matrlin(A,B))
        & v1_matrlin(k4_matrlin(A,B)) ) ) )).

fof(dt_k5_matrlin,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( v1_funct_1(k5_matrlin(A,B,C,D,E))
        & v1_funct_2(k5_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
        & m2_relset_1(k5_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) )).

fof(dt_k6_matrlin,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & v2_matrlin(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( v1_funct_1(k6_matrlin(A,B,C,D,E))
        & v1_funct_2(k6_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
        & m2_relset_1(k6_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) )).

fof(dt_k7_matrlin,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A)
        & m1_finseq_1(C,u1_struct_0(A))
        & m1_finseq_1(D,u1_struct_0(B)) )
     => m2_finseq_1(k7_matrlin(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k8_matrlin,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
     => m2_finseq_1(k8_matrlin(A,B),u1_struct_0(A)) ) )).

fof(dt_k9_matrlin,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_matrix_1(B)
        & m1_finseq_1(B,k3_finseq_2(A))
        & v1_matrix_1(C)
        & m1_finseq_1(C,k3_finseq_2(A)) )
     => ( v1_matrix_1(k9_matrlin(A,B,C))
        & m2_finseq_1(k9_matrlin(A,B,C),k3_finseq_2(A)) ) ) )).

fof(redefinition_k9_matrlin,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_matrix_1(B)
        & m1_finseq_1(B,k3_finseq_2(A))
        & v1_matrix_1(C)
        & m1_finseq_1(C,k3_finseq_2(A)) )
     => k9_matrlin(A,B,C) = k4_matrlin(B,C) ) )).

fof(dt_k10_matrlin,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_matrix_1(E,A,B,D)
        & m1_matrix_1(F,A,C,D) )
     => m1_matrix_1(k10_matrlin(A,B,C,D,E,F),A,k1_nat_1(B,C),D) ) )).

fof(redefinition_k10_matrlin,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_matrix_1(E,A,B,D)
        & m1_matrix_1(F,A,C,D) )
     => k10_matrlin(A,B,C,D,E,F) = k7_finseq_1(E,F) ) )).

fof(dt_k11_matrlin,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_finseq_1(C,A)
        & m1_finseq_1(D,A) )
     => m2_finseq_1(k11_matrlin(A,B,C,D),A) ) )).

fof(redefinition_k11_matrlin,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_finseq_1(C,A)
        & m1_finseq_1(D,A) )
     => k11_matrlin(A,B,C,D) = k3_funcop_1(B,C,D) ) )).

fof(dt_k12_matrlin,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A)
        & m1_matrlin(C,A,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => m2_finseq_1(k12_matrlin(A,B,C,D),u1_struct_0(A)) ) )).

fof(dt_k13_matrlin,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & v2_matrlin(B,A)
        & l4_vectsp_1(B,A)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,A)
        & v2_matrlin(C,A)
        & l4_vectsp_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
        & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
        & m1_finseq_1(E,u1_struct_0(B))
        & m1_matrlin(F,A,C) )
     => ( v1_matrix_1(k13_matrlin(A,B,C,D,E,F))
        & m2_finseq_1(k13_matrlin(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(A))) ) ) )).
%------------------------------------------------------------------------------