SET007 Axioms: SET007+788.ax
%------------------------------------------------------------------------------
% File : SET007+788 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 1417 ( 252 equ)
% Maximal formula atoms : 29 ( 21 avg)
% Number of connectives : 1491 ( 140 ~; 56 |; 997 &)
% ( 1 <=>; 297 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 15 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-4 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 235 ( 235 !; 0 ?)
% 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))) ) ) ).
%------------------------------------------------------------------------------