SET007 Axioms: SET007+372.ax
%------------------------------------------------------------------------------
% File : SET007+372 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Product and the Determinant of Matrices with Entries in a Field
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : matrix_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 2 unt; 0 def)
% Number of atoms : 1094 ( 104 equ)
% Maximal formula atoms : 27 ( 17 avg)
% Number of connectives : 1166 ( 134 ~; 7 |; 724 &)
% ( 7 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 17 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 64 ( 64 usr; 5 con; 0-6 aty)
% Number of variables : 296 ( 296 !; 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_3,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)
=> k1_matrix_3(A,B,C) = k4_finseqop(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(A))),B,k4_finseqop(u1_struct_0(A),C,k1_rlvect_1(A))) ) ) ) ).
fof(d2_matrix_3,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))) )
=> ( C = k2_matrix_3(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(B)
& k1_matrix_1(C) = k1_matrix_1(B)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
=> k3_matrix_1(u1_struct_0(A),C,D,E) = k5_rlvect_1(A,k3_matrix_1(u1_struct_0(A),B,D,E)) ) ) ) ) ) ) ) ) ).
fof(d3_matrix_3,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))) )
=> ( D = k3_matrix_3(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& k1_matrix_1(D) = k1_matrix_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
=> k3_matrix_1(u1_struct_0(A),D,E,F) = k4_rlvect_1(A,k3_matrix_1(u1_struct_0(A),B,E,F),k3_matrix_1(u1_struct_0(A),C,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t1_matrix_3,axiom,
$true ).
fof(t2_matrix_3,axiom,
$true ).
fof(t3_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k1_matrix_3(C,A,B)))
=> k3_matrix_1(u1_struct_0(C),k1_matrix_3(C,A,B),D,E) = k1_rlvect_1(C) ) ) ) ) ) ) ).
fof(t4_matrix_3,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) = k3_matrix_3(A,C,B) ) ) ) ) ).
fof(t5_matrix_3,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(B) = k3_finseq_1(D)
& k1_matrix_1(B) = k1_matrix_1(C)
& k1_matrix_1(B) = k1_matrix_1(D) )
=> k3_matrix_3(A,k3_matrix_3(A,B,C),D) = k3_matrix_3(A,B,k3_matrix_3(A,C,D)) ) ) ) ) ) ).
fof(t6_matrix_3,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] :
( m1_matrix_1(D,u1_struct_0(C),A,B)
=> k3_matrix_3(C,D,k1_matrix_3(C,A,B)) = D ) ) ) ) ).
fof(t7_matrix_3,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] :
( m1_matrix_1(D,u1_struct_0(C),A,B)
=> k3_matrix_3(C,D,k2_matrix_3(C,D)) = k1_matrix_3(C,A,B) ) ) ) ) ).
fof(d4_matrix_3,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_1(B) = k3_finseq_1(C)
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
=> ( D = k4_matrix_3(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& k1_matrix_1(D) = k1_matrix_1(C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(E,F),k2_matrix_1(D))
=> k3_matrix_1(u1_struct_0(A),D,E,F) = k14_fvsum_1(A,k7_matrix_1(u1_struct_0(A),B,E),k8_matrix_1(u1_struct_0(A),C,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_matrix_3,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) )
=> ( D = k6_matrix_3(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& k1_matrix_1(D) = k1_matrix_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B))
=> k3_matrix_1(u1_struct_0(A),D,E,F) = k10_group_1(A,C,k3_matrix_1(u1_struct_0(A),B,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(d6_matrix_3,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] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_matrix_3(A,B,C) = k6_matrix_3(A,B,C) ) ) ) ).
fof(t8_matrix_3,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)
=> ( k3_finseq_1(k11_fvsum_1(A,B,C)) = k3_finseq_1(B)
& k3_finseq_1(k11_fvsum_1(A,B,C)) = k3_finseq_1(C) ) ) ) ) ) ).
fof(t9_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
& D = C )
=> k1_funct_1(k7_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),C),D) = k2_group_1(B) ) ) ) ) ) ).
fof(t10_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
=> ( D = C
| k1_funct_1(k7_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),C),D) = k1_rlvect_1(B) ) ) ) ) ) ) ).
fof(t11_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
& C = D )
=> k1_funct_1(k8_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),D),C) = k2_group_1(B) ) ) ) ) ) ).
fof(t12_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
=> ( C = D
| k1_funct_1(k8_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),D),C) = k1_rlvect_1(B) ) ) ) ) ) ) ).
fof(t13_matrix_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> k9_rlvect_1(B,k4_finseqop(u1_struct_0(B),A,k1_rlvect_1(B))) = k1_rlvect_1(B) ) ) ).
fof(t14_matrix_3,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,k3_setwop_2(B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k3_setwop_2(B))
=> ( D = C
| k1_funct_1(B,D) = k1_rlvect_1(A) ) ) ) )
=> k9_rlvect_1(A,B) = k1_funct_1(B,C) ) ) ) ) ).
fof(t15_matrix_3,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(k11_fvsum_1(A,B,C)) = k3_square_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ).
fof(t16_matrix_3,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_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k3_setwop_2(B))
& k1_funct_1(B,D) = k2_group_1(A)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k3_setwop_2(B))
=> ( E = D
| k1_funct_1(B,E) = k1_rlvect_1(A) ) ) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k3_setwop_2(k11_fvsum_1(A,B,C)))
=> ( ( D = E
=> k1_funct_1(k11_fvsum_1(A,B,C),E) = k1_funct_1(C,D) )
& ( D != E
=> k1_funct_1(k11_fvsum_1(A,B,C),E) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ).
fof(t17_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
=> ( ( C = D
=> k1_funct_1(k7_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),C),D) = k2_group_1(B) )
& ( C != D
=> k1_funct_1(k7_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),C),D) = k1_rlvect_1(B) ) ) ) ) ) ) ) ).
fof(t18_matrix_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k11_matrix_1(B,A)))
=> ( ( C = D
=> k1_funct_1(k8_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),D),C) = k2_group_1(B) )
& ( C != D
=> k1_funct_1(k8_matrix_1(u1_struct_0(B),k11_matrix_1(B,A),D),C) = k1_rlvect_1(B) ) ) ) ) ) ) ) ).
fof(t19_matrix_3,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_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k3_setwop_2(B))
& r2_hidden(D,k3_setwop_2(C))
& k1_funct_1(B,D) = k2_group_1(A)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k3_setwop_2(B))
=> ( E = D
| k1_funct_1(B,E) = k1_rlvect_1(A) ) ) ) )
=> k9_rlvect_1(A,k11_fvsum_1(A,B,C)) = k1_funct_1(C,D) ) ) ) ) ) ).
fof(t20_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> k4_matrix_3(B,k11_matrix_1(B,A),C) = C ) ) ) ).
fof(t21_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> k4_matrix_3(B,C,k11_matrix_1(B,A)) = C ) ) ) ).
fof(t22_matrix_3,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] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_matrix_3(A,k5_matrix_2(u1_struct_0(A),np__1,k4_matrix_2(u1_struct_0(A),B)),k5_matrix_2(u1_struct_0(A),np__1,k4_matrix_2(u1_struct_0(A),C))) = k5_matrix_2(u1_struct_0(A),np__1,k4_matrix_2(u1_struct_0(A),k10_group_1(A,B,C))) ) ) ) ).
fof(t23_matrix_3,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> k4_matrix_3(A,k6_matrix_2(u1_struct_0(A),B,D,F,H),k6_matrix_2(u1_struct_0(A),C,E,G,I)) = k6_matrix_2(u1_struct_0(A),k4_rlvect_1(A,k10_group_1(A,B,C),k10_group_1(A,D,G)),k4_rlvect_1(A,k10_group_1(A,B,E),k10_group_1(A,D,I)),k4_rlvect_1(A,k10_group_1(A,F,C),k10_group_1(A,H,G)),k4_rlvect_1(A,k10_group_1(A,F,E),k10_group_1(A,H,I))) ) ) ) ) ) ) ) ) ) ).
fof(t24_matrix_3,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_1(B) = k3_finseq_1(C)
=> ( k1_matrix_1(C) = np__0
| k4_matrix_1(u1_struct_0(A),k4_matrix_3(A,B,C)) = k4_matrix_3(A,k4_matrix_1(u1_struct_0(A),C),k4_matrix_1(u1_struct_0(A),B)) ) ) ) ) ) ).
fof(t25_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m2_relset_1(D,k2_zfmisc_1(C,C),C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,C),C)
& m2_relset_1(E,k2_zfmisc_1(C,C),C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,C)
& m2_relset_1(F,A,C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,B,C)
& m2_relset_1(G,B,C) )
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(A))
=> ! [I] :
( m1_subset_1(I,k5_finsub_1(B))
=> ( ( v1_binop_1(D,C)
& v2_binop_1(D,C)
& v1_binop_1(E,C) )
=> ( ( k8_matrix_3(B,A,I,H) = k1_xboole_0
& ~ v1_setwiseo(D,C) )
| k7_setwiseo(k2_zfmisc_1(A,B),C,D,k8_matrix_3(A,B,H,I),k9_matrix_3(A,B,C,E,F,G)) = k7_setwiseo(k2_zfmisc_1(B,A),C,D,k8_matrix_3(B,A,I,H),k9_matrix_3(B,A,C,E,G,F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,C,A)
& m2_relset_1(G,C,A) )
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A) )
=> ! [H] :
( m1_subset_1(H,B)
=> ! [I] :
( m1_subset_1(I,C)
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,H),k2_setwiseo(C,I)),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(B,A,D,k2_setwiseo(B,H),k7_funcop_1(A,B,E,F,k7_setwiseo(C,A,D,k2_setwiseo(C,I),G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,C,A)
& m2_relset_1(G,C,A) )
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(B))
=> ! [I] :
( m1_subset_1(I,k5_finsub_1(C))
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A)
& v1_finseqop(D,A)
& r6_binop_1(A,E,D) )
=> ! [J] :
( m1_subset_1(J,B)
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,J),I),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(B,A,D,k2_setwiseo(B,J),k7_funcop_1(A,B,E,F,k7_setwiseo(C,A,D,I,G))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,C,A)
& m2_relset_1(G,C,A) )
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(B))
=> ! [I] :
( m1_subset_1(I,k5_finsub_1(C))
=> ( ( v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A)
& r6_binop_1(A,E,D) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,H,I),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(B,A,D,H,k7_funcop_1(A,B,E,F,k7_setwiseo(C,A,D,I,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,C,A)
& m2_relset_1(G,C,A) )
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A)
& v1_binop_1(E,A) )
=> ! [H] :
( m1_subset_1(H,B)
=> ! [I] :
( m1_subset_1(I,C)
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,H),k2_setwiseo(C,I)),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(C,A,D,k2_setwiseo(C,I),k8_funcop_1(A,C,E,k7_setwiseo(B,A,D,k2_setwiseo(B,H),F),G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,C,A)
& m2_relset_1(G,C,A) )
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(B))
=> ! [I] :
( m1_subset_1(I,k5_finsub_1(C))
=> ( ( v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A)
& r6_binop_1(A,E,D)
& v1_binop_1(E,A) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,H,I),k9_matrix_3(B,C,A,E,F,G)) = k7_setwiseo(C,A,D,I,k8_funcop_1(A,C,E,k7_setwiseo(B,A,D,H,F),G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,C),A)
& m2_relset_1(E,k2_zfmisc_1(B,C),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( m1_subset_1(G,k5_finsub_1(C))
=> ( ( v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> ! [H] :
( m1_subset_1(H,B)
=> ( ! [I] :
( m1_subset_1(I,B)
=> k8_funct_2(B,A,F,I) = k7_setwiseo(C,A,D,G,k1_cat_2(B,C,A,k1_fraenkel(C,A),k2_cat_2(B,C,A,E),I)) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,k2_setwiseo(B,H),G),E) = k7_setwiseo(B,A,D,k2_setwiseo(B,H),F) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,C),A)
& m2_relset_1(E,k2_zfmisc_1(B,C),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ! [G] :
( m1_subset_1(G,k5_finsub_1(B))
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(C))
=> ( ( ! [I] :
( m1_subset_1(I,B)
=> k8_funct_2(B,A,F,I) = k7_setwiseo(C,A,D,H,k1_cat_2(B,C,A,k1_fraenkel(C,A),k2_cat_2(B,C,A,E),I)) )
& v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,G,H),E) = k7_setwiseo(B,A,D,G,F) ) ) ) ) ) ) ) ) ) ).
fof(t33_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,C),A)
& m2_relset_1(E,k2_zfmisc_1(B,C),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,A)
& m2_relset_1(F,C,A) )
=> ! [G] :
( m1_subset_1(G,k5_finsub_1(B))
=> ( ( v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> ! [H] :
( m1_subset_1(H,C)
=> ( ! [I] :
( m1_subset_1(I,C)
=> k8_funct_2(C,A,F,I) = k7_setwiseo(B,A,D,G,k1_cat_2(C,B,A,k1_fraenkel(B,A),k3_cat_2(B,C,A,E),I)) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,G,k2_setwiseo(C,H)),E) = k7_setwiseo(C,A,D,k2_setwiseo(C,H),F) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_matrix_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,C),A)
& m2_relset_1(E,k2_zfmisc_1(B,C),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,A)
& m2_relset_1(F,C,A) )
=> ! [G] :
( m1_subset_1(G,k5_finsub_1(B))
=> ! [H] :
( m1_subset_1(H,k5_finsub_1(C))
=> ( ( ! [I] :
( m1_subset_1(I,C)
=> k8_funct_2(C,A,F,I) = k7_setwiseo(B,A,D,G,k1_cat_2(C,B,A,k1_fraenkel(B,A),k3_cat_2(B,C,A,E),I)) )
& v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> k7_setwiseo(k2_zfmisc_1(B,C),A,D,k8_matrix_3(B,C,G,H),E) = k7_setwiseo(C,A,D,H,F) ) ) ) ) ) ) ) ) ) ).
fof(t35_matrix_3,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))) )
=> ( ( k1_matrix_1(B) = k3_finseq_1(C)
& k1_matrix_1(C) = k3_finseq_1(D) )
=> k4_matrix_3(A,k4_matrix_3(A,B,C),D) = k4_matrix_3(A,B,k4_matrix_3(A,C,D)) ) ) ) ) ) ).
fof(d7_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> ! [D] :
( m3_matrix_2(D,k11_matrix_2(A))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(B))
=> ( E = k10_matrix_3(A,B,C,D)
<=> ( k3_finseq_1(E) = A
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,k3_setwop_2(E))
& G = k1_funct_1(D,F) )
=> k1_funct_1(E,F) = k3_matrix_1(u1_struct_0(B),C,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k11_matrix_2(A),u1_struct_0(B))
& m2_relset_1(D,k11_matrix_2(A),u1_struct_0(B)) )
=> ( D = k11_matrix_3(A,B,C)
<=> ! [E] :
( m3_matrix_2(E,k11_matrix_2(A))
=> k8_funct_2(k11_matrix_2(A),u1_struct_0(B),D,E) = k14_matrix_2(B,A,k2_finsop_1(u1_struct_0(B),k10_matrix_3(A,B,C,E),u1_group_1(B)),E) ) ) ) ) ) ) ).
fof(d9_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> k12_matrix_3(A,B,C) = k7_setwiseo(k11_matrix_2(A),u1_struct_0(B),u1_rlvect_1(B),k15_matrix_2(k11_matrix_2(A)),k11_matrix_3(A,B,C)) ) ) ) ).
fof(t36_matrix_3,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))
=> k12_matrix_3(np__1,A,k5_matrix_2(u1_struct_0(A),np__1,k4_matrix_2(u1_struct_0(A),B))) = B ) ) ).
fof(d10_matrix_3,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] :
( m1_matrix_1(C,u1_struct_0(B),A,A)
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ( D = k13_matrix_3(A,B,C)
<=> ( k3_finseq_1(D) = A
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_setwop_2(A))
=> k1_funct_1(D,E) = k3_matrix_1(u1_struct_0(B),C,E,E) ) ) ) ) ) ) ) ) ).
fof(dt_k1_matrix_3,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)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m1_matrix_1(k1_matrix_3(A,B,C),u1_struct_0(A),B,C) ) ).
fof(dt_k2_matrix_3,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)
& v1_matrix_1(B)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
=> ( v1_matrix_1(k2_matrix_3(A,B))
& m2_finseq_1(k2_matrix_3(A,B),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_k3_matrix_3,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(k3_matrix_3(A,B,C))
& m2_finseq_1(k3_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_k4_matrix_3,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(k4_matrix_3(A,B,C))
& m2_finseq_1(k4_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_k5_matrix_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& ~ 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)
& m1_matrix_1(E,u1_struct_0(D),A,B)
& m1_matrix_1(F,u1_struct_0(D),k1_matrix_1(E),C) )
=> m1_matrix_1(k5_matrix_3(A,B,C,D,E,F),u1_struct_0(D),k3_finseq_1(E),k1_matrix_1(F)) ) ).
fof(redefinition_k5_matrix_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& ~ 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)
& m1_matrix_1(E,u1_struct_0(D),A,B)
& m1_matrix_1(F,u1_struct_0(D),k1_matrix_1(E),C) )
=> k5_matrix_3(A,B,C,D,E,F) = k4_matrix_3(D,E,F) ) ).
fof(dt_k6_matrix_3,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)))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_matrix_1(k6_matrix_3(A,B,C))
& m2_finseq_1(k6_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_k7_matrix_3,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)))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_matrix_1(k7_matrix_3(A,B,C))
& m2_finseq_1(k7_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_k8_matrix_3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k5_finsub_1(A))
& m1_subset_1(D,k5_finsub_1(B)) )
=> m1_subset_1(k8_matrix_3(A,B,C,D),k5_finsub_1(k2_zfmisc_1(A,B))) ) ).
fof(redefinition_k8_matrix_3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k5_finsub_1(A))
& m1_subset_1(D,k5_finsub_1(B)) )
=> k8_matrix_3(A,B,C,D) = k2_zfmisc_1(C,D) ) ).
fof(dt_k9_matrix_3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m1_relset_1(D,k2_zfmisc_1(C,C),C)
& v1_funct_1(E)
& v1_funct_2(E,A,C)
& m1_relset_1(E,A,C)
& v1_funct_1(F)
& v1_funct_2(F,B,C)
& m1_relset_1(F,B,C) )
=> ( v1_funct_1(k9_matrix_3(A,B,C,D,E,F))
& v1_funct_2(k9_matrix_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),C)
& m2_relset_1(k9_matrix_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),C) ) ) ).
fof(redefinition_k9_matrix_3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,C),C)
& m1_relset_1(D,k2_zfmisc_1(C,C),C)
& v1_funct_1(E)
& v1_funct_2(E,A,C)
& m1_relset_1(E,A,C)
& v1_funct_1(F)
& v1_funct_2(F,B,C)
& m1_relset_1(F,B,C) )
=> k9_matrix_3(A,B,C,D,E,F) = k7_finseqop(D,E,F) ) ).
fof(dt_k10_matrix_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ 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)
& m1_matrix_1(C,u1_struct_0(B),A,A)
& m1_subset_1(D,k11_matrix_2(A)) )
=> m2_finseq_1(k10_matrix_3(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k11_matrix_3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& ~ 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)
& m1_matrix_1(C,u1_struct_0(B),A,A) )
=> ( v1_funct_1(k11_matrix_3(A,B,C))
& v1_funct_2(k11_matrix_3(A,B,C),k11_matrix_2(A),u1_struct_0(B))
& m2_relset_1(k11_matrix_3(A,B,C),k11_matrix_2(A),u1_struct_0(B)) ) ) ).
fof(dt_k12_matrix_3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& ~ 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)
& m1_matrix_1(C,u1_struct_0(B),A,A) )
=> m1_subset_1(k12_matrix_3(A,B,C),u1_struct_0(B)) ) ).
fof(dt_k13_matrix_3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& ~ 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)
& m1_matrix_1(C,u1_struct_0(B),A,A) )
=> m2_finseq_1(k13_matrix_3(A,B,C),u1_struct_0(B)) ) ).
%------------------------------------------------------------------------------