SET007 Axioms: SET007+85.ax
%------------------------------------------------------------------------------
% File : SET007+85 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Monotone Real Sequences. Subsequences
% 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 : seqm_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 110 ( 10 unt; 0 def)
% Number of atoms : 829 ( 27 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 735 ( 16 ~; 9 |; 415 &)
% ( 27 <=>; 268 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-4 aty)
% Number of variables : 214 ( 209 !; 5 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_seqm_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v1_seqm_3(A) )
=> ( v1_funct_1(A)
& v1_seq_1(A)
& v3_seqm_3(A) ) ) ) ).
fof(cc2_seqm_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v2_seqm_3(A) )
=> ( v1_funct_1(A)
& v1_seq_1(A)
& v4_seqm_3(A) ) ) ) ).
fof(cc3_seqm_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v5_seqm_3(A) )
=> ( v1_funct_1(A)
& v1_seq_1(A)
& v3_seqm_3(A)
& v4_seqm_3(A) ) ) ) ).
fof(cc4_seqm_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v3_seqm_3(A)
& v4_seqm_3(A) )
=> ( v1_funct_1(A)
& v1_seq_1(A)
& v5_seqm_3(A) ) ) ) ).
fof(rc1_seqm_3,axiom,
? [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seq_1(A)
& v1_seqm_3(A)
& v3_seqm_3(A)
& v7_seqm_3(A) ) ).
fof(fc1_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k1_seqm_3(A,B))
& v1_funct_1(k1_seqm_3(A,B))
& v1_funct_2(k1_seqm_3(A,B),k5_numbers,k1_numbers)
& v1_seq_1(k1_seqm_3(A,B))
& v1_seqm_3(k1_seqm_3(A,B))
& v3_seqm_3(k1_seqm_3(A,B))
& v7_seqm_3(k1_seqm_3(A,B)) ) ) ).
fof(fc2_seqm_3,axiom,
! [A,B] :
( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v5_seqm_3(k2_funcop_1(A,B)) ) ).
fof(d1_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& ~ r1_xreal_0(C,B)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) ).
fof(d2_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& ~ r1_xreal_0(C,B)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) ).
fof(d3_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r1_xreal_0(B,C) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) ).
fof(d4_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r1_xreal_0(B,C) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) ).
fof(d5_seqm_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v5_seqm_3(A)
<=> ! [B,C] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A)) )
=> k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ).
fof(d6_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
<=> ? [B] :
( v1_xreal_0(B)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,C) = B ) ) ) ) ).
fof(d7_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v6_seqm_3(A)
<=> ( v3_seqm_3(A)
| v4_seqm_3(A) ) ) ) ).
fof(t1_seqm_3,axiom,
$true ).
fof(t2_seqm_3,axiom,
$true ).
fof(t3_seqm_3,axiom,
$true ).
fof(t4_seqm_3,axiom,
$true ).
fof(t5_seqm_3,axiom,
$true ).
fof(t6_seqm_3,axiom,
$true ).
fof(t7_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,B)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) ).
fof(t8_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(B,np__1),C)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t9_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(B,np__1),C))) ) ) ) ) ).
fof(t10_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,B)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) ).
fof(t11_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C))) ) ) ) ) ).
fof(t12_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) ).
fof(t13_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t14_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) ).
fof(t15_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
<=> ? [B] :
( v1_xreal_0(B)
& k2_relat_1(A) = k1_tarski(B) ) ) ) ).
fof(t16_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)) ) ) ) ).
fof(t17_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C)) ) ) ) ) ).
fof(t18_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,C) ) ) ) ) ).
fof(t19_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,np__0)) ) ) ) ) ).
fof(t20_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,np__0),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t21_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,np__0),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t22_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,np__0)) ) ) ) ).
fof(t23_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
=> v3_seqm_3(A) ) ) ).
fof(t24_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
=> v4_seqm_3(A) ) ) ).
fof(t25_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
=> v3_seqm_3(A) ) ) ).
fof(t26_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
=> v4_seqm_3(A) ) ) ).
fof(t27_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(A)
& v4_seqm_3(A) )
=> v5_seqm_3(A) ) ) ).
fof(d8_seqm_3,axiom,
! [A] :
( v1_relat_1(A)
=> ( v7_seqm_3(A)
<=> r1_tarski(k2_relat_1(A),k5_numbers) ) ) ).
fof(d9_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( C = k1_seqm_3(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,B)) ) ) ) ) ) ).
fof(t28_seqm_3,axiom,
$true ).
fof(t29_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
<=> ( v1_seqm_3(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> m2_subset_1(k2_seq_1(k5_numbers,k1_numbers,A,B),k1_numbers,k5_numbers) ) ) ) ) ).
fof(t30_seqm_3,axiom,
$true ).
fof(t31_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_funct_1(k5_relat_1(B,A),C) = k2_seq_1(k5_numbers,k1_numbers,A,k2_seq_1(k5_numbers,k1_numbers,B,C)) ) ) ) ).
fof(d10_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( m1_seqm_3(B,A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers)
& B = k3_seqm_3(C,A) ) ) ) ) ).
fof(d11_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v1_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ).
fof(d12_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v2_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1))) ) ) ) ).
fof(d13_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1))) ) ) ) ).
fof(d14_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t32_seqm_3,axiom,
$true ).
fof(t33_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(B,k2_seqm_3(A,B)) ) ) ).
fof(t34_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k1_seqm_3(A,np__0) = A ) ).
fof(t35_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k1_seqm_3(C,A),B) = k1_seqm_3(k1_seqm_3(C,B),A) ) ) ) ).
fof(t36_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k1_seqm_3(C,A),B) = k1_seqm_3(C,k1_nat_1(A,B)) ) ) ) ).
fof(t37_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k9_seq_1(B,C),A) = k9_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) ).
fof(t38_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k1_seqm_3(k17_seq_1(B),A) = k17_seq_1(k1_seqm_3(B,A)) ) ) ).
fof(t39_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k10_seq_1(B,C),A) = k10_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) ).
fof(t40_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( v2_relat_1(B)
=> v2_relat_1(k1_seqm_3(B,A)) ) ) ) ).
fof(t41_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k1_seqm_3(k18_seq_1(B),A) = k18_seq_1(k1_seqm_3(B,A)) ) ) ).
fof(t42_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k11_seq_1(B,C),A) = k11_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) ).
fof(t43_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k19_seq_1(B,C),A) = k19_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) ).
fof(t44_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k14_seq_1(C,B),A) = k14_seq_1(k1_seqm_3(C,A),B) ) ) ) ).
fof(t45_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k1_seqm_3(k3_seqm_3(C,B),A) = k3_seqm_3(k1_seqm_3(C,A),B) ) ) ) ).
fof(t46_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> m1_seqm_3(A,A) ) ).
fof(t47_seqm_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> m1_seqm_3(k1_seqm_3(B,A),B) ) ) ).
fof(t48_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( ( m1_seqm_3(A,B)
& m1_seqm_3(B,C) )
=> m1_seqm_3(A,C) ) ) ) ) ).
fof(t49_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seqm_3(A)
& m1_seqm_3(B,A) )
=> v1_seqm_3(B) ) ) ) ).
fof(t50_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seqm_3(A)
& m1_seqm_3(B,A) )
=> v2_seqm_3(B) ) ) ) ).
fof(t51_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seqm_3(A)
& m1_seqm_3(B,A) )
=> v3_seqm_3(B) ) ) ) ).
fof(t52_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v4_seqm_3(A)
& m1_seqm_3(B,A) )
=> v4_seqm_3(B) ) ) ) ).
fof(t53_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v6_seqm_3(A)
& m1_seqm_3(B,A) )
=> v6_seqm_3(B) ) ) ) ).
fof(t54_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v5_seqm_3(A)
& m1_seqm_3(B,A) )
=> v5_seqm_3(B) ) ) ) ).
fof(t55_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v5_seqm_3(A)
& m1_seqm_3(B,A) )
=> A = B ) ) ) ).
fof(t56_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(A)
& m1_seqm_3(B,A) )
=> v1_seq_2(B) ) ) ) ).
fof(t57_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(A)
& m1_seqm_3(B,A) )
=> v2_seq_2(B) ) ) ) ).
fof(t58_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& m1_seqm_3(B,A) )
=> v3_seq_2(B) ) ) ) ).
fof(t59_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seqm_3(B)
=> ( r1_xreal_0(A,np__0)
| v1_seqm_3(k14_seq_1(B,A)) ) )
& ( np__0 = A
=> v5_seqm_3(k14_seq_1(B,A)) )
& ( v1_seqm_3(B)
=> ( r1_xreal_0(np__0,A)
| v2_seqm_3(k14_seq_1(B,A)) ) ) ) ) ) ).
fof(t60_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seqm_3(B)
=> ( r1_xreal_0(A,np__0)
| v2_seqm_3(k14_seq_1(B,A)) ) )
& ( v2_seqm_3(B)
=> ( r1_xreal_0(np__0,A)
| v1_seqm_3(k14_seq_1(B,A)) ) ) ) ) ) ).
fof(t61_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v3_seqm_3(B)
& r1_xreal_0(np__0,A) )
=> v3_seqm_3(k14_seq_1(B,A)) )
& ( ( v3_seqm_3(B)
& r1_xreal_0(A,np__0) )
=> v4_seqm_3(k14_seq_1(B,A)) ) ) ) ) ).
fof(t62_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v4_seqm_3(B)
& r1_xreal_0(np__0,A) )
=> v4_seqm_3(k14_seq_1(B,A)) )
& ( ( v4_seqm_3(B)
& r1_xreal_0(A,np__0) )
=> v3_seqm_3(k14_seq_1(B,A)) ) ) ) ) ).
fof(t63_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v1_seqm_3(A)
& v1_seqm_3(B) )
=> v1_seqm_3(k9_seq_1(A,B)) )
& ( ( v2_seqm_3(A)
& v2_seqm_3(B) )
=> v2_seqm_3(k9_seq_1(A,B)) )
& ( ( v3_seqm_3(A)
& v3_seqm_3(B) )
=> v3_seqm_3(k9_seq_1(A,B)) )
& ( ( v4_seqm_3(A)
& v4_seqm_3(B) )
=> v4_seqm_3(k9_seq_1(A,B)) ) ) ) ) ).
fof(t64_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v1_seqm_3(A)
& v5_seqm_3(B) )
=> v1_seqm_3(k9_seq_1(A,B)) )
& ( ( v2_seqm_3(A)
& v5_seqm_3(B) )
=> v2_seqm_3(k9_seq_1(A,B)) )
& ( ( v3_seqm_3(A)
& v5_seqm_3(B) )
=> v3_seqm_3(k9_seq_1(A,B)) )
& ( ( v4_seqm_3(A)
& v5_seqm_3(B) )
=> v4_seqm_3(k9_seq_1(A,B)) ) ) ) ) ).
fof(t65_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
=> ( ! [B] :
( v1_xreal_0(B)
=> v5_seqm_3(k14_seq_1(A,B)) )
& v5_seqm_3(k17_seq_1(A))
& v5_seqm_3(k22_seq_1(A)) ) ) ) ).
fof(t66_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v5_seqm_3(A)
& v5_seqm_3(B) )
=> ( v5_seqm_3(k11_seq_1(A,B))
& v5_seqm_3(k9_seq_1(A,B)) ) ) ) ) ).
fof(t67_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v5_seqm_3(A)
& v5_seqm_3(B) )
=> v5_seqm_3(k10_seq_1(A,B)) ) ) ) ).
fof(t68_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(B)
=> ( r1_xreal_0(A,np__0)
| v1_seq_2(k14_seq_1(B,A)) ) )
& ( np__0 = A
=> v3_seq_2(k14_seq_1(B,A)) )
& ( v1_seq_2(B)
=> ( r1_xreal_0(np__0,A)
| v2_seq_2(k14_seq_1(B,A)) ) ) ) ) ) ).
fof(t69_seqm_3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(B)
=> ( r1_xreal_0(A,np__0)
| v2_seq_2(k14_seq_1(B,A)) ) )
& ( v2_seq_2(B)
=> ( r1_xreal_0(np__0,A)
| v1_seq_2(k14_seq_1(B,A)) ) ) ) ) ) ).
fof(t70_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
=> ! [B] :
( v1_xreal_0(B)
=> v3_seq_2(k14_seq_1(A,B)) ) )
& ( v3_seq_2(A)
=> v3_seq_2(k17_seq_1(A)) )
& ( v3_seq_2(A)
=> v3_seq_2(k22_seq_1(A)) )
& ( v3_seq_2(k22_seq_1(A))
=> v3_seq_2(A) ) ) ) ).
fof(t71_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v1_seq_2(A)
& v1_seq_2(B) )
=> v1_seq_2(k9_seq_1(A,B)) )
& ( ( v2_seq_2(A)
& v2_seq_2(B) )
=> v2_seq_2(k9_seq_1(A,B)) )
& ( ( v3_seq_2(A)
& v3_seq_2(B) )
=> v3_seq_2(k9_seq_1(A,B)) ) ) ) ) ).
fof(t72_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v3_seq_2(A)
& v3_seq_2(B) )
=> ( v3_seq_2(k11_seq_1(A,B))
& v3_seq_2(k10_seq_1(A,B)) ) ) ) ) ).
fof(t73_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
=> v3_seq_2(A) ) ) ).
fof(t74_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v5_seqm_3(A)
=> ( ! [B] :
( v1_xreal_0(B)
=> v3_seq_2(k14_seq_1(A,B)) )
& v3_seq_2(k17_seq_1(A))
& v3_seq_2(k22_seq_1(A)) ) ) ) ).
fof(t75_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v1_seq_2(A)
& v5_seqm_3(B) )
=> v1_seq_2(k9_seq_1(A,B)) )
& ( ( v2_seq_2(A)
& v5_seqm_3(B) )
=> v2_seq_2(k9_seq_1(A,B)) )
& ( ( v3_seq_2(A)
& v5_seqm_3(B) )
=> v3_seq_2(k9_seq_1(A,B)) ) ) ) ) ).
fof(t76_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( ( v1_seq_2(A)
& v5_seqm_3(B) )
=> v1_seq_2(k10_seq_1(A,B)) )
& ( ( v2_seq_2(A)
& v5_seqm_3(B) )
=> v2_seq_2(k10_seq_1(A,B)) )
& ( ( v3_seq_2(A)
& v5_seqm_3(B) )
=> ( v3_seq_2(k10_seq_1(A,B))
& v3_seq_2(k10_seq_1(B,A))
& v3_seq_2(k11_seq_1(A,B)) ) ) ) ) ) ).
fof(t77_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v1_seq_2(A)
& v4_seqm_3(B) )
=> v1_seq_2(k9_seq_1(A,B)) ) ) ) ).
fof(t78_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( v2_seq_2(A)
& v3_seqm_3(B) )
=> v2_seq_2(k9_seq_1(A,B)) ) ) ) ).
fof(t79_seqm_3,axiom,
! [A,B] : v5_seqm_3(k2_funcop_1(A,B)) ).
fof(t80_seqm_3,axiom,
( v1_seqm_3(k6_funct_3(k1_numbers,k5_numbers))
& v7_seqm_3(k6_funct_3(k1_numbers,k5_numbers)) ) ).
fof(dt_m1_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m1_seqm_3(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) ) ) ) ).
fof(existence_m1_seqm_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> ? [B] : m1_seqm_3(B,A) ) ).
fof(dt_k1_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_funct_1(k1_seqm_3(A,B))
& v1_funct_2(k1_seqm_3(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k1_seqm_3(A,B),k5_numbers,k1_numbers) ) ) ).
fof(dt_k2_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k2_seqm_3(A,B),k1_numbers,k5_numbers) ) ).
fof(redefinition_k2_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> k2_seqm_3(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k3_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m1_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k3_seqm_3(A,B))
& v1_funct_2(k3_seqm_3(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k3_seqm_3(A,B),k5_numbers,k1_numbers) ) ) ).
fof(redefinition_k3_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m1_relset_1(B,k5_numbers,k1_numbers) )
=> k3_seqm_3(A,B) = k5_relat_1(A,B) ) ).
fof(dt_k4_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k4_seqm_3(A,B))
& v1_funct_2(k4_seqm_3(A,B),k5_numbers,k1_numbers)
& v1_seqm_3(k4_seqm_3(A,B))
& v7_seqm_3(k4_seqm_3(A,B))
& m2_relset_1(k4_seqm_3(A,B),k5_numbers,k1_numbers) ) ) ).
fof(redefinition_k4_seqm_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seqm_3(A)
& v7_seqm_3(A)
& m1_relset_1(A,k5_numbers,k1_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers) )
=> k4_seqm_3(A,B) = k5_relat_1(A,B) ) ).
%------------------------------------------------------------------------------