SET007 Axioms: SET007+150.ax
%------------------------------------------------------------------------------
% File : SET007+150 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Convergence and the Limit of Complex Sequences. Series
% 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 : comseq_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 119 ( 1 unt; 0 def)
% Number of atoms : 993 ( 108 equ)
% Maximal formula atoms : 17 ( 8 avg)
% Number of connectives : 909 ( 35 ~; 9 |; 549 &)
% ( 13 <=>; 303 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 9 con; 0-4 aty)
% Number of variables : 268 ( 250 !; 18 ?)
% 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_comseq_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_series_1(A) )
=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seq_1(A)
& v4_seq_2(A) ) ) ) ).
fof(cc2_comseq_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k1_numbers)
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v2_series_1(A) )
=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v1_seq_1(A)
& v4_seq_2(A)
& v1_series_1(A) ) ) ) ).
fof(rc1_comseq_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)
& v4_seq_2(A)
& v1_series_1(A)
& v2_series_1(A) ) ).
fof(fc1_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v1_funct_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v1_funct_2(k1_series_1(k9_comseq_1(k5_numbers,A)),k5_numbers,k1_numbers)
& v1_seq_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) ) ).
fof(fc2_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_2(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k3_comseq_3(A))
& v1_funct_1(k3_comseq_3(A))
& v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
& v1_seq_1(k3_comseq_3(A))
& v4_seq_2(k3_comseq_3(A)) ) ) ).
fof(fc3_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_2(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k4_comseq_3(A))
& v1_funct_1(k4_comseq_3(A))
& v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
& v1_seq_1(k4_comseq_3(A))
& v4_seq_2(k4_comseq_3(A)) ) ) ).
fof(rc2_comseq_3,axiom,
? [A] :
( m1_relset_1(A,k5_numbers,k2_numbers)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A) ) ).
fof(fc4_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( ~ v1_xboole_0(k7_comseq_3(A))
& v1_relat_1(k7_comseq_3(A))
& v1_funct_1(k7_comseq_3(A))
& v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
& v1_comseq_2(k7_comseq_3(A))
& v2_comseq_2(k7_comseq_3(A))
& v1_partfun1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) ).
fof(rc3_comseq_3,axiom,
? [A] :
( m1_relset_1(A,k5_numbers,k2_numbers)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_3(A) ) ).
fof(fc5_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( ~ v1_xboole_0(k9_comseq_1(k5_numbers,A))
& v1_relat_1(k9_comseq_1(k5_numbers,A))
& v1_funct_1(k9_comseq_1(k5_numbers,A))
& v1_funct_2(k9_comseq_1(k5_numbers,A),k5_numbers,k1_numbers)
& v1_seq_1(k9_comseq_1(k5_numbers,A))
& v4_seq_2(k9_comseq_1(k5_numbers,A))
& v1_series_1(k9_comseq_1(k5_numbers,A))
& v1_partfun1(k9_comseq_1(k5_numbers,A),k5_numbers,k1_numbers) ) ) ).
fof(cc3_comseq_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k2_numbers)
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A) )
=> ( ~ v1_xboole_0(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_2(A)
& v2_comseq_2(A)
& v1_partfun1(A,k5_numbers,k2_numbers) ) ) ) ).
fof(fc6_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k3_comseq_3(A))
& v1_funct_1(k3_comseq_3(A))
& v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
& v1_seq_1(k3_comseq_3(A))
& v4_seq_2(k3_comseq_3(A))
& v1_series_1(k3_comseq_3(A)) ) ) ).
fof(fc7_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k4_comseq_3(A))
& v1_funct_1(k4_comseq_3(A))
& v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
& v1_seq_1(k4_comseq_3(A))
& v4_seq_2(k4_comseq_3(A))
& v1_series_1(k4_comseq_3(A)) ) ) ).
fof(fc8_comseq_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& v1_comseq_3(B)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> ( ~ v1_xboole_0(k2_comseq_1(k5_numbers,A,B))
& v1_relat_1(k2_comseq_1(k5_numbers,A,B))
& v1_funct_1(k2_comseq_1(k5_numbers,A,B))
& v1_funct_2(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
& v1_comseq_2(k2_comseq_1(k5_numbers,A,B))
& v2_comseq_2(k2_comseq_1(k5_numbers,A,B))
& v1_partfun1(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
& v1_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) ).
fof(fc9_comseq_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& v1_comseq_3(B)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> ( ~ v1_xboole_0(k6_comseq_1(k5_numbers,A,B))
& v1_relat_1(k6_comseq_1(k5_numbers,A,B))
& v1_funct_1(k6_comseq_1(k5_numbers,A,B))
& v1_funct_2(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
& v1_comseq_2(k6_comseq_1(k5_numbers,A,B))
& v2_comseq_2(k6_comseq_1(k5_numbers,A,B))
& v1_partfun1(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
& v1_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ).
fof(fc10_comseq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& v1_comseq_3(B)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> ( ~ v1_xboole_0(k4_comseq_1(k5_numbers,B,A))
& v1_relat_1(k4_comseq_1(k5_numbers,B,A))
& v1_funct_1(k4_comseq_1(k5_numbers,B,A))
& v1_funct_2(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
& v1_comseq_2(k4_comseq_1(k5_numbers,B,A))
& v2_comseq_2(k4_comseq_1(k5_numbers,B,A))
& v1_partfun1(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
& v1_comseq_3(k4_comseq_1(k5_numbers,B,A)) ) ) ).
fof(fc11_comseq_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k6_comseq_3(A,B))
& v1_relat_1(k6_comseq_3(A,B))
& v1_funct_1(k6_comseq_3(A,B))
& v1_funct_2(k6_comseq_3(A,B),k5_numbers,k2_numbers)
& v1_comseq_2(k6_comseq_3(A,B))
& v2_comseq_2(k6_comseq_3(A,B))
& v1_partfun1(k6_comseq_3(A,B),k5_numbers,k2_numbers)
& v1_comseq_3(k6_comseq_3(A,B)) ) ) ).
fof(fc12_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_3(A)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_relat_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v1_funct_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v1_funct_2(k1_series_1(k9_comseq_1(k5_numbers,A)),k5_numbers,k1_numbers)
& v1_seq_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v1_seq_2(k1_series_1(k9_comseq_1(k5_numbers,A)))
& v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) ) ).
fof(cc4_comseq_3,axiom,
! [A] :
( m1_relset_1(A,k5_numbers,k2_numbers)
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_3(A) )
=> ( ~ v1_xboole_0(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_2(A)
& v2_comseq_2(A)
& v1_partfun1(A,k5_numbers,k2_numbers)
& v1_comseq_3(A) ) ) ) ).
fof(rc4_comseq_3,axiom,
? [A] :
( m1_relset_1(A,k5_numbers,k2_numbers)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v1_comseq_2(A)
& v2_comseq_2(A)
& v1_partfun1(A,k5_numbers,k2_numbers)
& v1_comseq_3(A)
& v2_comseq_3(A) ) ).
fof(t1_comseq_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k1_nat_1(A,np__1) != k5_complex1
& k3_xcmplx_0(k1_nat_1(A,np__1),k7_complex1) != k5_complex1 ) ) ).
fof(t2_comseq_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)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k22_seq_1(A)),B) = np__0 ) ) ) ).
fof(t3_comseq_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)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 )
=> v2_series_1(A) ) ) ).
fof(t4_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v4_seq_2(A)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& r1_xreal_0(C,E)
& r1_xreal_0(B,k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,A,D),k2_seq_1(k5_numbers,k1_numbers,A,E)))) ) ) ) ) ) ) ) ).
fof(t5_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),k1_nat_1(C,D)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C)),k4_real_1(B,D)) ) ) ) ) ) ).
fof(t6_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k4_real_1(B,k1_nat_1(C,np__1))) ) ) ) ) ).
fof(t7_comseq_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,C)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,E),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,B,E))) ) )
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),C))) ) ) ) ) ) ).
fof(t8_comseq_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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,C)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,E),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,B,E))) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,C)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(E,F),C)
=> r1_xreal_0(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),k1_nat_1(E,F)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),E)),k4_real_1(D,k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),k1_nat_1(E,F)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),E)))) ) ) ) ) ) ) ) ) ) ).
fof(t9_comseq_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)
=> r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B))) = k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B)) ) ) )
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k18_complex1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B)) = k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B) ) ) ) ) ).
fof(t10_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( v2_comseq_2(A)
& v2_comseq_2(B)
& k2_comseq_2(k6_comseq_1(k5_numbers,A,B)) = k5_complex1 )
=> k2_comseq_2(A) = k2_comseq_2(B) ) ) ) ).
fof(d1_comseq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( B = k1_comseq_3(A)
<=> ( k1_comseq_1(B,np__0) = k6_complex1
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(B,k1_nat_1(C,np__1)) = k3_xcmplx_0(k1_comseq_1(B,C),A) ) ) ) ) ) ).
fof(d2_comseq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v4_ordinal2(B)
=> k2_comseq_3(A,B) = k1_funct_1(k1_comseq_3(A),B) ) ) ).
fof(t11_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_comseq_3(A,np__0) = k6_complex1 ) ).
fof(d3_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( B = k3_comseq_3(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_complex1(k1_comseq_1(A,C)) ) ) ) ) ).
fof(d4_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( B = k4_comseq_3(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_complex1(k1_comseq_1(A,C)) ) ) ) ) ).
fof(t12_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> r1_xreal_0(k17_complex1(A),k3_real_1(k18_complex1(k3_complex1(A)),k18_complex1(k4_complex1(A)))) ) ).
fof(t13_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( r1_xreal_0(k18_complex1(k3_complex1(A)),k17_complex1(A))
& r1_xreal_0(k18_complex1(k4_complex1(A)),k17_complex1(A)) ) ) ).
fof(t14_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( k3_comseq_3(A) = k3_comseq_3(B)
& k4_comseq_3(A) = k4_comseq_3(B) )
=> A = B ) ) ) ).
fof(t15_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( k9_seq_1(k3_comseq_3(A),k3_comseq_3(B)) = k3_comseq_3(k2_comseq_1(k5_numbers,A,B))
& k9_seq_1(k4_comseq_3(A),k4_comseq_3(B)) = k4_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t16_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( k17_seq_1(k3_comseq_3(A)) = k3_comseq_3(k5_comseq_1(k5_numbers,A))
& k17_seq_1(k4_comseq_3(A)) = k4_comseq_3(k5_comseq_1(k5_numbers,A)) ) ) ).
fof(t17_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( k4_real_1(A,k3_complex1(B)) = k3_complex1(k3_xcmplx_0(A,B))
& k4_real_1(A,k4_complex1(B)) = k4_complex1(k3_xcmplx_0(A,B)) ) ) ) ).
fof(t18_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( k10_seq_1(k3_comseq_3(A),k3_comseq_3(B)) = k3_comseq_3(k6_comseq_1(k5_numbers,A,B))
& k10_seq_1(k4_comseq_3(A),k4_comseq_3(B)) = k4_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t19_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k14_seq_1(k3_comseq_3(A),B) = k3_comseq_3(k4_comseq_1(k5_numbers,A,B))
& k14_seq_1(k4_comseq_3(A),B) = k4_comseq_3(k4_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t20_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( k3_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k10_seq_1(k14_seq_1(k3_comseq_3(A),k3_complex1(B)),k14_seq_1(k4_comseq_3(A),k4_complex1(B)))
& k4_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k9_seq_1(k14_seq_1(k4_comseq_3(A),k3_complex1(B)),k14_seq_1(k3_comseq_3(A),k4_complex1(B))) ) ) ) ).
fof(t21_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( k3_comseq_3(k3_comseq_1(k5_numbers,A,B)) = k10_seq_1(k11_seq_1(k3_comseq_3(A),k3_comseq_3(B)),k11_seq_1(k4_comseq_3(A),k4_comseq_3(B)))
& k4_comseq_3(k3_comseq_1(k5_numbers,A,B)) = k9_seq_1(k11_seq_1(k3_comseq_3(A),k4_comseq_3(B)),k11_seq_1(k4_comseq_3(A),k3_comseq_3(B))) ) ) ) ).
fof(t22_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_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) )
=> ( k3_comseq_3(k5_comseq_3(B,A)) = k3_seqm_3(B,k3_comseq_3(A))
& k4_comseq_3(k5_comseq_3(B,A)) = k3_seqm_3(B,k4_comseq_3(A)) ) ) ) ).
fof(d5_comseq_3,axiom,
$true ).
fof(d6_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( C = k6_comseq_3(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_comseq_1(C,D) = k1_comseq_1(A,k1_nat_1(D,B)) ) ) ) ) ) ).
fof(t23_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k1_seqm_3(k3_comseq_3(A),B) = k3_comseq_3(k6_comseq_3(A,B))
& k1_seqm_3(k4_comseq_3(A),B) = k4_comseq_3(k6_comseq_3(A,B)) ) ) ) ).
fof(d7_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( B = k7_comseq_3(A)
<=> ( k1_comseq_1(B,np__0) = k1_comseq_1(A,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(B,k1_nat_1(C,np__1)) = k8_complex1(k1_comseq_1(B,C),k1_comseq_1(A,k1_nat_1(C,np__1))) ) ) ) ) ) ).
fof(d8_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k8_comseq_3(A) = k2_comseq_2(k7_comseq_3(A)) ) ).
fof(t24_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k5_complex1 )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(k7_comseq_3(A),B) = k5_complex1 ) ) ) ).
fof(t25_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k5_complex1 )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B) = np__0 ) ) ) ).
fof(t26_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( k1_series_1(k3_comseq_3(A)) = k3_comseq_3(k7_comseq_3(A))
& k1_series_1(k4_comseq_3(A)) = k4_comseq_3(k7_comseq_3(A)) ) ) ).
fof(t27_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> k2_comseq_1(k5_numbers,k7_comseq_3(A),k7_comseq_3(B)) = k7_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) ).
fof(t28_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> k6_comseq_1(k5_numbers,k7_comseq_3(A),k7_comseq_3(B)) = k7_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ).
fof(t29_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k7_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k4_comseq_1(k5_numbers,k7_comseq_3(A),B) ) ) ).
fof(t30_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k17_complex1(k1_comseq_1(k7_comseq_3(A),B)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B)) ) ) ).
fof(t31_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k17_complex1(k11_complex1(k1_comseq_1(k7_comseq_3(A),B),k1_comseq_1(k7_comseq_3(A),C))),k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),C)))) ) ) ) ).
fof(t32_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k1_seqm_3(k1_series_1(k3_comseq_3(A)),B) = k3_comseq_3(k6_comseq_3(k7_comseq_3(A),B))
& k1_seqm_3(k1_series_1(k4_comseq_3(A)),B) = k4_comseq_3(k6_comseq_3(k7_comseq_3(A),B)) ) ) ) ).
fof(t33_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,C) = k1_comseq_1(B,np__0) )
=> k7_comseq_3(k6_comseq_3(B,np__1)) = k6_comseq_1(k5_numbers,k6_comseq_3(k7_comseq_3(B),np__1),A) ) ) ) ).
fof(t34_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) ).
fof(t35_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,C)
=> k1_comseq_1(A,D) = k1_comseq_1(B,D) ) )
=> k1_comseq_1(k7_comseq_3(A),C) = k1_comseq_1(k7_comseq_3(B),C) ) ) ) ) ).
fof(t36_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( k6_complex1 != A
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(k7_comseq_3(k1_comseq_3(A)),B) = k13_complex1(k11_complex1(k6_complex1,k2_comseq_3(A,k1_nat_1(B,np__1))),k11_complex1(k6_complex1,A)) ) ) ) ).
fof(t37_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(B,k1_comseq_1(A,C)) )
=> ( B = k6_complex1
| ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(k7_comseq_3(A),C) = k9_complex1(k1_comseq_1(A,np__0),k13_complex1(k11_complex1(k6_complex1,k2_comseq_3(B,k1_nat_1(C,np__1))),k11_complex1(k6_complex1,B))) ) ) ) ) ) ).
fof(t38_comseq_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,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
& k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
=> ( ( v4_seq_2(A)
& v4_seq_2(B) )
<=> v2_comseq_2(C) ) ) ) ) ) ).
fof(t39_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& v4_seq_2(A)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v4_seq_2(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
& k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
=> ( v2_comseq_2(C)
& k2_comseq_2(C) = k2_xcmplx_0(k2_seq_2(A),k3_xcmplx_0(k2_seq_2(B),k7_complex1)) ) ) ) ) ) ).
fof(t40_comseq_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,k2_numbers)
& v2_comseq_2(C)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
& k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
=> ( v4_seq_2(A)
& v4_seq_2(B)
& k2_seq_2(A) = k3_complex1(k2_comseq_2(C))
& k2_seq_2(B) = k4_complex1(k2_comseq_2(C)) ) ) ) ) ) ).
fof(t41_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& v2_comseq_2(A)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v4_seq_2(k3_comseq_3(A))
& v4_seq_2(k4_comseq_3(A))
& k2_seq_2(k3_comseq_3(A)) = k3_complex1(k2_comseq_2(A))
& k2_seq_2(k4_comseq_3(A)) = k4_complex1(k2_comseq_2(A)) ) ) ).
fof(t42_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ( v4_seq_2(k3_comseq_3(A))
& v4_seq_2(k4_comseq_3(A)) )
=> ( v2_comseq_2(A)
& k3_complex1(k2_comseq_2(A)) = k2_seq_2(k3_comseq_3(A))
& k4_complex1(k2_comseq_2(A)) = k2_seq_2(k4_comseq_3(A)) ) ) ) ).
fof(t43_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( ( k1_comseq_1(A,np__0) = B
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(k1_comseq_1(A,C),B) ) )
=> ( r1_xreal_0(k17_complex1(B),np__0)
| r1_xreal_0(np__1,k17_complex1(B))
| ( v2_comseq_2(A)
& k2_comseq_2(A) = k5_complex1 ) ) ) ) ) ).
fof(t44_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,C) = k2_comseq_3(B,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(np__1,k17_complex1(B))
| ( v2_comseq_2(A)
& k2_comseq_2(A) = k5_complex1 ) ) ) ) ) ).
fof(t45_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(B,k17_complex1(k1_comseq_1(A,D))) ) ) )
& v4_seq_2(k9_comseq_1(k5_numbers,A))
& k2_seq_2(k9_comseq_1(k5_numbers,A)) = np__0 ) ) ) ).
fof(t46_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v2_comseq_2(A)
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(A,D),k1_comseq_1(A,C)))) ) ) ) ) ) ) ).
fof(t47_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v2_comseq_2(A)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& r1_xreal_0(C,E)
& r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(A,D),k1_comseq_1(A,E)))) ) ) ) ) ) ) ) ).
fof(t48_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k17_complex1(k1_comseq_1(B,C)),k2_seq_1(k5_numbers,k1_numbers,A,C)) )
& v4_seq_2(A)
& k2_seq_2(A) = np__0 )
=> ( v2_comseq_2(B)
& k2_comseq_2(B) = k5_complex1 ) ) ) ) ).
fof(d9_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( m1_comseq_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 = k5_comseq_3(C,A) ) ) ) ) ).
fof(t49_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( m1_comseq_3(A,B)
=> ( m1_seqm_3(k3_comseq_3(A),k3_comseq_3(B))
& m1_seqm_3(k4_comseq_3(A),k4_comseq_3(B)) ) ) ) ) ).
fof(t50_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( m1_comseq_3(A,B)
& m1_comseq_3(B,C) )
=> m1_comseq_3(A,C) ) ) ) ) ).
fof(t51_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ~ ( v1_comseq_2(A)
& ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ~ ( m1_comseq_3(B,A)
& v2_comseq_2(B) ) ) ) ) ).
fof(d10_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
<=> v2_comseq_2(k7_comseq_3(A)) ) ) ).
fof(d11_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v2_comseq_3(A)
<=> v1_series_1(k9_comseq_1(k5_numbers,A)) ) ) ).
fof(t52_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k5_complex1 )
=> v2_comseq_3(A) ) ) ).
fof(t53_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
=> ( v2_comseq_2(A)
& k2_comseq_2(A) = k5_complex1 ) ) ) ).
fof(t54_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
=> ( v1_series_1(k3_comseq_3(A))
& v1_series_1(k4_comseq_3(A))
& k8_comseq_3(A) = k2_xcmplx_0(k2_series_1(k3_comseq_3(A)),k3_xcmplx_0(k2_series_1(k4_comseq_3(A)),k7_complex1)) ) ) ) ).
fof(t55_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_3(A)
& v1_comseq_3(B) )
=> ( v1_comseq_3(k2_comseq_1(k5_numbers,A,B))
& k8_comseq_3(k2_comseq_1(k5_numbers,A,B)) = k8_complex1(k8_comseq_3(A),k8_comseq_3(B)) ) ) ) ) ).
fof(t56_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_3(A)
& v1_comseq_3(B) )
=> ( v1_comseq_3(k6_comseq_1(k5_numbers,A,B))
& k8_comseq_3(k6_comseq_1(k5_numbers,A,B)) = k11_complex1(k8_comseq_3(A),k8_comseq_3(B)) ) ) ) ) ).
fof(t57_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( v1_comseq_3(A)
=> ( v1_comseq_3(k4_comseq_1(k5_numbers,A,B))
& k8_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k9_complex1(B,k8_comseq_3(A)) ) ) ) ) ).
fof(t58_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ( v1_series_1(k3_comseq_3(A))
& v1_series_1(k4_comseq_3(A)) )
=> ( v1_comseq_3(A)
& k8_comseq_3(A) = k2_xcmplx_0(k2_series_1(k3_comseq_3(A)),k3_xcmplx_0(k2_series_1(k4_comseq_3(A)),k7_complex1)) ) ) ) ).
fof(t59_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> v1_comseq_3(k6_comseq_3(A,B)) ) ) ) ).
fof(t60_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_comseq_3(k6_comseq_3(A,B)) )
=> v1_comseq_3(A) ) ) ).
fof(t61_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k8_comseq_3(A) = k8_complex1(k1_comseq_1(k7_comseq_3(A),B),k8_comseq_3(k6_comseq_3(A,k1_nat_1(B,np__1)))) ) ) ) ).
fof(t62_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_seq_2(k1_series_1(k9_comseq_1(k5_numbers,A)))
<=> v2_comseq_3(A) ) ) ).
fof(t63_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_3(A)
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(k7_comseq_3(A),D),k1_comseq_1(k7_comseq_3(A),C)))) ) ) ) ) ) ) ).
fof(t64_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v2_comseq_3(A)
=> v1_comseq_3(A) ) ) ).
fof(t65_comseq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( ~ r1_xreal_0(np__1,k17_complex1(A))
=> ( v1_comseq_3(k1_comseq_3(A))
& k8_comseq_3(k1_comseq_3(A)) = k13_complex1(k6_complex1,k11_complex1(k6_complex1,A)) ) ) ) ).
fof(t66_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(B,k1_comseq_1(A,C)) )
=> ( r1_xreal_0(np__1,k17_complex1(B))
| ( v1_comseq_3(A)
& k8_comseq_3(A) = k13_complex1(k1_comseq_1(A,np__0),k11_complex1(k6_complex1,B)) ) ) ) ) ) ).
fof(t67_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( v1_series_1(A)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& ~ r1_xreal_0(k17_complex1(k1_comseq_1(B,D)),k2_seq_1(k5_numbers,k1_numbers,A,D)) ) )
| v2_comseq_3(B) ) ) ) ) ).
fof(t68_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))
& r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) ) )
& v2_comseq_3(B) )
=> ( v2_comseq_3(A)
& r1_xreal_0(k2_series_1(k9_comseq_1(k5_numbers,A)),k2_series_1(k9_comseq_1(k5_numbers,B))) ) ) ) ) ).
fof(t69_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ~ ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),B),np__0) )
& ? [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(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))) ) ) )
& v2_comseq_3(A) ) ) ).
fof(t70_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
& v4_seq_2(A) )
=> ( r1_xreal_0(np__1,k2_seq_2(A))
| v2_comseq_3(B) ) ) ) ) ).
fof(t71_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) )
& v1_series_1(k9_comseq_1(k5_numbers,B)) ) ) ) ).
fof(t72_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
& v4_seq_2(A)
& ~ r1_xreal_0(k2_seq_2(A),np__1)
& v2_comseq_3(B) ) ) ) ).
fof(t73_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( v4_seqm_3(k9_comseq_1(k5_numbers,B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,C) = k4_real_1(k4_power(np__2,C),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),k4_power(np__2,C))) ) )
=> ( v2_comseq_3(B)
<=> v1_series_1(A) ) ) ) ) ).
fof(t74_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,C)
=> k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C) = k6_real_1(np__1,k4_power(C,B)) ) )
=> ( r1_xreal_0(B,np__1)
| v2_comseq_3(A) ) ) ) ) ).
fof(t75_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( r1_xreal_0(B,np__1)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,C)
=> k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C) = k6_real_1(np__1,k4_power(C,B)) ) )
& v2_comseq_3(A) ) ) ) ).
fof(t76_comseq_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,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k1_comseq_1(B,C) != k5_complex1
& k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) ) )
& v4_seq_2(A) )
=> ( r1_xreal_0(np__1,k2_seq_2(A))
| v2_comseq_3(B) ) ) ) ) ).
fof(t77_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ~ ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) != k5_complex1 )
& ? [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(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))) ) ) )
& v2_comseq_3(A) ) ) ).
fof(dt_m1_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( m1_comseq_3(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) ) ) ) ).
fof(existence_m1_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ? [B] : m1_comseq_3(B,A) ) ).
fof(dt_k1_comseq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( v1_funct_1(k1_comseq_3(A))
& v1_funct_2(k1_comseq_3(A),k5_numbers,k2_numbers)
& m2_relset_1(k1_comseq_3(A),k5_numbers,k2_numbers) ) ) ).
fof(dt_k2_comseq_3,axiom,
! [A,B] :
( ( v1_xcmplx_0(A)
& v4_ordinal2(B) )
=> m1_subset_1(k2_comseq_3(A,B),k2_numbers) ) ).
fof(dt_k3_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k3_comseq_3(A))
& v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
& m2_relset_1(k3_comseq_3(A),k5_numbers,k1_numbers) ) ) ).
fof(dt_k4_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k4_comseq_3(A))
& v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
& m2_relset_1(k4_comseq_3(A),k5_numbers,k1_numbers) ) ) ).
fof(dt_k5_comseq_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,k2_numbers)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k5_comseq_3(A,B))
& v1_funct_2(k5_comseq_3(A,B),k5_numbers,k2_numbers)
& m2_relset_1(k5_comseq_3(A,B),k5_numbers,k2_numbers) ) ) ).
fof(redefinition_k5_comseq_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,k2_numbers)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> k5_comseq_3(A,B) = k5_relat_1(A,B) ) ).
fof(dt_k6_comseq_3,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_funct_1(k6_comseq_3(A,B))
& v1_funct_2(k6_comseq_3(A,B),k5_numbers,k2_numbers)
& m2_relset_1(k6_comseq_3(A,B),k5_numbers,k2_numbers) ) ) ).
fof(dt_k7_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k7_comseq_3(A))
& v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
& m2_relset_1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) ).
fof(dt_k8_comseq_3,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers) )
=> m1_subset_1(k8_comseq_3(A),k2_numbers) ) ).
%------------------------------------------------------------------------------