SET007 Axioms: SET007+128.ax
%------------------------------------------------------------------------------
% File : SET007+128 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex Sequences
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 87 ( 3 unt; 0 def)
% Number of atoms : 703 ( 89 equ)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 650 ( 34 ~; 2 |; 386 &)
% ( 17 <=>; 211 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 5 con; 0-4 aty)
% Number of variables : 220 ( 217 !; 3 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_comseq_1,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_partfun1(A,k5_numbers,k2_numbers)
& v1_comseq_1(A) ) ).
fof(fc1_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,k2_numbers)
& m1_relset_1(C,A,k2_numbers) )
=> ( ~ v1_xboole_0(k2_comseq_1(A,B,C))
& v1_relat_1(k2_comseq_1(A,B,C))
& v1_funct_1(k2_comseq_1(A,B,C))
& v1_funct_2(k2_comseq_1(A,B,C),A,k2_numbers)
& v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(fc2_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,k2_numbers)
& m1_relset_1(C,A,k2_numbers) )
=> ( ~ v1_xboole_0(k3_comseq_1(A,B,C))
& v1_relat_1(k3_comseq_1(A,B,C))
& v1_funct_1(k3_comseq_1(A,B,C))
& v1_funct_2(k3_comseq_1(A,B,C),A,k2_numbers)
& v1_partfun1(k3_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(fc3_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers)
& v1_xcmplx_0(C) )
=> ( ~ v1_xboole_0(k4_comseq_1(A,B,C))
& v1_relat_1(k4_comseq_1(A,B,C))
& v1_funct_1(k4_comseq_1(A,B,C))
& v1_funct_2(k4_comseq_1(A,B,C),A,k2_numbers)
& v1_partfun1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(fc4_comseq_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers) )
=> ( ~ v1_xboole_0(k5_comseq_1(A,B))
& v1_relat_1(k5_comseq_1(A,B))
& v1_funct_1(k5_comseq_1(A,B))
& v1_funct_2(k5_comseq_1(A,B),A,k2_numbers)
& v1_partfun1(k5_comseq_1(A,B),A,k2_numbers) ) ) ).
fof(fc5_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,k2_numbers)
& m1_relset_1(C,A,k2_numbers) )
=> ( ~ v1_xboole_0(k6_comseq_1(A,B,C))
& v1_relat_1(k6_comseq_1(A,B,C))
& v1_funct_1(k6_comseq_1(A,B,C))
& v1_funct_2(k6_comseq_1(A,B,C),A,k2_numbers)
& v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(fc6_comseq_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m1_relset_1(B,A,k2_numbers) )
=> ( ~ v1_xboole_0(k9_comseq_1(A,B))
& v1_relat_1(k9_comseq_1(A,B))
& v1_funct_1(k9_comseq_1(A,B))
& v1_funct_2(k9_comseq_1(A,B),A,k1_numbers)
& v1_partfun1(k9_comseq_1(A,B),A,k1_numbers) ) ) ).
fof(t1_comseq_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
<=> ( k1_relat_1(A) = k5_numbers
& ! [B] :
( r2_hidden(B,k5_numbers)
=> m1_subset_1(k1_funct_1(A,B),k2_numbers) ) ) ) ) ).
fof(t2_comseq_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
<=> ( k1_relat_1(A) = k5_numbers
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> m1_subset_1(k1_funct_1(A,B),k2_numbers) ) ) ) ) ).
fof(d1_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
<=> r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_xboole_0(k2_numbers,k1_tarski(k5_complex1))) ) ) ).
fof(t3_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
<=> ! [B] :
~ ( r2_hidden(B,k5_numbers)
& k1_funct_1(A,B) = k5_complex1 ) ) ) ).
fof(t4_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) != k5_complex1 ) ) ) ).
fof(t5_comseq_1,axiom,
$true ).
fof(t6_comseq_1,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,C) )
=> A = B ) ) ) ).
fof(t7_comseq_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers)
& k5_relset_1(k5_numbers,k2_numbers,B) = k1_tarski(A) ) ) ).
fof(d2_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k2_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,k2_numbers,D))
=> k1_funct_1(D,E) = k8_complex1(k4_finseq_4(A,k2_numbers,B,E),k4_finseq_4(A,k2_numbers,C,E)) ) ) ) ) ) ) ) ) ).
fof(d3_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k3_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,k2_numbers,D))
=> k1_funct_1(D,E) = k9_complex1(k4_finseq_4(A,k2_numbers,B,E),k4_finseq_4(A,k2_numbers,C,E)) ) ) ) ) ) ) ) ) ).
fof(d4_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k2_numbers)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k2_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = A
& ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(D,E) = k8_complex1(k8_funct_2(A,k2_numbers,B,E),k8_funct_2(A,k2_numbers,C,E)) ) ) ) ) ) ) ) ).
fof(d5_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k2_numbers)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k3_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = A
& ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(D,E) = k9_complex1(k8_funct_2(A,k2_numbers,B,E),k8_funct_2(A,k2_numbers,C,E)) ) ) ) ) ) ) ) ).
fof(d6_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k4_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = k4_relset_1(A,k2_numbers,B)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,k2_numbers,D))
=> k1_funct_1(D,E) = k3_xcmplx_0(C,k4_finseq_4(A,k2_numbers,B,E)) ) ) ) ) ) ) ) ) ).
fof(d7_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k4_comseq_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = A
& ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(D,E) = k3_xcmplx_0(C,k8_funct_2(A,k2_numbers,B,E)) ) ) ) ) ) ) ) ).
fof(d8_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( C = k5_comseq_1(A,B)
<=> ( k4_relset_1(A,k2_numbers,C) = k4_relset_1(A,k2_numbers,B)
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,C))
=> k1_funct_1(C,D) = k10_complex1(k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) ) ).
fof(d9_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( C = k5_comseq_1(A,B)
<=> ( k4_relset_1(A,k2_numbers,C) = A
& ! [D] :
( m1_subset_1(D,A)
=> k1_funct_1(C,D) = k10_complex1(k8_funct_2(A,k2_numbers,B,D)) ) ) ) ) ) ) ).
fof(d10_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k6_comseq_1(A,B,C) = k2_comseq_1(A,B,k5_comseq_1(A,C)) ) ) ) ).
fof(d11_comseq_1,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_1(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(B,C) = k12_complex1(k1_comseq_1(A,C)) ) ) ) ) ).
fof(d12_comseq_1,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) )
=> k8_comseq_1(A,B) = k3_comseq_1(k5_numbers,A,k7_comseq_1(B)) ) ) ).
fof(d13_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ( C = k9_comseq_1(A,B)
<=> ( k4_relset_1(A,k1_numbers,C) = k4_relset_1(A,k2_numbers,B)
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k1_numbers,C))
=> k2_seq_1(A,k1_numbers,C,D) = k17_complex1(k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) ) ).
fof(d14_comseq_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k2_numbers)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ( C = k9_comseq_1(A,B)
<=> ( k4_relset_1(A,k1_numbers,C) = A
& ! [D] :
( m1_subset_1(D,A)
=> k2_seq_1(A,k1_numbers,C,D) = k17_complex1(k8_funct_2(A,k2_numbers,B,D)) ) ) ) ) ) ) ).
fof(t8_comseq_1,axiom,
$true ).
fof(t9_comseq_1,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) )
=> k2_comseq_1(k5_numbers,k2_comseq_1(k5_numbers,A,B),C) = k2_comseq_1(k5_numbers,A,k2_comseq_1(k5_numbers,B,C)) ) ) ) ).
fof(t10_comseq_1,axiom,
$true ).
fof(t11_comseq_1,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) )
=> k3_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B),C) = k3_comseq_1(k5_numbers,A,k3_comseq_1(k5_numbers,B,C)) ) ) ) ).
fof(t12_comseq_1,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) )
=> k3_comseq_1(k5_numbers,k2_comseq_1(k5_numbers,A,B),C) = k2_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,C),k3_comseq_1(k5_numbers,B,C)) ) ) ) ).
fof(t13_comseq_1,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) )
=> k3_comseq_1(k5_numbers,A,k2_comseq_1(k5_numbers,B,C)) = k2_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B),k3_comseq_1(k5_numbers,A,C)) ) ) ) ).
fof(t14_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k5_comseq_1(k5_numbers,A) = k4_comseq_1(k5_numbers,A,k10_complex1(k6_complex1)) ) ).
fof(t15_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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) )
=> k4_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,B,C),A) = k3_comseq_1(k5_numbers,k4_comseq_1(k5_numbers,B,A),C) ) ) ) ).
fof(t16_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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) )
=> k4_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,B,C),A) = k3_comseq_1(k5_numbers,B,k4_comseq_1(k5_numbers,C,A)) ) ) ) ).
fof(t17_comseq_1,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) )
=> k3_comseq_1(k5_numbers,k6_comseq_1(k5_numbers,A,B),C) = k6_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,C),k3_comseq_1(k5_numbers,B,C)) ) ) ) ).
fof(t18_comseq_1,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) )
=> k6_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B),k3_comseq_1(k5_numbers,A,C)) = k3_comseq_1(k5_numbers,A,k6_comseq_1(k5_numbers,B,C)) ) ) ) ).
fof(t19_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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) )
=> k4_comseq_1(k5_numbers,k2_comseq_1(k5_numbers,B,C),A) = k2_comseq_1(k5_numbers,k4_comseq_1(k5_numbers,B,A),k4_comseq_1(k5_numbers,C,A)) ) ) ) ).
fof(t20_comseq_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> k4_comseq_1(k5_numbers,C,k9_complex1(A,B)) = k4_comseq_1(k5_numbers,k4_comseq_1(k5_numbers,C,B),A) ) ) ) ).
fof(t21_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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) )
=> k4_comseq_1(k5_numbers,k6_comseq_1(k5_numbers,B,C),A) = k6_comseq_1(k5_numbers,k4_comseq_1(k5_numbers,B,A),k4_comseq_1(k5_numbers,C,A)) ) ) ) ).
fof(t22_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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) )
=> k4_comseq_1(k5_numbers,k8_comseq_1(B,C),A) = k8_comseq_1(k4_comseq_1(k5_numbers,B,A),C) ) ) ) ).
fof(t23_comseq_1,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) )
=> k6_comseq_1(k5_numbers,A,k2_comseq_1(k5_numbers,B,C)) = k6_comseq_1(k5_numbers,k6_comseq_1(k5_numbers,A,B),C) ) ) ) ).
fof(t24_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k4_comseq_1(k5_numbers,A,k6_complex1) = A ) ).
fof(t25_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k5_comseq_1(k5_numbers,k5_comseq_1(k5_numbers,A)) = A ) ).
fof(t26_comseq_1,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,A,k5_comseq_1(k5_numbers,B)) = k2_comseq_1(k5_numbers,A,B) ) ) ).
fof(t27_comseq_1,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) )
=> k6_comseq_1(k5_numbers,A,k6_comseq_1(k5_numbers,B,C)) = k2_comseq_1(k5_numbers,k6_comseq_1(k5_numbers,A,B),C) ) ) ) ).
fof(t28_comseq_1,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) )
=> k2_comseq_1(k5_numbers,A,k6_comseq_1(k5_numbers,B,C)) = k6_comseq_1(k5_numbers,k2_comseq_1(k5_numbers,A,B),C) ) ) ) ).
fof(t29_comseq_1,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_1(k5_numbers,k5_comseq_1(k5_numbers,A),B) = k5_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B))
& k3_comseq_1(k5_numbers,A,k5_comseq_1(k5_numbers,B)) = k5_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t30_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
=> v1_comseq_1(k7_comseq_1(A)) ) ) ).
fof(t31_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k7_comseq_1(k7_comseq_1(A)) = A ) ).
fof(t32_comseq_1,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_1(A)
& v1_comseq_1(B) )
<=> v1_comseq_1(k3_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t33_comseq_1,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_1(A)
& v1_comseq_1(B) )
=> k3_comseq_1(k5_numbers,k7_comseq_1(A),k7_comseq_1(B)) = k7_comseq_1(k3_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t34_comseq_1,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_1(A)
=> k3_comseq_1(k5_numbers,k8_comseq_1(B,A),A) = B ) ) ) ).
fof(t35_comseq_1,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) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_1(A)
& v1_comseq_1(B) )
=> k3_comseq_1(k5_numbers,k8_comseq_1(C,A),k8_comseq_1(D,B)) = k8_comseq_1(k3_comseq_1(k5_numbers,C,D),k3_comseq_1(k5_numbers,A,B)) ) ) ) ) ) ).
fof(t36_comseq_1,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_1(A)
& v1_comseq_1(B) )
=> v1_comseq_1(k8_comseq_1(A,B)) ) ) ) ).
fof(t37_comseq_1,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_1(A)
& v1_comseq_1(B) )
=> k7_comseq_1(k8_comseq_1(A,B)) = k8_comseq_1(B,A) ) ) ) ).
fof(t38_comseq_1,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) )
=> k3_comseq_1(k5_numbers,A,k8_comseq_1(B,C)) = k8_comseq_1(k3_comseq_1(k5_numbers,A,B),C) ) ) ) ).
fof(t39_comseq_1,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) )
=> ( ( v1_comseq_1(A)
& v1_comseq_1(B) )
=> k8_comseq_1(C,k8_comseq_1(A,B)) = k8_comseq_1(k3_comseq_1(k5_numbers,C,B),A) ) ) ) ) ).
fof(t40_comseq_1,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) )
=> ( ( v1_comseq_1(A)
& v1_comseq_1(B) )
=> k8_comseq_1(C,A) = k8_comseq_1(k3_comseq_1(k5_numbers,C,B),k3_comseq_1(k5_numbers,A,B)) ) ) ) ) ).
fof(t41_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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_1(B)
=> ( A = k5_complex1
| v1_comseq_1(k4_comseq_1(k5_numbers,B,A)) ) ) ) ) ).
fof(t42_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
=> v1_comseq_1(k5_comseq_1(k5_numbers,A)) ) ) ).
fof(t43_comseq_1,axiom,
! [A] :
( m1_subset_1(A,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_1(B)
=> ( A = k5_complex1
| k7_comseq_1(k4_comseq_1(k5_numbers,B,A)) = k4_comseq_1(k5_numbers,k7_comseq_1(B),k12_complex1(A)) ) ) ) ) ).
fof(t44_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
=> k7_comseq_1(k5_comseq_1(k5_numbers,A)) = k4_comseq_1(k5_numbers,k7_comseq_1(A),k10_complex1(k6_complex1)) ) ) ).
fof(t45_comseq_1,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_1(A)
=> ( k5_comseq_1(k5_numbers,k8_comseq_1(B,A)) = k8_comseq_1(k5_comseq_1(k5_numbers,B),A)
& k8_comseq_1(B,k5_comseq_1(k5_numbers,A)) = k5_comseq_1(k5_numbers,k8_comseq_1(B,A)) ) ) ) ) ).
fof(t46_comseq_1,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) )
=> ( k2_comseq_1(k5_numbers,k8_comseq_1(A,B),k8_comseq_1(C,B)) = k8_comseq_1(k2_comseq_1(k5_numbers,A,C),B)
& k6_comseq_1(k5_numbers,k8_comseq_1(A,B),k8_comseq_1(C,B)) = k8_comseq_1(k6_comseq_1(k5_numbers,A,C),B) ) ) ) ) ).
fof(t47_comseq_1,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) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_1(A)
& v1_comseq_1(B) )
=> ( k2_comseq_1(k5_numbers,k8_comseq_1(C,A),k8_comseq_1(D,B)) = k8_comseq_1(k2_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,C,B),k3_comseq_1(k5_numbers,D,A)),k3_comseq_1(k5_numbers,A,B))
& k6_comseq_1(k5_numbers,k8_comseq_1(C,A),k8_comseq_1(D,B)) = k8_comseq_1(k6_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,C,B),k3_comseq_1(k5_numbers,D,A)),k3_comseq_1(k5_numbers,A,B)) ) ) ) ) ) ) ).
fof(t48_comseq_1,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) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k2_numbers)
& m2_relset_1(D,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_1(A)
& v1_comseq_1(B)
& v1_comseq_1(C) )
=> k8_comseq_1(k8_comseq_1(D,A),k8_comseq_1(B,C)) = k8_comseq_1(k3_comseq_1(k5_numbers,D,C),k3_comseq_1(k5_numbers,A,B)) ) ) ) ) ) ).
fof(t49_comseq_1,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_comseq_1(k5_numbers,k3_comseq_1(k5_numbers,A,B)) = k11_seq_1(k9_comseq_1(k5_numbers,A),k9_comseq_1(k5_numbers,B)) ) ) ).
fof(t50_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_1(A)
=> v2_relat_1(k9_comseq_1(k5_numbers,A)) ) ) ).
fof(t51_comseq_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k18_seq_1(k9_comseq_1(k5_numbers,A)) = k9_comseq_1(k5_numbers,k7_comseq_1(A)) ) ).
fof(t52_comseq_1,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_comseq_1(k5_numbers,k8_comseq_1(A,B)) = k19_seq_1(k9_comseq_1(k5_numbers,A),k9_comseq_1(k5_numbers,B)) ) ) ).
fof(t53_comseq_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> k9_comseq_1(k5_numbers,k4_comseq_1(k5_numbers,B,A)) = k14_seq_1(k9_comseq_1(k5_numbers,B),k17_complex1(A)) ) ) ).
fof(s1_comseq_1,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) = f1_s1_comseq_1(B) ) ) ).
fof(dt_k1_comseq_1,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) )
=> m1_subset_1(k1_comseq_1(A,B),k2_numbers) ) ).
fof(redefinition_k1_comseq_1,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) )
=> k1_comseq_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k2_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> ( v1_funct_1(k2_comseq_1(A,B,C))
& m2_relset_1(k2_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(commutativity_k2_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> k2_comseq_1(A,B,C) = k2_comseq_1(A,C,B) ) ).
fof(dt_k3_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> ( v1_funct_1(k3_comseq_1(A,B,C))
& m2_relset_1(k3_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(commutativity_k3_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> k3_comseq_1(A,B,C) = k3_comseq_1(A,C,B) ) ).
fof(dt_k4_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_xcmplx_0(C) )
=> ( v1_funct_1(k4_comseq_1(A,B,C))
& m2_relset_1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(dt_k5_comseq_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers) )
=> ( v1_funct_1(k5_comseq_1(A,B))
& m2_relset_1(k5_comseq_1(A,B),A,k2_numbers) ) ) ).
fof(dt_k6_comseq_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> ( v1_funct_1(k6_comseq_1(A,B,C))
& m2_relset_1(k6_comseq_1(A,B,C),A,k2_numbers) ) ) ).
fof(dt_k7_comseq_1,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_1(A))
& v1_funct_2(k7_comseq_1(A),k5_numbers,k2_numbers)
& m2_relset_1(k7_comseq_1(A),k5_numbers,k2_numbers) ) ) ).
fof(dt_k8_comseq_1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m1_relset_1(A,k5_numbers,k2_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m1_relset_1(B,k5_numbers,k2_numbers) )
=> ( v1_funct_1(k8_comseq_1(A,B))
& v1_funct_2(k8_comseq_1(A,B),k5_numbers,k2_numbers)
& m2_relset_1(k8_comseq_1(A,B),k5_numbers,k2_numbers) ) ) ).
fof(dt_k9_comseq_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers) )
=> ( v1_funct_1(k9_comseq_1(A,B))
& m2_relset_1(k9_comseq_1(A,B),A,k1_numbers) ) ) ).
%------------------------------------------------------------------------------