SET007 Axioms: SET007+154.ax
%------------------------------------------------------------------------------
% File : SET007+154 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Property of Complex Sequence and Continuity of Complex Function
% 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 : cfcont_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 3 unt; 0 def)
% Number of atoms : 674 ( 69 equ)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 620 ( 28 ~; 10 |; 321 &)
% ( 15 <=>; 246 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 6 con; 0-4 aty)
% Number of variables : 216 ( 208 !; 8 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,A))
=> k1_cfcont_1(A,B) = k5_relat_1(B,A) ) ) ) ).
fof(d2_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( r1_cfcont_1(A,B)
<=> ( r2_hidden(B,k4_relset_1(k2_numbers,k2_numbers,A))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),k4_relset_1(k2_numbers,k2_numbers,A))
& v2_comseq_2(C)
& k2_comseq_2(C) = B )
=> ( v2_comseq_2(k1_cfcont_1(A,C))
& k4_finseq_4(k2_numbers,k2_numbers,A,B) = k2_comseq_2(k1_cfcont_1(A,C)) ) ) ) ) ) ) ) ).
fof(t1_cfcont_1,axiom,
$true ).
fof(t2_cfcont_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) )
=> ( A = k6_comseq_1(k5_numbers,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_comseq_1(A,D) = k11_complex1(k1_comseq_1(B,D),k1_comseq_1(C,D)) ) ) ) ) ) ).
fof(t3_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> r1_tarski(k5_relset_1(k5_numbers,k2_numbers,k6_comseq_3(B,A)),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) ).
fof(t4_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
=> r2_hidden(k1_comseq_1(B,A),k4_relset_1(k2_numbers,k2_numbers,C)) ) ) ) ) ).
fof(t5_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( r2_hidden(A,k5_relset_1(k5_numbers,k2_numbers,B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = k1_comseq_1(B,C) ) ) ) ).
fof(t6_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> r2_hidden(k1_comseq_1(B,A),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) ).
fof(t7_cfcont_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) )
=> ( m1_comseq_3(A,B)
=> r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) ) ).
fof(t8_cfcont_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) )
=> ( ( m1_comseq_3(A,B)
& v1_comseq_1(B) )
=> v1_comseq_1(A) ) ) ) ).
fof(t9_cfcont_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,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( k5_comseq_3(C,k2_comseq_1(k5_numbers,A,B)) = k2_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B))
& k5_comseq_3(C,k6_comseq_1(k5_numbers,A,B)) = k6_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B))
& k5_comseq_3(C,k3_comseq_1(k5_numbers,A,B)) = k3_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B)) ) ) ) ) ).
fof(t10_cfcont_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,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k5_comseq_3(C,k4_comseq_1(k5_numbers,B,A)) = k4_comseq_1(k5_numbers,k5_comseq_3(C,B),A) ) ) ) ).
fof(t11_cfcont_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,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( k5_comseq_3(B,k5_comseq_1(k5_numbers,A)) = k5_comseq_1(k5_numbers,k5_comseq_3(B,A))
& k3_seqm_3(B,k9_comseq_1(k5_numbers,A)) = k9_comseq_1(k5_numbers,k5_comseq_3(B,A)) ) ) ) ).
fof(t12_cfcont_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,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k7_comseq_1(k5_comseq_3(B,A)) = k5_comseq_3(B,k7_comseq_1(A)) ) ) ).
fof(t13_cfcont_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,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k5_comseq_3(C,k8_comseq_1(A,B)) = k8_comseq_1(k5_comseq_3(C,A),k5_comseq_3(C,B)) ) ) ) ).
fof(t14_cfcont_1,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_zfmisc_1(k2_numbers))
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r2_hidden(k1_comseq_1(A,C),B) )
=> r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),B) ) ) ) ).
fof(t15_cfcont_1,axiom,
$true ).
fof(t16_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
=> k1_comseq_1(k1_cfcont_1(C,B),A) = k4_finseq_4(k2_numbers,k2_numbers,C,k1_comseq_1(B,A)) ) ) ) ) ).
fof(t17_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
=> k6_comseq_3(k1_cfcont_1(C,B),A) = k1_cfcont_1(C,k6_comseq_3(B,A)) ) ) ) ) ).
fof(t18_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k5_subset_1(k2_numbers,k4_relset_1(k2_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C)))
=> ( k1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A) = k2_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
& k1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A) = k6_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
& k1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) = k3_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A)) ) ) ) ) ) ).
fof(t19_cfcont_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
=> k1_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) = k4_comseq_1(k5_numbers,k1_cfcont_1(C,B),A) ) ) ) ) ).
fof(t20_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
=> k5_comseq_1(k5_numbers,k1_cfcont_1(B,A)) = k1_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) ) ).
fof(t21_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,B)))
=> v1_comseq_1(k1_cfcont_1(B,A)) ) ) ) ).
fof(t22_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,B)))
=> k1_cfcont_1(k2_cfunct_1(k2_numbers,B),A) = k7_comseq_1(k1_cfcont_1(B,A)) ) ) ) ).
fof(t23_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_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) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
=> k3_comseq_3(k5_comseq_3(C,k1_cfcont_1(B,A))) = k3_comseq_3(k1_cfcont_1(B,k5_comseq_3(C,A))) ) ) ) ) ).
fof(t24_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_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) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
=> k4_comseq_3(k5_comseq_3(C,k1_cfcont_1(B,A))) = k4_comseq_3(k1_cfcont_1(B,k5_comseq_3(C,A))) ) ) ) ) ).
fof(t25_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_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) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
=> k5_comseq_3(C,k1_cfcont_1(B,A)) = k1_cfcont_1(B,k5_comseq_3(C,A)) ) ) ) ) ).
fof(t26_cfcont_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,C))
& m1_comseq_3(B,A) )
=> m1_comseq_3(k1_cfcont_1(C,B),k1_cfcont_1(C,A)) ) ) ) ) ).
fof(t27_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( v1_partfun1(C,k2_numbers,k2_numbers)
=> k1_comseq_1(k1_cfcont_1(C,B),A) = k4_finseq_4(k2_numbers,k2_numbers,C,k1_comseq_1(B,A)) ) ) ) ) ).
fof(t28_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( v1_partfun1(C,k2_numbers,k2_numbers)
=> k1_cfcont_1(C,k6_comseq_3(B,A)) = k6_comseq_3(k1_cfcont_1(C,B),A) ) ) ) ) ).
fof(t29_cfcont_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)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( v1_partfun1(B,k2_numbers,k2_numbers)
& v1_partfun1(C,k2_numbers,k2_numbers) )
=> ( k1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A) = k2_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
& k1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A) = k6_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
& k1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) = k3_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A)) ) ) ) ) ) ).
fof(t30_cfcont_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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( v1_partfun1(C,k2_numbers,k2_numbers)
=> k1_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) = k4_comseq_1(k5_numbers,k1_cfcont_1(C,B),A) ) ) ) ) ).
fof(t31_cfcont_1,axiom,
! [A,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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,C,A)))
=> k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,C,A),B) = k1_cfcont_1(C,B) ) ) ) ).
fof(t32_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k2_numbers))
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k2_numbers,k2_numbers) )
=> ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,D,A)))
=> ( ( ~ r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,D,C)))
& ~ r1_tarski(A,C) )
| k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,D,A),B) = k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,D,C),B) ) ) ) ) ) ).
fof(t33_cfcont_1,axiom,
! [A,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)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,C,A)))
& k11_relset_1(k2_numbers,k2_numbers,C,k1_tarski(np__0)) = k1_xboole_0 )
=> k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,C),A),B) = k7_comseq_1(k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,C,A),B)) ) ) ) ).
fof(d3_cfcont_1,axiom,
$true ).
fof(d4_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
<=> ? [B] :
( m1_subset_1(B,k2_numbers)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,C) = B ) ) ) ) ).
fof(t34_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
<=> ? [B] :
( m1_subset_1(B,k2_numbers)
& k5_relset_1(k5_numbers,k2_numbers,A) = k1_tarski(B) ) ) ) ).
fof(t35_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k1_comseq_1(A,k1_nat_1(B,np__1)) ) ) ) ).
fof(t36_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k1_comseq_1(A,k1_nat_1(B,C)) ) ) ) ) ).
fof(t37_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k1_comseq_1(A,C) ) ) ) ) ).
fof(t38_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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(k6_comseq_3(B,A),B) ) ) ).
fof(t39_cfcont_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) )
=> ( ( m1_comseq_3(A,B)
& v2_comseq_2(B) )
=> v2_comseq_2(A) ) ) ) ).
fof(t40_cfcont_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) )
=> ( ( m1_comseq_3(A,B)
& v2_comseq_2(B) )
=> k2_comseq_2(A) = k2_comseq_2(B) ) ) ) ).
fof(t41_cfcont_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) )
=> ( v2_comseq_2(A)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& k1_comseq_1(B,D) != k1_comseq_1(A,D) ) )
| v2_comseq_2(B) ) ) ) ) ).
fof(t42_cfcont_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) )
=> ( v2_comseq_2(A)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(C,D)
& k1_comseq_1(B,D) != k1_comseq_1(A,D) ) )
| k2_comseq_2(A) = k2_comseq_2(B) ) ) ) ) ).
fof(t43_cfcont_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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(B)
=> ( v2_comseq_2(k6_comseq_3(B,A))
& k2_comseq_2(k6_comseq_3(B,A)) = k2_comseq_2(B) ) ) ) ) ).
fof(t44_cfcont_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) )
=> ( v2_comseq_2(A)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> A != k6_comseq_3(B,C) )
| v2_comseq_2(B) ) ) ) ) ).
fof(t45_cfcont_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) )
=> ( v2_comseq_2(A)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> A != k6_comseq_3(B,C) )
| k2_comseq_2(B) = k2_comseq_2(A) ) ) ) ) ).
fof(t46_cfcont_1,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)
& k2_comseq_2(A) != np__0
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ v1_comseq_1(k6_comseq_3(A,B)) ) ) ) ).
fof(t47_cfcont_1,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)
& k2_comseq_2(A) != np__0
& ! [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)
& v1_comseq_1(B) ) ) ) ) ).
fof(t48_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
=> v2_comseq_2(A) ) ) ).
fof(t49_cfcont_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) )
=> ( ( ( v5_seqm_3(B)
& r2_hidden(A,k5_relset_1(k5_numbers,k2_numbers,B)) )
| ( v5_seqm_3(B)
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& k1_comseq_1(B,C) = A ) ) )
=> k2_comseq_2(B) = A ) ) ) ).
fof(t50_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v5_seqm_3(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_comseq_2(A) = k1_comseq_1(A,B) ) ) ) ).
fof(t51_cfcont_1,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)
=> ( k2_comseq_2(A) = np__0
| ! [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)
& v1_comseq_1(B) )
=> k2_comseq_2(k7_comseq_1(B)) = k12_complex1(k2_comseq_2(A)) ) ) ) ) ) ).
fof(t52_cfcont_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) )
=> ( ( v5_seqm_3(A)
& v2_comseq_2(B) )
=> ( k2_comseq_2(k2_comseq_1(k5_numbers,A,B)) = k8_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B))
& k2_comseq_2(k6_comseq_1(k5_numbers,A,B)) = k11_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B))
& k2_comseq_2(k6_comseq_1(k5_numbers,B,A)) = k11_complex1(k2_comseq_2(B),k1_comseq_1(A,np__0))
& k2_comseq_2(k3_comseq_1(k5_numbers,A,B)) = k9_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B)) ) ) ) ) ).
fof(t53_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_cfcont_1(B,A)
<=> ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),k4_relset_1(k2_numbers,k2_numbers,B))
& v2_comseq_2(C)
& k2_comseq_2(C) = A
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_comseq_1(C,D) != A ) )
=> ( v2_comseq_2(k1_cfcont_1(B,C))
& k4_finseq_4(k2_numbers,k2_numbers,B,A) = k2_comseq_2(k1_cfcont_1(B,C)) ) ) ) ) ) ) ) ).
fof(t54_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_cfcont_1(B,A)
<=> ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k2_numbers)
=> ~ ( r2_hidden(E,k4_relset_1(k2_numbers,k2_numbers,B))
& ~ r1_xreal_0(D,k17_complex1(k11_complex1(E,A)))
& r1_xreal_0(C,k17_complex1(k11_complex1(k4_finseq_4(k2_numbers,k2_numbers,B,E),k4_finseq_4(k2_numbers,k2_numbers,B,A)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t55_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r1_cfcont_1(B,A)
& r1_cfcont_1(C,A) )
=> ( r1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A)
& r1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A)
& r1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) ) ) ) ) ) ).
fof(t56_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r1_cfcont_1(C,A)
=> r1_cfcont_1(k4_comseq_1(k2_numbers,C,B),A) ) ) ) ) ).
fof(t57_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_cfcont_1(B,A)
=> r1_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) ) ).
fof(t58_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r1_cfcont_1(B,A)
=> ( k4_finseq_4(k2_numbers,k2_numbers,B,A) = np__0
| r1_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) ) ) ).
fof(t59_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r1_cfcont_1(B,A)
& r1_cfcont_1(C,A) )
=> ( k4_finseq_4(k2_numbers,k2_numbers,B,A) = np__0
| r1_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) ) ) ).
fof(d5_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ! [B] :
( r2_cfcont_1(A,B)
<=> ( r1_tarski(B,k4_relset_1(k2_numbers,k2_numbers,A))
& ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( r2_hidden(C,B)
=> r1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,A,B),C) ) ) ) ) ) ).
fof(t60_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r2_cfcont_1(B,A)
<=> ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),A)
& v2_comseq_2(C)
& r2_hidden(k2_comseq_2(C),A) )
=> ( v2_comseq_2(k1_cfcont_1(B,C))
& k4_finseq_4(k2_numbers,k2_numbers,B,k2_comseq_2(C)) = k2_comseq_2(k1_cfcont_1(B,C)) ) ) ) ) ) ) ).
fof(t61_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r2_cfcont_1(B,A)
<=> ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
& ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r2_hidden(C,A)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,k2_numbers)
=> ~ ( r2_hidden(F,A)
& ~ r1_xreal_0(E,k17_complex1(k11_complex1(F,C)))
& r1_xreal_0(D,k17_complex1(k11_complex1(k4_finseq_4(k2_numbers,k2_numbers,B,F),k4_finseq_4(k2_numbers,k2_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t62_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r2_cfcont_1(B,A)
<=> r2_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,B,A),A) ) ) ).
fof(t63_cfcont_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(C,A)
& r1_tarski(B,A) )
=> r2_cfcont_1(C,B) ) ) ).
fof(t64_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
=> r2_cfcont_1(B,k1_tarski(A)) ) ) ) ).
fof(t65_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(B,A)
& r2_cfcont_1(C,A) )
=> ( r2_cfcont_1(k2_comseq_1(k2_numbers,B,C),A)
& r2_cfcont_1(k6_comseq_1(k2_numbers,B,C),A)
& r2_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) ) ) ) ) ).
fof(t66_cfcont_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(C,A)
& r2_cfcont_1(D,B) )
=> ( r2_cfcont_1(k2_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B))
& r2_cfcont_1(k6_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B))
& r2_cfcont_1(k3_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ) ).
fof(t67_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( r2_cfcont_1(C,B)
=> r2_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) ) ) ) ).
fof(t68_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( r2_cfcont_1(B,A)
=> r2_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) ).
fof(t69_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(B,A)
& k11_relset_1(k2_numbers,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0 )
=> r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) ).
fof(t70_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(B,A)
& k11_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,B,A),k1_tarski(np__0)) = k1_xboole_0 )
=> r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) ).
fof(t71_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_numbers,k2_numbers) )
=> ( ( r2_cfcont_1(B,A)
& k11_relset_1(k2_numbers,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0
& r2_cfcont_1(C,A) )
=> r2_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) ).
fof(t72_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ( ( v1_partfun1(A,k2_numbers,k2_numbers)
& ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k4_finseq_4(k2_numbers,k2_numbers,A,k8_complex1(B,C)) = k8_complex1(k4_finseq_4(k2_numbers,k2_numbers,A,B),k4_finseq_4(k2_numbers,k2_numbers,A,C)) ) ) )
=> ( ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ r1_cfcont_1(A,B) )
| r2_cfcont_1(A,k2_numbers) ) ) ) ).
fof(d6_cfcont_1,axiom,
! [A] :
( v1_cfcont_1(A)
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ~ ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),A)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ~ ( m1_comseq_3(C,B)
& v2_comseq_2(C)
& r2_hidden(k2_comseq_2(C),A) ) ) ) ) ) ).
fof(t73_cfcont_1,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ( ( v1_cfcont_1(k4_relset_1(k2_numbers,k2_numbers,A))
& r2_cfcont_1(A,k4_relset_1(k2_numbers,k2_numbers,A)) )
=> v1_cfcont_1(k5_relset_1(k2_numbers,k2_numbers,A)) ) ) ).
fof(t74_cfcont_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k2_numbers))
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_numbers,k2_numbers) )
=> ( ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
& v1_cfcont_1(A)
& r2_cfcont_1(B,A) )
=> v1_cfcont_1(k10_relset_1(k2_numbers,k2_numbers,B,A)) ) ) ) ).
fof(s1_cfcont_1,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( m1_subset_1(B,k2_numbers)
& p1_s1_cfcont_1(A,B) ) )
=> ? [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)
=> p1_s1_cfcont_1(B,k1_comseq_1(A,B)) ) ) ) ).
fof(dt_k1_cfcont_1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& m1_relset_1(A,k2_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(k1_cfcont_1(A,B))
& v1_funct_2(k1_cfcont_1(A,B),k5_numbers,k2_numbers)
& m2_relset_1(k1_cfcont_1(A,B),k5_numbers,k2_numbers) ) ) ).
%------------------------------------------------------------------------------