SET007 Axioms: SET007+899.ax
%------------------------------------------------------------------------------
% File : SET007+899 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Limit of Sequence of Subsets
% 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 : setlim_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 126 ( 2 unt; 0 def)
% Number of atoms : 706 ( 114 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 590 ( 10 ~; 3 |; 263 &)
% ( 21 <=>; 293 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 5 con; 0-4 aty)
% Number of variables : 406 ( 393 !; 13 ?)
% 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(fc1_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_relat_1(k1_setlim_1(A,B))
& v1_funct_1(k1_setlim_1(A,B))
& v1_funct_2(k1_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A))
& v3_prob_1(k1_setlim_1(A,B),A) ) ) ).
fof(fc2_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_relat_1(k2_setlim_1(A,B))
& v1_funct_1(k2_setlim_1(A,B))
& v1_funct_2(k2_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A))
& v2_prob_1(k2_setlim_1(A,B),A) ) ) ).
fof(fc3_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> ( v1_relat_1(k5_setlim_1(A,B,C))
& v1_funct_1(k5_setlim_1(A,B,C))
& v1_funct_2(k5_setlim_1(A,B,C),k5_numbers,k1_zfmisc_1(A))
& v2_prob_1(k5_setlim_1(A,B,C),A) ) ) ).
fof(fc4_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> ( v1_relat_1(k4_setlim_1(A,B,C))
& v1_funct_1(k4_setlim_1(A,B,C))
& v1_funct_2(k4_setlim_1(A,B,C),k5_numbers,k1_zfmisc_1(A))
& v3_prob_1(k4_setlim_1(A,B,C),A) ) ) ).
fof(t1_setlim_1,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
=> C = B )
=> ( A = k1_xboole_0
| k3_tarski(A) = B ) ) ).
fof(t2_setlim_1,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
=> C = B )
=> ( A = k1_xboole_0
| k1_setfam_1(A) = B ) ) ).
fof(t7_setlim_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ( r2_hidden(A,k5_relset_1(k5_numbers,B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,B,C,D) ) ) ) ) ).
fof(t8_setlim_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( k5_relset_1(A,B,C) != k1_xboole_0
& C != k1_xboole_0 ) ) ) ) ).
fof(t11_setlim_1,axiom,
$true ).
fof(t12_setlim_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( r2_hidden(B,k6_setfam_1(A,k5_relset_1(k5_numbers,k1_zfmisc_1(A),C)))
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r2_hidden(B,k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D)) ) ) ) ).
fof(t13_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k4_prob_1(A,B) = k6_setfam_1(A,k5_relset_1(k5_numbers,k1_zfmisc_1(A),B)) ) ).
fof(t14_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> r1_tarski(k4_prob_1(A,B),k1_kurato_2(A,B)) ) ).
fof(t15_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = B )
=> k1_kurato_2(A,C) = B ) ) ) ).
fof(t16_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = B )
=> k4_prob_1(A,C) = B ) ) ) ).
fof(t17_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v5_seqm_3(B)
=> k1_kurato_2(A,B) = k4_prob_1(A,B) ) ) ).
fof(d1_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_setlim_1(B,A)
<=> ( v3_prob_1(B,A)
| v2_prob_1(B,A) ) ) ) ).
fof(t22_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,B),np__0) = k4_prob_1(A,B) ) ).
fof(t23_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,B),np__0) = k1_kurato_2(A,B) ) ).
fof(t24_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(B)) )
=> ( r2_hidden(C,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,D),A))
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(C,k8_funct_2(k5_numbers,k1_zfmisc_1(B),D,k1_nat_1(A,E))) ) ) ) ) ).
fof(t25_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(B)) )
=> ( r2_hidden(C,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,D),A))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r2_hidden(C,k8_funct_2(k5_numbers,k1_zfmisc_1(B),D,k1_nat_1(A,E))) ) ) ) ) ).
fof(t26_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A) = k5_subset_1(B,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),k1_nat_1(A,np__1)),k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A)) ) ) ).
fof(t27_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A) = k4_subset_1(B,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),k1_nat_1(A,np__1)),k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A)) ) ) ).
fof(t28_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> v3_prob_1(k1_setlim_1(A,B),A) ) ).
fof(t29_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> v2_prob_1(k2_setlim_1(A,B),A) ) ).
fof(t30_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_setlim_1(k1_setlim_1(A,B),A)
& v1_setlim_1(k2_setlim_1(A,B),A) ) ) ).
fof(t31_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> r1_tarski(k4_prob_1(B,C),k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A)) ) ) ).
fof(t32_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A),k1_kurato_2(B,C)) ) ) ).
fof(t34_setlim_1,axiom,
$true ).
fof(t35_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k1_kurato_2(A,B) = k3_subset_1(A,k4_prob_1(A,k3_prob_1(A,B))) ) ).
fof(t36_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A) = k3_subset_1(B,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,k3_prob_1(B,C)),A)) ) ) ).
fof(t37_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A) = k3_subset_1(B,k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,k3_prob_1(B,C)),A)) ) ) ).
fof(t38_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k3_prob_1(A,k1_setlim_1(A,B)) = k2_setlim_1(A,k3_prob_1(A,B)) ) ).
fof(t39_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k3_prob_1(A,k2_setlim_1(A,B)) = k1_setlim_1(A,k3_prob_1(A,B)) ) ).
fof(t40_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,E) = k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,E)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,C),E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,D),E)),k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,B),E)) ) ) ) ) ) ).
fof(t41_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,E) = k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,E)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,B),E) = k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,C),E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,D),E)) ) ) ) ) ) ).
fof(t42_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,E) = k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,E)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,B),E) = k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,C),E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,D),E)) ) ) ) ) ) ).
fof(t43_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),B,E) = k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,E)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,B),E),k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,C),E),k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,D),E))) ) ) ) ) ) ).
fof(t44_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ( v5_seqm_3(C)
& k1_yellow_6(C) = B )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k1_setlim_1(A,C),D) = B ) ) ) ) ).
fof(t45_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ( v5_seqm_3(C)
& k1_yellow_6(C) = B )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),k2_setlim_1(A,C),D) = B ) ) ) ) ).
fof(t46_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v3_prob_1(C,B)
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A),k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),k1_nat_1(A,np__1))) ) ) ) ).
fof(t47_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v3_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A) = k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),k1_nat_1(A,np__1)) ) ) ) ).
fof(t48_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v3_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A) = k1_kurato_2(B,C) ) ) ) ).
fof(t49_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_prob_1(B,A)
=> k4_prob_1(A,k2_setlim_1(A,B)) = k1_kurato_2(A,B) ) ) ).
fof(t50_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v3_prob_1(C,B)
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A),k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),k1_nat_1(A,np__1))) ) ) ) ).
fof(t51_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v3_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A) = k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A) ) ) ) ).
fof(t52_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_prob_1(B,A)
=> k1_setlim_1(A,B) = B ) ) ).
fof(t53_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v2_prob_1(C,B)
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),k1_nat_1(A,np__1)),k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A)) ) ) ) ).
fof(t54_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v2_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k2_setlim_1(B,C),A) = k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A) ) ) ) ).
fof(t55_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_prob_1(B,A)
=> k2_setlim_1(A,B) = B ) ) ).
fof(t56_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v2_prob_1(C,B)
=> r1_tarski(k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),k1_nat_1(A,np__1)),k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,A)) ) ) ) ).
fof(t57_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v2_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A) = k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),k1_nat_1(A,np__1)) ) ) ) ).
fof(t58_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B)) )
=> ( v2_prob_1(C,B)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(B),k1_setlim_1(B,C),A) = k4_prob_1(B,C) ) ) ) ).
fof(t59_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_prob_1(B,A)
=> k1_kurato_2(A,k1_setlim_1(A,B)) = k4_prob_1(A,B) ) ) ).
fof(d4_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k4_kurato_2(A,B) = k1_kurato_2(A,k1_setlim_1(A,B)) ) ).
fof(d5_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k5_kurato_2(A,B) = k4_prob_1(A,k2_setlim_1(A,B)) ) ).
fof(d6_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_kurato_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( C = k3_setlim_1(A,B)
<=> ( C = k5_kurato_2(A,B)
& C = k4_kurato_2(A,B) ) ) ) ) ) ).
fof(t60_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> r1_tarski(k4_prob_1(A,B),k4_kurato_2(A,B)) ) ).
fof(t61_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k4_kurato_2(A,B) = k3_setlim_1(A,k1_setlim_1(A,B)) ) ).
fof(t62_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k5_kurato_2(A,B) = k3_setlim_1(A,k2_setlim_1(A,B)) ) ).
fof(t63_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> k5_kurato_2(A,B) = k3_subset_1(A,k4_kurato_2(A,k3_prob_1(A,B))) ) ).
fof(t64_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ( v5_seqm_3(C)
& k1_yellow_6(C) = B )
=> ( v3_kurato_2(C,A)
& k3_setlim_1(A,C) = B
& k4_kurato_2(A,C) = B
& k5_kurato_2(A,C) = B ) ) ) ) ).
fof(t65_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_prob_1(B,A)
=> k5_kurato_2(A,B) = k1_kurato_2(A,B) ) ) ).
fof(t66_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_prob_1(B,A)
=> k4_kurato_2(A,B) = k1_kurato_2(A,B) ) ) ).
fof(t67_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_prob_1(B,A)
=> k5_kurato_2(A,B) = k4_prob_1(A,B) ) ) ).
fof(t68_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_prob_1(B,A)
=> k4_kurato_2(A,B) = k4_prob_1(A,B) ) ) ).
fof(t69_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v3_prob_1(B,A)
=> ( v3_kurato_2(B,A)
& k3_setlim_1(A,B) = k1_kurato_2(A,B) ) ) ) ).
fof(t70_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v2_prob_1(B,A)
=> ( v3_kurato_2(B,A)
& k3_setlim_1(A,B) = k4_prob_1(A,B) ) ) ) ).
fof(t71_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_setlim_1(B,A)
=> v3_kurato_2(B,A) ) ) ).
fof(d7_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v5_seqm_3(C)
<=> ? [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,E) = D ) ) ) ) ) ).
fof(d8_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k4_setlim_1(A,B,C) = k1_setlim_1(A,C) ) ) ).
fof(d9_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k5_setlim_1(A,B,C) = k2_setlim_1(A,C) ) ) ).
fof(t72_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> v2_prob_1(k5_setlim_1(A,B,C),A) ) ) ).
fof(t73_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> v3_prob_1(k4_setlim_1(A,B,C),A) ) ) ).
fof(d10_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k6_setlim_1(A,B,C) = k1_kurato_2(A,k4_setlim_1(A,B,C)) ) ) ).
fof(d11_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k7_setlim_1(A,B,C) = k4_prob_1(A,k5_setlim_1(A,B,C)) ) ) ).
fof(d12_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v3_setlim_1(C,A,B)
<=> k7_setlim_1(A,B,C) = k6_setlim_1(A,B,C) ) ) ) ).
fof(d13_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v3_setlim_1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( D = k8_setlim_1(A,B,C)
<=> ( D = k7_setlim_1(A,B,C)
& D = k6_setlim_1(A,B,C) ) ) ) ) ) ) ).
fof(t74_setlim_1,axiom,
! [A,B,C] :
( m1_prob_1(C,A)
=> ! [D] :
( m2_prob_1(D,A,C)
=> ( r2_hidden(B,k7_setlim_1(A,C,D))
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r2_hidden(B,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,k1_nat_1(E,F))) ) ) ) ) ) ).
fof(t75_setlim_1,axiom,
! [A,B,C] :
( m1_prob_1(C,A)
=> ! [D] :
( m2_prob_1(D,A,C)
=> ( r2_hidden(B,k6_setlim_1(A,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> r2_hidden(B,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,k1_nat_1(E,F))) ) ) ) ) ) ).
fof(t76_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> r1_tarski(k4_prob_1(A,C),k6_setlim_1(A,B,C)) ) ) ).
fof(t77_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> r1_tarski(k7_setlim_1(A,B,C),k1_kurato_2(A,C)) ) ) ).
fof(t78_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> r1_tarski(k6_setlim_1(A,B,C),k7_setlim_1(A,B,C)) ) ) ).
fof(d14_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k9_setlim_1(A,B,C) = k3_prob_1(A,C) ) ) ).
fof(t79_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k6_setlim_1(A,B,C) = k3_subset_1(A,k7_setlim_1(A,B,k9_setlim_1(A,B,C))) ) ) ).
fof(t80_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> k7_setlim_1(A,B,C) = k3_subset_1(A,k6_setlim_1(A,B,k9_setlim_1(A,B,C))) ) ) ).
fof(t81_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ! [D] :
( m2_prob_1(D,A,B)
=> ! [E] :
( m2_prob_1(E,A,B)
=> ( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,F) = k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,F),k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F)) )
=> r1_tarski(k4_subset_1(A,k6_setlim_1(A,B,D),k6_setlim_1(A,B,E)),k6_setlim_1(A,B,C)) ) ) ) ) ) ).
fof(t82_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ! [D] :
( m2_prob_1(D,A,B)
=> ! [E] :
( m2_prob_1(E,A,B)
=> ( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,F) = k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,F),k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F)) )
=> k6_setlim_1(A,B,C) = k5_subset_1(A,k6_setlim_1(A,B,D),k6_setlim_1(A,B,E)) ) ) ) ) ) ).
fof(t83_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ! [D] :
( m2_prob_1(D,A,B)
=> ! [E] :
( m2_prob_1(E,A,B)
=> ( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,F) = k4_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,F),k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F)) )
=> k7_setlim_1(A,B,C) = k4_subset_1(A,k7_setlim_1(A,B,D),k7_setlim_1(A,B,E)) ) ) ) ) ) ).
fof(t84_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ! [D] :
( m2_prob_1(D,A,B)
=> ! [E] :
( m2_prob_1(E,A,B)
=> ( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,F) = k5_subset_1(A,k8_funct_2(k5_numbers,k1_zfmisc_1(A),D,F),k8_funct_2(k5_numbers,k1_zfmisc_1(A),E,F)) )
=> r1_tarski(k7_setlim_1(A,B,C),k5_subset_1(A,k7_setlim_1(A,B,D),k7_setlim_1(A,B,E))) ) ) ) ) ) ).
fof(t85_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_prob_1(C,A)
=> ! [D] :
( m2_prob_1(D,A,C)
=> ( ( v5_seqm_3(D)
& k1_yellow_6(D) = B )
=> ( v3_setlim_1(D,A,C)
& k8_setlim_1(A,C,D) = B
& k6_setlim_1(A,C,D) = B
& k7_setlim_1(A,C,D) = B ) ) ) ) ) ).
fof(t86_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v3_prob_1(C,A)
=> k7_setlim_1(A,B,C) = k1_kurato_2(A,C) ) ) ) ).
fof(t87_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v3_prob_1(C,A)
=> k6_setlim_1(A,B,C) = k1_kurato_2(A,C) ) ) ) ).
fof(t88_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v3_prob_1(C,A)
=> ( v3_setlim_1(C,A,B)
& k8_setlim_1(A,B,C) = k1_kurato_2(A,C) ) ) ) ) ).
fof(t89_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v2_prob_1(C,A)
=> k7_setlim_1(A,B,C) = k4_prob_1(A,C) ) ) ) ).
fof(t90_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v2_prob_1(C,A)
=> k6_setlim_1(A,B,C) = k4_prob_1(A,C) ) ) ) ).
fof(t91_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v2_prob_1(C,A)
=> ( v3_setlim_1(C,A,B)
& k8_setlim_1(A,B,C) = k4_prob_1(A,C) ) ) ) ) ).
fof(t92_setlim_1,axiom,
! [A,B] :
( m1_prob_1(B,A)
=> ! [C] :
( m2_prob_1(C,A,B)
=> ( v1_setlim_1(C,A)
=> v3_setlim_1(C,A,B) ) ) ) ).
fof(redefinition_v2_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> ( v2_setlim_1(C,A,B)
<=> v5_seqm_3(C) ) ) ).
fof(dt_k1_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_funct_1(k1_setlim_1(A,B))
& v1_funct_2(k1_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(k1_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A)) ) ) ).
fof(dt_k2_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ( v1_funct_1(k2_setlim_1(A,B))
& v1_funct_2(k2_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(k2_setlim_1(A,B),k5_numbers,k1_zfmisc_1(A)) ) ) ).
fof(dt_k3_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> m1_subset_1(k3_setlim_1(A,B),k1_zfmisc_1(A)) ) ).
fof(dt_k4_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_prob_1(k4_setlim_1(A,B,C),A,B) ) ).
fof(dt_k5_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_prob_1(k5_setlim_1(A,B,C),A,B) ) ).
fof(dt_k6_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_subset_1(k6_setlim_1(A,B,C),k1_zfmisc_1(A),B) ) ).
fof(dt_k7_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_subset_1(k7_setlim_1(A,B,C),k1_zfmisc_1(A),B) ) ).
fof(dt_k8_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_subset_1(k8_setlim_1(A,B,C),k1_zfmisc_1(A),B) ) ).
fof(dt_k9_setlim_1,axiom,
! [A,B,C] :
( ( m1_prob_1(B,A)
& m2_prob_1(C,A,B) )
=> m2_prob_1(k9_setlim_1(A,B,C),A,B) ) ).
fof(t3_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,A)
& m2_relset_1(B,k5_numbers,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> a_3_0_setlim_1(A,B,C) != k1_xboole_0 ) ) ).
fof(t4_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> r2_hidden(k8_funct_2(k5_numbers,C,D,k1_nat_1(A,B)),a_3_1_setlim_1(A,C,D)) ) ) ) ).
fof(t5_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> a_3_1_setlim_1(A,B,C) = k2_xboole_0(a_3_2_setlim_1(A,B,C),k1_tarski(k8_funct_2(k5_numbers,B,C,A))) ) ) ).
fof(t6_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,B)
& m2_relset_1(D,k5_numbers,B) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(C,k8_funct_2(k5_numbers,B,D,k1_nat_1(A,E))) )
<=> ! [E] :
( r2_hidden(E,a_3_1_setlim_1(A,B,D))
=> r2_hidden(C,E) ) ) ) ) ).
fof(t9_setlim_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,A)
& m2_relset_1(B,k5_numbers,A) )
=> k5_relset_1(k5_numbers,A,B) = a_2_0_setlim_1(A,B) ) ) ).
fof(t10_setlim_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> k5_relset_1(k5_numbers,B,k3_kurato_2(B,C,A)) = a_3_3_setlim_1(A,B,C) ) ) ) ).
fof(t18_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ( v5_seqm_3(C)
& k1_yellow_6(C) = B )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_tarski(a_3_4_setlim_1(A,C,D)) = B ) ) ) ) ).
fof(t19_setlim_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( ( v5_seqm_3(C)
& k1_yellow_6(C) = B )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_setfam_1(a_3_4_setlim_1(A,C,D)) = B ) ) ) ) ).
fof(t20_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( E = a_3_4_setlim_1(A,B,D)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = k1_setfam_1(E) ) ) ) ) ).
fof(t21_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( E = a_3_4_setlim_1(A,B,D)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = k3_tarski(E) ) ) ) ) ).
fof(d2_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( C = k1_setlim_1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( E = a_3_4_setlim_1(A,B,D)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = k1_setfam_1(E) ) ) ) ) ) ).
fof(d3_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
=> ( C = k2_setlim_1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( E = a_3_4_setlim_1(A,B,D)
=> k8_funct_2(k5_numbers,k1_zfmisc_1(A),C,D) = k3_tarski(E) ) ) ) ) ) ).
fof(t33_setlim_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> m1_subset_1(a_3_4_setlim_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ).
fof(fraenkel_a_3_0_setlim_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_3_0_setlim_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,B,C,E)
& r1_xreal_0(D,E) ) ) ) ).
fof(fraenkel_a_3_1_setlim_1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> ( r2_hidden(A,a_3_1_setlim_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,C,D,E)
& r1_xreal_0(B,E) ) ) ) ).
fof(fraenkel_a_3_2_setlim_1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> ( r2_hidden(A,a_3_2_setlim_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,C,D,E)
& r1_xreal_0(k1_nat_1(B,np__1),E) ) ) ) ).
fof(fraenkel_a_2_0_setlim_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ( r2_hidden(A,a_2_0_setlim_1(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,B,C,D)
& r1_xreal_0(np__0,D) ) ) ) ).
fof(fraenkel_a_3_3_setlim_1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> ( r2_hidden(A,a_3_3_setlim_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,C,D,E)
& r1_xreal_0(B,E) ) ) ) ).
fof(fraenkel_a_3_4_setlim_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_zfmisc_1(B))
& m2_relset_1(C,k5_numbers,k1_zfmisc_1(B))
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_3_4_setlim_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k8_funct_2(k5_numbers,k1_zfmisc_1(B),C,E)
& r1_xreal_0(D,E) ) ) ) ).
%------------------------------------------------------------------------------