SET007 Axioms: SET007+113.ax
%------------------------------------------------------------------------------
% File : SET007+113 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Limit of a Composition of Real Functions
% 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 : limfunc4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 0 unt; 0 def)
% Number of atoms : 1307 ( 40 equ)
% Maximal formula atoms : 26 ( 16 avg)
% Number of connectives : 1611 ( 381 ~; 45 |; 685 &)
% ( 0 <=>; 500 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 19 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 0 prp; 1-3 aty)
% Number of functors : 21 ( 21 usr; 3 con; 0-6 aty)
% Number of variables : 473 ( 425 !; 48 ?)
% 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(t1_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( r1_tarski(k1_rfunct_2(C),k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)),D))
=> ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)))
& r1_tarski(k1_rfunct_2(C),D)
& r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,B))
& r1_tarski(k1_rfunct_2(C),k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),D))
& r1_tarski(k1_rfunct_2(k2_rfunct_2(B,C)),k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ) ).
fof(t2_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( r1_tarski(k1_rfunct_2(C),k4_xboole_0(k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)),D))
=> ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)))
& r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,B))
& r1_tarski(k1_rfunct_2(C),k4_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),D))
& r1_tarski(k1_rfunct_2(k2_rfunct_2(B,C)),k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ) ).
fof(t3_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v4_limfunc1(A)
& v4_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t4_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v4_limfunc1(A)
& v5_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t5_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v5_limfunc1(A)
& v7_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t6_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v5_limfunc1(A)
& v8_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t7_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v7_limfunc1(A)
& v4_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t8_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v7_limfunc1(A)
& v5_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t9_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v8_limfunc1(A)
& v7_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t10_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v8_limfunc1(A)
& v8_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ).
fof(t11_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc2(B,A)
& v4_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t12_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc2(B,A)
& v5_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t13_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc2(B,A)
& v7_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t14_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc2(B,A)
& v8_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t15_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r5_limfunc2(B,A)
& v4_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t16_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r5_limfunc2(B,A)
& v5_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t17_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r6_limfunc2(B,A)
& v7_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t18_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r6_limfunc2(B,A)
& v8_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t19_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r2_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t20_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r3_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t21_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r5_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
| r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t22_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r6_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
| r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t23_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r5_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
| r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t24_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r6_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
| r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t25_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r2_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t26_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r3_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t27_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r2_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t28_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r3_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t29_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r5_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
| v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t30_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r6_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
| v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t31_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r2_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t32_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r3_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t33_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r5_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
| v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t34_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r6_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
| v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t35_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc3(B,A)
& v4_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t36_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc3(B,A)
& v5_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t37_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc3(B,A)
& v7_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t38_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc3(B,A)
& v8_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ).
fof(t39_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r2_limfunc3(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
| r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t40_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r3_limfunc3(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
| r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t41_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r5_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
| r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t42_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r6_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
| r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t43_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r2_limfunc3(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
| r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t44_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r3_limfunc3(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
| r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t45_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r2_limfunc3(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
| v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t46_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r3_limfunc3(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
| v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t47_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r2_limfunc3(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
| v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t48_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r3_limfunc3(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
| v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t49_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r2_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t50_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r3_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t51_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r2_limfunc3(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
| r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t52_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r3_limfunc3(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
| r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) ).
fof(t53_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v4_limfunc1(A)
& v3_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_limfunc1(B) ) ) ) ) ).
fof(t54_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v5_limfunc1(A)
& v6_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_limfunc1(B) ) ) ) ) ).
fof(t55_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v7_limfunc1(A)
& v3_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_limfunc1(B) ) ) ) ) ).
fof(t56_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v8_limfunc1(A)
& v6_limfunc1(B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_limfunc1(B) ) ) ) ) ).
fof(t57_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc2(B,A)
& v3_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) ).
fof(t58_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc2(B,A)
& v6_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) ).
fof(t59_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r5_limfunc2(B,A)
& v3_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) ).
fof(t60_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r6_limfunc2(B,A)
& v6_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) ).
fof(t61_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r1_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k1_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t62_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r4_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
| ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k2_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t63_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r4_limfunc2(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
| ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k1_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t64_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r1_limfunc2(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k2_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t65_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r1_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc2(B,k5_limfunc1(A)) ) ) ) ) ) ).
fof(t66_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r4_limfunc2(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
| ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_limfunc2(B,k5_limfunc1(A)) ) ) ) ) ) ).
fof(t67_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r1_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
| ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc2(B,k6_limfunc1(A)) ) ) ) ) ) ).
fof(t68_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r4_limfunc2(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
| ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_limfunc2(B,k6_limfunc1(A)) ) ) ) ) ) ).
fof(t69_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_limfunc3(B,A)
& v3_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) ).
fof(t70_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_limfunc3(B,A)
& v6_limfunc1(C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) ).
fof(t71_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v3_limfunc1(A)
& r1_limfunc3(B,k5_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
| ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc3(B,k5_limfunc1(A)) ) ) ) ) ) ).
fof(t72_limfunc4,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( v6_limfunc1(A)
& r1_limfunc3(B,k6_limfunc1(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(C,D)
& r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
& k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
| ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
& k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc3(B,k6_limfunc1(A)) ) ) ) ) ) ).
fof(t73_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r1_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
| ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) ).
fof(t74_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc2(B,A)
& r1_limfunc3(C,k1_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,D)
& ~ r1_xreal_0(A,E)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
| ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k1_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t75_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r4_limfunc2(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
| ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) ).
fof(t76_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r4_limfunc2(B,A)
& r1_limfunc3(C,k2_limfunc2(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& ~ r1_xreal_0(E,A)
& r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
| ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k2_limfunc2(B,A)) ) ) ) ) ) ) ).
fof(t77_limfunc4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_limfunc3(B,A)
& r1_limfunc3(C,k1_limfunc3(B,A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(A,D)
& ~ r1_xreal_0(E,A)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,D)
& ~ r1_xreal_0(A,F)
& r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
& ~ r1_xreal_0(E,G)
& ~ r1_xreal_0(G,A)
& r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
& k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
| ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
& k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k1_limfunc3(B,A)) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------