SET007 Axioms: SET007+155.ax
%------------------------------------------------------------------------------
% File : SET007+155 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The sigma-additive Measure Theory
% 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 : measure1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 116 ( 27 unt; 0 def)
% Number of atoms : 717 ( 54 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 695 ( 94 ~; 3 |; 371 &)
% ( 13 <=>; 214 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-4 aty)
% Number of functors : 35 ( 35 usr; 9 con; 0-5 aty)
% Number of variables : 333 ( 313 !; 20 ?)
% 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_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ~ v1_xboole_0(k7_setfam_1(A,B)) ) ).
fof(cc1_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( v1_finsub_1(B)
& v1_prob_1(B,A) )
=> v2_finsub_1(B) ) ) ).
fof(cc2_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( v2_finsub_1(B)
& v1_prob_1(B,A) )
=> v1_finsub_1(B) ) ) ).
fof(rc1_measure1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(B)
& v1_finsub_1(B)
& v2_finsub_1(B)
& v1_prob_1(B,A) ) ).
fof(rc2_measure1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(B)
& v1_card_4(B) ) ).
fof(rc3_measure1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A) ) ).
fof(cc3_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A) )
=> ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A) ) ) ) ).
fof(rc4_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( m1_relset_1(C,k5_numbers,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& v1_prob_2(C) ) ) ).
fof(cc4_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A) )
=> ( ~ v1_xboole_0(B)
& v1_finsub_1(B) ) ) ) ).
fof(t1_measure1,axiom,
! [A,B] : k3_tarski(k1_enumset1(A,B,k1_xboole_0)) = k3_tarski(k2_tarski(A,B)) ).
fof(t2_measure1,axiom,
$true ).
fof(t3_measure1,axiom,
$true ).
fof(t4_measure1,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k3_supinf_1)
=> ( ( r1_supinf_1(k1_supinf_2,A)
& r1_supinf_1(k1_supinf_2,C)
& r1_supinf_1(A,B)
& r1_supinf_1(C,D) )
=> r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) ).
fof(t5_measure1,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ( ( r1_supinf_1(k1_supinf_2,B)
& r1_supinf_1(k1_supinf_2,C)
& A = k2_supinf_2(B,C) )
=> ( r1_supinf_1(k4_supinf_1,B)
| C = k4_supinf_2(A,B) ) ) ) ) ) ).
fof(t6_measure1,axiom,
$true ).
fof(t7_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ).
fof(t8_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( ~ v1_xboole_0(k1_enumset1(B,C,D))
& m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ) ).
fof(t9_measure1,axiom,
! [A] : m1_subset_1(k1_tarski(k1_xboole_0),k1_zfmisc_1(k1_zfmisc_1(A))) ).
fof(t10_measure1,axiom,
$true ).
fof(t11_measure1,axiom,
$true ).
fof(t12_measure1,axiom,
$true ).
fof(t13_measure1,axiom,
$true ).
fof(t14_measure1,axiom,
$true ).
fof(t15_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( k6_setfam_1(A,B) = k4_xboole_0(A,k5_setfam_1(A,k7_setfam_1(A,B)))
& k5_setfam_1(A,B) = k4_xboole_0(A,k6_setfam_1(A,k7_setfam_1(A,B))) ) ) ).
fof(d1_measure1,axiom,
$true ).
fof(d2_measure1,axiom,
$true ).
fof(d3_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( v1_prob_1(B,A)
<=> ! [C] :
( r2_hidden(C,B)
=> r2_hidden(k4_xboole_0(A,C),B) ) ) ) ).
fof(t16_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( v1_finsub_1(B)
& v1_prob_1(B,A) )
=> v2_finsub_1(B) ) ) ).
fof(t17_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> B = k7_setfam_1(A,B) ) ).
fof(t18_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
<=> ? [C] :
( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
& B = C
& ! [D] :
( r2_hidden(D,C)
=> ( r2_hidden(k4_xboole_0(A,D),C)
& ! [E,F] :
( ( r2_hidden(E,C)
& r2_hidden(F,C) )
=> r2_hidden(k2_xboole_0(E,F),C) ) ) ) ) ) ).
fof(t19_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
<=> ! [C] :
( r2_hidden(C,B)
=> ( r2_hidden(k4_xboole_0(A,C),B)
& ! [D,E] :
( ( r2_hidden(D,B)
& r2_hidden(E,B) )
=> r2_hidden(k3_xboole_0(D,E),B) ) ) ) ) ) ).
fof(t20_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_xboole_0(C,D),B) ) ) ).
fof(t21_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r2_hidden(k1_xboole_0,B)
& r2_hidden(A,B) ) ) ).
fof(d4_measure1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k3_supinf_1)
& m2_relset_1(B,A,k3_supinf_1) )
=> ( v6_supinf_2(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> r1_supinf_1(k1_supinf_2,k1_measure1(A,B,C)) ) ) ) ) ).
fof(t22_measure1,axiom,
$true ).
fof(t23_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1)
& v6_supinf_2(C,B)
& k1_funct_1(C,k1_xboole_0) = k1_supinf_2
& ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_xboole_0(D,E)
=> k1_funct_1(C,k4_subset_1(A,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ).
fof(d5_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1) )
=> ( m1_measure1(C,A,B)
<=> ( v6_supinf_2(C,B)
& k1_funct_1(C,k1_xboole_0) = k1_supinf_2
& ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_xboole_0(D,E)
=> k1_funct_1(C,k4_subset_1(A,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ) ) ).
fof(t24_measure1,axiom,
$true ).
fof(t25_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,E)
=> r1_supinf_1(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ).
fof(t26_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,E)
=> ( r1_supinf_1(k4_supinf_1,k1_measure1(B,C,D))
| k1_funct_1(C,k6_subset_1(A,E,D)) = k4_supinf_2(k1_measure1(B,C,E),k1_measure1(B,C,D)) ) ) ) ) ) ) ).
fof(t27_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> r1_supinf_1(k1_measure1(B,C,k2_measure1(A,B,D,E)),k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E))) ) ) ) ) ).
fof(d6_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( r1_measure1(A,B,C,D)
<=> r2_hidden(D,B) ) ) ) ).
fof(t28_measure1,axiom,
$true ).
fof(t29_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ( r1_measure1(A,B,C,k1_xboole_0)
& r1_measure1(A,B,C,A)
& ! [D,E] :
( ( r1_measure1(A,B,C,D)
& r1_measure1(A,B,C,E) )
=> ( r1_measure1(A,B,C,k4_xboole_0(A,D))
& r1_measure1(A,B,C,k2_xboole_0(D,E))
& r1_measure1(A,B,C,k3_xboole_0(D,E)) ) ) ) ) ) ).
fof(d7_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( m2_measure1(D,A,B,C)
<=> k1_measure1(B,C,D) = k1_supinf_2 ) ) ) ) ).
fof(t30_measure1,axiom,
$true ).
fof(t31_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_measure1(E,A,B,C)
=> ( r1_tarski(D,E)
=> m2_measure1(D,A,B,C) ) ) ) ) ) ).
fof(t32_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_measure1(D,A,B,C)
=> ! [E] :
( m2_measure1(E,A,B,C)
=> ( m2_measure1(k2_measure1(A,B,D,E),A,B,C)
& m2_measure1(k3_measure1(A,B,D,E),A,B,C)
& m2_measure1(k4_measure1(A,B,D,E),A,B,C) ) ) ) ) ) ).
fof(t33_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_measure1(E,A,B,C)
=> ( k1_measure1(B,C,k2_measure1(A,B,D,E)) = k1_measure1(B,C,D)
& k1_measure1(B,C,k3_measure1(A,B,D,E)) = k1_supinf_2
& k1_measure1(B,C,k4_measure1(A,B,D,E)) = k1_measure1(B,C,D) ) ) ) ) ) ).
fof(t34_measure1,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))
& k2_relat_1(C) = k1_tarski(B) ) ) ).
fof(t35_measure1,axiom,
! [A] :
? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_tarski(A))
& m2_relset_1(B,k5_numbers,k1_tarski(A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_tarski(A),B,C) = A ) ) ).
fof(t36_measure1,axiom,
$true ).
fof(t37_measure1,axiom,
$true ).
fof(t38_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,k1_zfmisc_1(A))
& m2_relset_1(E,k5_numbers,k1_zfmisc_1(A))
& k2_relat_1(E) = k1_enumset1(B,C,D)
& k1_prob_1(A,E,np__0) = B
& k1_prob_1(A,E,np__1) = C
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(F,np__1)
=> k1_prob_1(A,E,F) = D ) ) ) ) ) ) ).
fof(t39_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( ~ v1_xboole_0(k1_enumset1(B,C,k1_xboole_0))
& v1_card_4(k1_enumset1(B,C,k1_xboole_0))
& m1_subset_1(k1_enumset1(B,C,k1_xboole_0),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ).
fof(t40_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,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))
& k2_relat_1(D) = k2_tarski(B,C)
& k1_prob_1(A,D,np__0) = B
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(E,np__0)
=> k1_prob_1(A,D,E) = C ) ) ) ) ) ).
fof(t41_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( ~ v1_xboole_0(k2_tarski(B,C))
& v1_card_4(k2_tarski(B,C))
& m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ).
fof(t42_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_card_4(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ~ v1_xboole_0(k7_setfam_1(A,B))
& v1_card_4(k7_setfam_1(A,B))
& m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ).
fof(d8_measure1,axiom,
$true ).
fof(d9_measure1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( v1_measure1(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_card_4(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r1_tarski(C,B)
=> r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) ).
fof(t43_measure1,axiom,
$true ).
fof(t44_measure1,axiom,
$true ).
fof(t45_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r2_hidden(k1_xboole_0,B)
& r2_hidden(A,B) ) ) ).
fof(t46_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> ( r2_hidden(k2_xboole_0(C,D),B)
& r2_hidden(k3_xboole_0(C,D),B) ) ) ) ).
fof(t47_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_xboole_0(C,D),B) ) ) ).
fof(t48_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> B = k7_setfam_1(A,B) ) ).
fof(t49_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ( ! [C] :
( r2_hidden(C,B)
=> r2_hidden(k4_xboole_0(A,C),B) )
& ! [C] :
( ( ~ v1_xboole_0(C)
& v1_card_4(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r1_tarski(C,B)
=> r2_hidden(k6_setfam_1(A,C),B) ) ) )
<=> ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ).
fof(t50_measure1,axiom,
$true ).
fof(t51_measure1,axiom,
$true ).
fof(t52_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ( ~ v1_xboole_0(k5_measure1(A,B,C))
& v1_card_4(k5_measure1(A,B,C))
& m1_subset_1(k5_measure1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ).
fof(t53_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> m2_subset_1(k5_setfam_1(A,k5_measure1(A,B,C)),k1_zfmisc_1(A),B) ) ) ).
fof(t54_measure1,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) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,k3_supinf_1)
& m2_relset_1(D,B,k3_supinf_1) )
=> ( v6_supinf_2(D,B)
=> v6_supinf_2(k7_funct_2(A,B,k3_supinf_1,C,D),A) ) ) ) ) ) ).
fof(t55_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k3_supinf_1)
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,B,k3_supinf_1)
& m2_relset_1(E,B,k3_supinf_1)
& ! [F] :
( m2_subset_1(F,k1_zfmisc_1(A),B)
=> ( ( F = k1_xboole_0
=> k1_measure1(B,E,F) = C )
& ( F != k1_xboole_0
=> k1_measure1(B,E,F) = D ) ) ) ) ) ) ) ).
fof(t56_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1)
& ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( ( D = k1_xboole_0
=> k1_measure1(B,C,D) = k1_supinf_2 )
& ( D != k1_xboole_0
=> k1_measure1(B,C,D) = k4_supinf_1 ) ) ) ) ) ).
fof(t57_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1)
& ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> k1_measure1(B,C,D) = k1_supinf_2 ) ) ) ).
fof(t58_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1)
& v6_supinf_2(C,B)
& k1_funct_1(C,k1_xboole_0) = k1_supinf_2
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,B)
& v1_prob_2(D)
& m2_relset_1(D,k5_numbers,B) )
=> k19_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)) = k1_funct_1(C,k5_setfam_1(A,k5_measure1(A,B,D))) ) ) ) ).
fof(d10_measure1,axiom,
$true ).
fof(d11_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1) )
=> ( m3_measure1(C,A,B)
<=> ( v6_supinf_2(C,B)
& k1_funct_1(C,k1_xboole_0) = k1_supinf_2
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,B)
& v1_prob_2(D)
& m2_relset_1(D,k5_numbers,B) )
=> k19_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)) = k1_funct_1(C,k5_setfam_1(A,k5_measure1(A,B,D))) ) ) ) ) ) ).
fof(t59_measure1,axiom,
$true ).
fof(t60_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> m1_measure1(C,A,B) ) ) ).
fof(t61_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_xboole_0(D,E)
=> k1_measure1(B,C,k2_measure1(A,B,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ).
fof(t62_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,E)
=> r1_supinf_1(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ).
fof(t63_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,E)
=> ( r1_supinf_1(k4_supinf_1,k1_measure1(B,C,D))
| k1_measure1(B,C,k4_measure1(A,B,E,D)) = k4_supinf_2(k1_measure1(B,C,E),k1_measure1(B,C,D)) ) ) ) ) ) ) ).
fof(t64_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> r1_supinf_1(k1_measure1(B,C,k2_measure1(A,B,D,E)),k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E))) ) ) ) ) ).
fof(d12_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( r2_measure1(A,B,C,D)
<=> r2_hidden(D,B) ) ) ) ).
fof(t65_measure1,axiom,
$true ).
fof(t66_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ( r2_measure1(A,B,C,k1_xboole_0)
& r2_measure1(A,B,C,A)
& ! [D,E] :
( ( r2_measure1(A,B,C,D)
& r2_measure1(A,B,C,E) )
=> ( r2_measure1(A,B,C,k4_xboole_0(A,D))
& r2_measure1(A,B,C,k2_xboole_0(D,E))
& r2_measure1(A,B,C,k3_xboole_0(D,E)) ) ) ) ) ) ).
fof(t67_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_card_4(D)
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ! [E] :
( r2_hidden(E,D)
=> r2_measure1(A,B,C,E) )
=> ( r2_measure1(A,B,C,k5_setfam_1(A,D))
& r2_measure1(A,B,C,k6_setfam_1(A,D)) ) ) ) ) ) ).
fof(d13_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( m4_measure1(D,A,B,C)
<=> k1_measure1(B,C,D) = k1_supinf_2 ) ) ) ) ).
fof(t68_measure1,axiom,
$true ).
fof(t69_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m4_measure1(E,A,B,C)
=> ( r1_tarski(D,E)
=> m4_measure1(D,A,B,C) ) ) ) ) ) ).
fof(t70_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m4_measure1(D,A,B,C)
=> ! [E] :
( m4_measure1(E,A,B,C)
=> ( m4_measure1(k2_measure1(A,B,D,E),A,B,C)
& m4_measure1(k3_measure1(A,B,D,E),A,B,C)
& m4_measure1(k4_measure1(A,B,D,E),A,B,C) ) ) ) ) ) ).
fof(t71_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m4_measure1(E,A,B,C)
=> ( k1_measure1(B,C,k2_measure1(A,B,D,E)) = k1_measure1(B,C,D)
& k1_measure1(B,C,k3_measure1(A,B,D,E)) = k1_supinf_2
& k1_measure1(B,C,k4_measure1(A,B,D,E)) = k1_measure1(B,C,D) ) ) ) ) ) ).
fof(s1_measure1,axiom,
( ? [A] :
( r1_tarski(A,f1_s1_measure1)
& p1_s1_measure1(A) )
=> ? [A] :
( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(f1_s1_measure1)))
& ! [B] :
( r2_hidden(B,A)
<=> ( r1_tarski(B,f1_s1_measure1)
& p1_s1_measure1(B) ) ) ) ) ).
fof(dt_m1_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m1_measure1(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1) ) ) ) ).
fof(existence_m1_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] : m1_measure1(C,A,B) ) ).
fof(dt_m2_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_measure1(C,A,B) )
=> ! [D] :
( m2_measure1(D,A,B,C)
=> m2_subset_1(D,k1_zfmisc_1(A),B) ) ) ).
fof(existence_m2_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_measure1(C,A,B) )
=> ? [D] : m2_measure1(D,A,B,C) ) ).
fof(dt_m3_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( m3_measure1(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,B,k3_supinf_1)
& m2_relset_1(C,B,k3_supinf_1) ) ) ) ).
fof(existence_m3_measure1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ? [C] : m3_measure1(C,A,B) ) ).
fof(dt_m4_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m3_measure1(C,A,B) )
=> ! [D] :
( m4_measure1(D,A,B,C)
=> m2_subset_1(D,k1_zfmisc_1(A),B) ) ) ).
fof(existence_m4_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m3_measure1(C,A,B) )
=> ? [D] : m4_measure1(D,A,B,C) ) ).
fof(dt_k1_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k3_supinf_1)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,A) )
=> m1_subset_1(k1_measure1(A,B,C),k3_supinf_1) ) ).
fof(redefinition_k1_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k3_supinf_1)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,A) )
=> k1_measure1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k2_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_finsub_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> m2_subset_1(k2_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ).
fof(commutativity_k2_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_finsub_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k2_measure1(A,B,C,D) = k2_measure1(A,B,D,C) ) ).
fof(idempotence_k2_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_finsub_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k2_measure1(A,B,C,C) = C ) ).
fof(redefinition_k2_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_finsub_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k2_measure1(A,B,C,D) = k2_xboole_0(C,D) ) ).
fof(dt_k3_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> m2_subset_1(k3_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ).
fof(commutativity_k3_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k3_measure1(A,B,C,D) = k3_measure1(A,B,D,C) ) ).
fof(idempotence_k3_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k3_measure1(A,B,C,C) = C ) ).
fof(redefinition_k3_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k3_measure1(A,B,C,D) = k3_xboole_0(C,D) ) ).
fof(dt_k4_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> m2_subset_1(k4_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) ).
fof(redefinition_k4_measure1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v2_finsub_1(B)
& v1_prob_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,B)
& m1_subset_1(D,B) )
=> k4_measure1(A,B,C,D) = k4_xboole_0(C,D) ) ).
fof(dt_k5_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m1_relset_1(C,k5_numbers,B) )
=> ( ~ v1_xboole_0(k5_measure1(A,B,C))
& m1_subset_1(k5_measure1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ).
fof(redefinition_k5_measure1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m1_relset_1(C,k5_numbers,B) )
=> k5_measure1(A,B,C) = k2_relat_1(C) ) ).
%------------------------------------------------------------------------------