SET007 Axioms: SET007+184.ax
%------------------------------------------------------------------------------
% File : SET007+184 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The One-Dimensional Lebesgue Measure
% 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 : measure7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 10 unt; 0 def)
% Number of atoms : 385 ( 42 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 334 ( 13 ~; 0 |; 171 &)
% ( 12 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 9 con; 0-5 aty)
% Number of variables : 139 ( 134 !; 5 ?)
% 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_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ~ v1_xboole_0(k9_measure7(A)) ) ).
fof(t1_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,A,B) = k1_supinf_2 )
=> k19_supinf_2(A) = k1_supinf_2 ) ) ).
fof(t2_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v6_supinf_2(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,A,B),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),B)) ) ) ) ).
fof(t3_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_supinf_1)
& m2_relset_1(C,k5_numbers,k3_supinf_1) )
=> ( ( v6_supinf_2(B,k5_numbers)
& v6_supinf_2(C,k5_numbers)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,A,D) = k2_supinf_2(k8_funct_2(k5_numbers,k3_supinf_1,B,D),k8_funct_2(k5_numbers,k3_supinf_1,C,D)) ) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),D) = k2_supinf_2(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(B),D),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(C),D)) ) ) ) ) ) ).
fof(t4_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_supinf_1)
& m2_relset_1(C,k5_numbers,k3_supinf_1) )
=> ( ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,A,D) = k2_supinf_2(k8_funct_2(k5_numbers,k3_supinf_1,B,D),k8_funct_2(k5_numbers,k3_supinf_1,C,D)) )
& v6_supinf_2(B,k5_numbers)
& v6_supinf_2(C,k5_numbers) )
=> r1_supinf_1(k19_supinf_2(A),k2_supinf_2(k19_supinf_2(B),k19_supinf_2(C))) ) ) ) ) ).
fof(t5_measure7,axiom,
$true ).
fof(t6_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) )
=> ( ( v6_supinf_2(A,k5_numbers)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,A,C),k8_funct_2(k5_numbers,k3_supinf_1,B,C)) ) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),C),k19_supinf_2(B)) ) ) ) ) ).
fof(t7_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v6_supinf_2(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),B),k19_supinf_2(A)) ) ) ) ).
fof(d1_measure7,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) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_supinf_1)
& m2_relset_1(C,k5_numbers,k3_supinf_1) )
=> ( C = k2_measure7(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,A)
=> k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k1_funct_1(B,D) )
& ( ~ r2_hidden(D,A)
=> k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k1_supinf_2 ) ) ) ) ) ) ) ).
fof(t8_measure7,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)
=> v6_supinf_2(k2_measure7(A,B),k5_numbers) ) ) ) ).
fof(t9_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v6_supinf_2(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),B),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(A),C)) ) ) ) ) ) ).
fof(t10_measure7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C != A
=> k8_funct_2(k5_numbers,k3_supinf_1,B,C) = k1_supinf_2 ) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,C)
=> k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(B),C) = k1_supinf_2 ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,C)
=> k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(B),C) = k8_funct_2(k5_numbers,k3_supinf_1,B,A) ) ) ) ) ) ) ).
fof(t11_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v6_supinf_2(A,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k5_numbers)
& m2_relset_1(C,B,k5_numbers) )
=> ( v2_funct_1(C)
=> r1_supinf_1(k19_supinf_2(k2_measure7(B,k7_funct_2(B,k5_numbers,k3_supinf_1,C,A))),k19_supinf_2(A)) ) ) ) ) ) ).
fof(t12_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) )
=> ( ( v6_supinf_2(A,k5_numbers)
& v6_supinf_2(B,k5_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k5_numbers)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,k5_numbers)
& m2_relset_1(D,C,k5_numbers) )
=> ( ( v2_funct_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,C)
=> k8_funct_2(k5_numbers,k3_supinf_1,A,E) = k1_funct_1(k7_funct_2(C,k5_numbers,k3_supinf_1,D,B),E) )
& ( ~ r2_hidden(E,C)
=> k8_funct_2(k5_numbers,k3_supinf_1,A,E) = k1_supinf_2 ) ) ) )
=> r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) ) ) ) ).
fof(d2_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ( m1_measure7(B,A)
<=> ( r1_tarski(A,k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,B)))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v5_measure5(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),B,C))
& m1_subset_1(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),B,C),k1_zfmisc_1(k6_supinf_1)) ) ) ) ) ) ) ).
fof(d3_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)))
& m2_relset_1(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) )
=> ( m2_measure7(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> m1_measure7(k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)),B,C),k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,C)) ) ) ) ) ).
fof(d4_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( m1_measure7(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_supinf_1)
& m2_relset_1(C,k5_numbers,k3_supinf_1) )
=> ( C = k4_measure7(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k5_measure5(k3_measure7(A,B,D)) ) ) ) ) ) ).
fof(t13_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( m1_measure7(B,A)
=> v6_supinf_2(k4_measure7(A,B),k5_numbers) ) ) ).
fof(d5_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_funct_2(k5_numbers,k3_supinf_1))
& m2_relset_1(C,k5_numbers,k1_funct_2(k5_numbers,k3_supinf_1)) )
=> ( C = k6_measure7(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_funct_2(k5_numbers,k3_supinf_1),C,D) = k4_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,D),k5_measure7(A,B,D)) ) ) ) ) ) ).
fof(d6_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( m1_measure7(B,A)
=> k7_measure7(A,B) = k19_supinf_2(k4_measure7(A,B)) ) ) ).
fof(d7_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k3_supinf_1)
& m2_relset_1(C,k5_numbers,k3_supinf_1) )
=> ( C = k8_measure7(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_supinf_1,C,D) = k7_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,D),k5_measure7(A,B,D)) ) ) ) ) ) ).
fof(t14_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_supinf_1(k1_supinf_2,k8_funct_2(k5_numbers,k3_supinf_1,k8_measure7(A,B),C)) ) ) ) ).
fof(d8_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
=> ( B = k9_measure7(A)
<=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ( r2_hidden(C,B)
<=> ? [D] :
( m1_measure7(D,A)
& C = k7_measure7(A,D) ) ) ) ) ) ) ).
fof(d9_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> k10_measure7(A) = k10_supinf_1(k9_measure7(A)) ) ).
fof(d10_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_zfmisc_1(k6_supinf_1),k3_supinf_1)
& m2_relset_1(A,k1_zfmisc_1(k6_supinf_1),k3_supinf_1) )
=> ( A = k11_measure7
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k6_supinf_1))
=> k8_funct_2(k1_zfmisc_1(k6_supinf_1),k3_supinf_1,A,B) = k10_supinf_1(k9_measure7(B)) ) ) ) ).
fof(d11_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k5_numbers)
& m2_relset_1(B,k5_numbers,k5_numbers) )
=> ( B = k12_measure7(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),A,C) = k4_tarski(k8_funct_2(k5_numbers,k5_numbers,B,C),D) ) ) ) ) ) ).
fof(d12_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k5_numbers)
& m2_relset_1(B,k5_numbers,k5_numbers) )
=> ( B = k13_measure7(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),A,C) = k4_tarski(k8_funct_2(k5_numbers,k5_numbers,k12_measure7(A),C),k8_funct_2(k5_numbers,k5_numbers,B,C)) ) ) ) ) ).
fof(d13_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ( k9_funcop_1(k5_numbers,k5_numbers,k5_numbers,C) = k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)
=> ! [D] :
( m1_measure7(D,k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A)))
=> ( D = k14_measure7(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k3_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A)),D,E) = k3_measure7(k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,k8_funct_2(k5_numbers,k5_numbers,k12_measure7(C),E)),k5_measure7(A,B,k8_funct_2(k5_numbers,k5_numbers,k12_measure7(C),E)),k8_funct_2(k5_numbers,k5_numbers,k13_measure7(C),E)) ) ) ) ) ) ) ) ).
fof(t15_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ( ( v2_funct_1(A)
& k9_funcop_1(k5_numbers,k5_numbers,k5_numbers,A) = k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(D,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [E] :
( m2_measure7(E,D)
=> r1_supinf_1(k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k4_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,D)),k14_measure7(D,E,A))),B),k8_funct_2(k5_numbers,k3_supinf_1,k18_supinf_2(k8_measure7(D,E)),C)) ) ) ) ) ) ) ).
fof(t16_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> r1_supinf_1(k10_supinf_1(k9_measure7(k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A)))),k19_supinf_2(k8_measure7(A,B))) ) ) ).
fof(t17_measure7,axiom,
m1_measure4(k11_measure7,k6_supinf_1) ).
fof(d14_measure7,axiom,
k16_measure7 = k3_measure4(k6_supinf_1,k15_measure7) ).
fof(d15_measure7,axiom,
k17_measure7 = k7_measure4(k6_supinf_1,k15_measure7) ).
fof(t18_measure7,axiom,
r1_measure3(k6_supinf_1,k16_measure7,k17_measure7) ).
fof(t19_measure7,axiom,
$true ).
fof(t20_measure7,axiom,
$true ).
fof(t21_measure7,axiom,
! [A] :
( r2_hidden(A,k16_measure7)
=> r2_hidden(k4_xboole_0(k6_supinf_1,A),k16_measure7) ) ).
fof(dt_m1_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ! [B] :
( m1_measure7(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(k6_supinf_1)) ) ) ) ).
fof(existence_m1_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ? [B] : m1_measure7(B,A) ) ).
fof(dt_m2_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ! [B] :
( m2_measure7(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1)))
& m2_relset_1(B,k5_numbers,k1_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1))) ) ) ) ).
fof(existence_m2_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1)) )
=> ? [B] : m2_measure7(B,A) ) ).
fof(dt_k1_measure7,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers))
& v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m1_relset_1(B,A,k5_numbers)
& m1_subset_1(C,A) )
=> m2_subset_1(k1_measure7(A,B,C),k1_numbers,k5_numbers) ) ).
fof(redefinition_k1_measure7,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers))
& v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m1_relset_1(B,A,k5_numbers)
& m1_subset_1(C,A) )
=> k1_measure7(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k2_measure7,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k3_supinf_1)
& m1_relset_1(B,A,k3_supinf_1) )
=> ( v1_funct_1(k2_measure7(A,B))
& v1_funct_2(k2_measure7(A,B),k5_numbers,k3_supinf_1)
& m2_relset_1(k2_measure7(A,B),k5_numbers,k3_supinf_1) ) ) ).
fof(dt_k3_measure7,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
& m1_measure7(B,A)
& m1_subset_1(C,k5_numbers) )
=> ( v5_measure5(k3_measure7(A,B,C))
& m1_subset_1(k3_measure7(A,B,C),k1_zfmisc_1(k6_supinf_1)) ) ) ).
fof(redefinition_k3_measure7,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
& m1_measure7(B,A)
& m1_subset_1(C,k5_numbers) )
=> k3_measure7(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k4_measure7,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
& m1_measure7(B,A) )
=> ( v1_funct_1(k4_measure7(A,B))
& v1_funct_2(k4_measure7(A,B),k5_numbers,k3_supinf_1)
& m2_relset_1(k4_measure7(A,B),k5_numbers,k3_supinf_1) ) ) ).
fof(dt_k5_measure7,axiom,
! [A,B,C] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_measure7(B,A)
& m1_subset_1(C,k5_numbers) )
=> m1_measure7(k5_measure7(A,B,C),k8_funct_2(k5_numbers,k1_zfmisc_1(k6_supinf_1),A,C)) ) ).
fof(redefinition_k5_measure7,axiom,
! [A,B,C] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_measure7(B,A)
& m1_subset_1(C,k5_numbers) )
=> k5_measure7(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k6_measure7,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_measure7(B,A) )
=> ( v1_funct_1(k6_measure7(A,B))
& v1_funct_2(k6_measure7(A,B),k5_numbers,k1_funct_2(k5_numbers,k3_supinf_1))
& m2_relset_1(k6_measure7(A,B),k5_numbers,k1_funct_2(k5_numbers,k3_supinf_1)) ) ) ).
fof(dt_k7_measure7,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
& m1_measure7(B,A) )
=> m1_subset_1(k7_measure7(A,B),k3_supinf_1) ) ).
fof(dt_k8_measure7,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_measure7(B,A) )
=> ( v1_funct_1(k8_measure7(A,B))
& v1_funct_2(k8_measure7(A,B),k5_numbers,k3_supinf_1)
& m2_relset_1(k8_measure7(A,B),k5_numbers,k3_supinf_1) ) ) ).
fof(dt_k9_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> m1_subset_1(k9_measure7(A),k1_zfmisc_1(k3_supinf_1)) ) ).
fof(dt_k10_measure7,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> m1_subset_1(k10_measure7(A),k3_supinf_1) ) ).
fof(dt_k11_measure7,axiom,
( v1_funct_1(k11_measure7)
& v1_funct_2(k11_measure7,k1_zfmisc_1(k6_supinf_1),k3_supinf_1)
& m2_relset_1(k11_measure7,k1_zfmisc_1(k6_supinf_1),k3_supinf_1) ) ).
fof(dt_k12_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ( v1_funct_1(k12_measure7(A))
& v1_funct_2(k12_measure7(A),k5_numbers,k5_numbers)
& m2_relset_1(k12_measure7(A),k5_numbers,k5_numbers) ) ) ).
fof(redefinition_k12_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> k12_measure7(A) = k15_mcart_1(A) ) ).
fof(dt_k13_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> ( v1_funct_1(k13_measure7(A))
& v1_funct_2(k13_measure7(A),k5_numbers,k5_numbers)
& m2_relset_1(k13_measure7(A),k5_numbers,k5_numbers) ) ) ).
fof(redefinition_k13_measure7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m1_relset_1(A,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> k13_measure7(A) = k16_mcart_1(A) ) ).
fof(dt_k14_measure7,axiom,
! [A,B,C] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m1_relset_1(A,k5_numbers,k1_zfmisc_1(k6_supinf_1))
& m2_measure7(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m1_relset_1(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) )
=> m1_measure7(k14_measure7(A,B,C),k5_setfam_1(k6_supinf_1,k1_measure4(k6_supinf_1,A))) ) ).
fof(dt_k15_measure7,axiom,
m1_measure4(k15_measure7,k6_supinf_1) ).
fof(redefinition_k15_measure7,axiom,
k15_measure7 = k11_measure7 ).
fof(dt_k16_measure7,axiom,
( ~ v1_xboole_0(k16_measure7)
& v1_prob_1(k16_measure7,k6_supinf_1)
& v1_measure1(k16_measure7,k6_supinf_1)
& m1_subset_1(k16_measure7,k1_zfmisc_1(k1_zfmisc_1(k6_supinf_1))) ) ).
fof(dt_k17_measure7,axiom,
m3_measure1(k17_measure7,k6_supinf_1,k16_measure7) ).
%------------------------------------------------------------------------------