SET007 Axioms: SET007+151.ax
%------------------------------------------------------------------------------
% File : SET007+151 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Series of Positive Real Numbers. 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 : supinf_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 130 ( 3 unt; 0 def)
% Number of atoms : 977 ( 158 equ)
% Maximal formula atoms : 35 ( 7 avg)
% Number of connectives : 1079 ( 232 ~; 4 |; 482 &)
% ( 40 <=>; 321 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 0 prp; 1-3 aty)
% Number of functors : 37 ( 37 usr; 9 con; 0-5 aty)
% Number of variables : 330 ( 312 !; 18 ?)
% 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_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ~ v1_xboole_0(k5_supinf_2(A,B)) ) ).
fof(fc2_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ~ v1_xboole_0(k6_supinf_2(A)) ) ).
fof(cc1_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v3_supinf_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v1_supinf_2(C,A,B)
& v2_supinf_2(C,A,B) ) ) ) ) ).
fof(cc2_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v1_supinf_2(C,A,B)
& v2_supinf_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v3_supinf_2(C,A,B) ) ) ) ) ).
fof(rc1_supinf_2,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& ~ v1_xboole_0(A)
& v1_card_4(A) ) ).
fof(rc2_supinf_2,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A) ) ).
fof(d1_supinf_2,axiom,
k1_supinf_2 = np__0 ).
fof(d2_supinf_2,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)
=> ( ( ( r2_hidden(A,k6_supinf_1)
& r2_hidden(B,k6_supinf_1) )
=> ( C = k2_supinf_2(A,B)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ? [E] :
( m1_subset_1(E,k1_numbers)
& A = D
& B = E
& C = k3_real_1(D,E) ) ) ) )
& ( ( ( A = k4_supinf_1
& B != k5_supinf_1 )
| ( B = k4_supinf_1
& A != k5_supinf_1 ) )
=> ( C = k2_supinf_2(A,B)
<=> C = k4_supinf_1 ) )
& ( ( ( A = k5_supinf_1
& B != k4_supinf_1 )
| ( B = k5_supinf_1
& A != k4_supinf_1 ) )
=> ( C = k2_supinf_2(A,B)
<=> C = k5_supinf_1 ) )
& ~ ( ~ ( r2_hidden(A,k6_supinf_1)
& r2_hidden(B,k6_supinf_1) )
& ~ ( A = k4_supinf_1
& B != k5_supinf_1 )
& ~ ( B = k4_supinf_1
& A != k5_supinf_1 )
& ~ ( A = k5_supinf_1
& B != k4_supinf_1 )
& ~ ( B = k5_supinf_1
& A != k4_supinf_1 )
& ~ ( C = k2_supinf_2(A,B)
<=> C = k1_supinf_2 ) ) ) ) ) ) ).
fof(t1_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( A = C
& B = D )
=> k2_supinf_2(A,B) = k3_real_1(C,D) ) ) ) ) ) ).
fof(t2_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ~ ( ~ r2_hidden(A,k6_supinf_1)
& A != k4_supinf_1
& A != k5_supinf_1 ) ) ).
fof(d3_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( ( r2_hidden(A,k6_supinf_1)
=> ( B = k3_supinf_2(A)
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = C
& B = k1_real_1(C) ) ) )
& ( A = k4_supinf_1
=> ( B = k3_supinf_2(A)
<=> B = k5_supinf_1 ) )
& ~ ( ~ r2_hidden(A,k6_supinf_1)
& A != k4_supinf_1
& ~ ( B = k3_supinf_2(A)
<=> B = k4_supinf_1 ) ) ) ) ) ).
fof(d4_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> k4_supinf_2(A,B) = k2_supinf_2(A,k3_supinf_2(B)) ) ) ).
fof(t3_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( A = B
=> k3_supinf_2(A) = k1_real_1(B) ) ) ) ).
fof(t4_supinf_2,axiom,
k3_supinf_2(k5_supinf_1) = k4_supinf_1 ).
fof(t5_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( A = C
& B = D )
=> k4_supinf_2(A,B) = k5_real_1(C,D) ) ) ) ) ) ).
fof(t6_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( A != k4_supinf_1
=> ( k4_supinf_2(k4_supinf_1,A) = k4_supinf_1
& k4_supinf_2(A,k4_supinf_1) = k5_supinf_1 ) ) ) ).
fof(t7_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( A != k5_supinf_1
=> ( k4_supinf_2(k5_supinf_1,A) = k5_supinf_1
& k4_supinf_2(A,k5_supinf_1) = k4_supinf_1 ) ) ) ).
fof(t8_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( k2_supinf_2(A,B) = k4_supinf_1
& A != k4_supinf_1
& B != k4_supinf_1 ) ) ) ).
fof(t9_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( k2_supinf_2(A,B) = k5_supinf_1
& A != k5_supinf_1
& B != k5_supinf_1 ) ) ) ).
fof(t10_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( k4_supinf_2(A,B) = k4_supinf_1
& A != k4_supinf_1
& B != k5_supinf_1 ) ) ) ).
fof(t11_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( k4_supinf_2(A,B) = k5_supinf_1
& A != k5_supinf_1
& B != k4_supinf_1 ) ) ) ).
fof(t12_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( ~ ( A = k4_supinf_1
& B = k5_supinf_1 )
& ~ ( A = k5_supinf_1
& B = k4_supinf_1 )
& r2_hidden(k2_supinf_2(A,B),k6_supinf_1)
& ~ ( r2_hidden(A,k6_supinf_1)
& r2_hidden(B,k6_supinf_1) ) ) ) ) ).
fof(t13_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ~ ( ~ ( A = k4_supinf_1
& B = k4_supinf_1 )
& ~ ( A = k5_supinf_1
& B = k5_supinf_1 )
& r2_hidden(k4_supinf_2(A,B),k6_supinf_1)
& ~ ( r2_hidden(A,k6_supinf_1)
& r2_hidden(B,k6_supinf_1) ) ) ) ) ).
fof(t14_supinf_2,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)
=> ~ ( ~ ( A = k4_supinf_1
& C = k5_supinf_1 )
& ~ ( A = k5_supinf_1
& C = k4_supinf_1 )
& ~ ( B = k4_supinf_1
& D = k5_supinf_1 )
& ~ ( B = k5_supinf_1
& D = k4_supinf_1 )
& r1_supinf_1(A,B)
& r1_supinf_1(C,D)
& ~ r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) ).
fof(t15_supinf_2,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)
=> ~ ( ~ ( A = k4_supinf_1
& D = k4_supinf_1 )
& ~ ( A = k5_supinf_1
& D = k5_supinf_1 )
& ~ ( B = k4_supinf_1
& C = k4_supinf_1 )
& ~ ( B = k5_supinf_1
& C = k5_supinf_1 )
& r1_supinf_1(A,B)
& r1_supinf_1(C,D)
& ~ r1_supinf_1(k4_supinf_2(A,D),k4_supinf_2(B,C)) ) ) ) ) ) ).
fof(t16_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( r1_supinf_1(A,B)
<=> r1_supinf_1(k3_supinf_2(B),k3_supinf_2(A)) ) ) ) ).
fof(t17_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( ~ ( ~ r1_supinf_1(B,A)
& r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B)) )
& ~ ( ~ r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B))
& r1_supinf_1(B,A) ) ) ) ) ).
fof(t18_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( k2_supinf_2(A,k1_supinf_2) = A
& k2_supinf_2(k1_supinf_2,A) = A ) ) ).
fof(t19_supinf_2,axiom,
( ~ r1_supinf_1(k1_supinf_2,k5_supinf_1)
& ~ r1_supinf_1(k4_supinf_1,k1_supinf_2) ) ).
fof(t20_supinf_2,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,C)
& r1_supinf_1(k1_supinf_2,A)
& B = k2_supinf_2(A,C) )
=> r1_supinf_1(A,B) ) ) ) ) ).
fof(t21_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( r2_hidden(A,k5_numbers)
=> r1_supinf_1(k1_supinf_2,A) ) ) ).
fof(d5_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
=> ( C = k5_supinf_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k3_supinf_1)
=> ( r2_hidden(D,C)
<=> ? [E] :
( m1_subset_1(E,k3_supinf_1)
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& r2_hidden(E,A)
& r2_hidden(F,B)
& D = k2_supinf_2(E,F) ) ) ) ) ) ) ) ) ).
fof(d6_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
=> ( B = k6_supinf_2(A)
<=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ( r2_hidden(C,B)
<=> ? [D] :
( m1_subset_1(D,k3_supinf_1)
& r2_hidden(D,A)
& C = k3_supinf_2(D) ) ) ) ) ) ) ).
fof(t22_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> k6_supinf_2(k6_supinf_2(A)) = A ) ).
fof(t23_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( r2_hidden(B,A)
<=> r2_hidden(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) ).
fof(t24_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ( r1_tarski(A,B)
<=> r1_tarski(k6_supinf_2(A),k6_supinf_2(B)) ) ) ) ).
fof(t25_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( r2_hidden(A,k6_supinf_1)
<=> r2_hidden(k3_supinf_2(A),k6_supinf_1) ) ) ).
fof(t26_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ~ ( ~ ( r2_hidden(k5_supinf_1,A)
& r2_hidden(k4_supinf_1,B) )
& ~ ( r2_hidden(k4_supinf_1,A)
& r2_hidden(k5_supinf_1,B) )
& ~ ( k9_supinf_1(A) = k4_supinf_1
& k9_supinf_1(B) = k5_supinf_1 )
& ~ ( k9_supinf_1(A) = k5_supinf_1
& k9_supinf_1(B) = k4_supinf_1 )
& ~ r1_supinf_1(k9_supinf_1(k5_supinf_2(A,B)),k2_supinf_2(k9_supinf_1(A),k9_supinf_1(B))) ) ) ) ).
fof(t27_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ~ ( ~ ( r2_hidden(k5_supinf_1,A)
& r2_hidden(k4_supinf_1,B) )
& ~ ( r2_hidden(k4_supinf_1,A)
& r2_hidden(k5_supinf_1,B) )
& ~ ( k10_supinf_1(A) = k4_supinf_1
& k10_supinf_1(B) = k5_supinf_1 )
& ~ ( k10_supinf_1(A) = k5_supinf_1
& k10_supinf_1(B) = k4_supinf_1 )
& ~ r1_supinf_1(k2_supinf_2(k10_supinf_1(A),k10_supinf_1(B)),k10_supinf_1(k5_supinf_2(A,B))) ) ) ) ).
fof(t28_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ( ( v4_supinf_1(A)
& v4_supinf_1(B) )
=> r1_supinf_1(k9_supinf_1(k5_supinf_2(A,B)),k2_supinf_2(k9_supinf_1(A),k9_supinf_1(B))) ) ) ) ).
fof(t29_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ( ( v5_supinf_1(A)
& v5_supinf_1(B) )
=> r1_supinf_1(k2_supinf_2(k10_supinf_1(A),k10_supinf_1(B)),k10_supinf_1(k5_supinf_2(A,B))) ) ) ) ).
fof(t30_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( m1_supinf_1(B,A)
<=> m2_supinf_1(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) ).
fof(t31_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( m2_supinf_1(B,A)
<=> m1_supinf_1(k3_supinf_2(B),k6_supinf_2(A)) ) ) ) ).
fof(t32_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> k10_supinf_1(k6_supinf_2(A)) = k3_supinf_2(k9_supinf_1(A)) ) ).
fof(t33_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> k9_supinf_1(k6_supinf_2(A)) = k3_supinf_2(k10_supinf_1(A)) ) ).
fof(d7_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> k8_supinf_2(A,B,C) = k9_supinf_1(k7_supinf_2(A,B,C)) ) ) ) ).
fof(d8_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> k9_supinf_2(A,B,C) = k10_supinf_1(k7_supinf_2(A,B,C)) ) ) ) ).
fof(d9_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,k5_supinf_2(B,C))
& m2_relset_1(F,A,k5_supinf_2(B,C)) )
=> ( F = k11_supinf_2(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,A)
=> k10_supinf_2(A,k5_supinf_2(B,C),F,G) = k2_supinf_2(k10_supinf_2(A,B,D,G),k10_supinf_2(A,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(t34_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> r1_tarski(k7_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E)),k5_supinf_2(k7_supinf_2(A,B,D),k7_supinf_2(A,C,E))) ) ) ) ) ) ).
fof(t35_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ~ ( ~ ( r2_hidden(k5_supinf_1,B)
& r2_hidden(k4_supinf_1,C) )
& ~ ( r2_hidden(k4_supinf_1,B)
& r2_hidden(k5_supinf_1,C) )
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C)
& ~ ( k8_supinf_2(A,B,D) = k4_supinf_1
& k8_supinf_2(A,C,E) = k5_supinf_1 )
& ~ ( k8_supinf_2(A,B,D) = k5_supinf_1
& k8_supinf_2(A,C,E) = k4_supinf_1 )
& ~ r1_supinf_1(k8_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E)),k2_supinf_2(k8_supinf_2(A,B,D),k8_supinf_2(A,C,E))) ) ) ) ) ) ) ).
fof(t36_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ~ ( ~ ( r2_hidden(k5_supinf_1,B)
& r2_hidden(k4_supinf_1,C) )
& ~ ( r2_hidden(k4_supinf_1,B)
& r2_hidden(k5_supinf_1,C) )
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C)
& ~ ( k9_supinf_2(A,B,D) = k4_supinf_1
& k9_supinf_2(A,C,E) = k5_supinf_1 )
& ~ ( k9_supinf_2(A,B,D) = k5_supinf_1
& k9_supinf_2(A,C,E) = k4_supinf_1 )
& ~ r1_supinf_1(k2_supinf_2(k9_supinf_2(A,B,D),k9_supinf_2(A,C,E)),k9_supinf_2(A,k5_supinf_2(B,C),k11_supinf_2(A,B,C,D,E))) ) ) ) ) ) ) ).
fof(d10_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [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,A,k6_supinf_2(B))
& m2_relset_1(D,A,k6_supinf_2(B)) )
=> ( D = k12_supinf_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k10_supinf_2(A,k6_supinf_2(B),D,E) = k3_supinf_2(k10_supinf_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t37_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> k7_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k6_supinf_2(k7_supinf_2(A,B,C)) ) ) ) ).
fof(t38_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( k9_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k3_supinf_2(k8_supinf_2(A,B,C))
& k8_supinf_2(A,k6_supinf_2(B),k12_supinf_2(A,B,C)) = k3_supinf_2(k9_supinf_2(A,B,C)) ) ) ) ) ).
fof(d11_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v1_supinf_2(C,A,B)
<=> ~ r1_supinf_1(k4_supinf_1,k8_supinf_2(A,B,C)) ) ) ) ) ).
fof(d12_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_supinf_2(C,A,B)
<=> ~ r1_supinf_1(k9_supinf_2(A,B,C),k5_supinf_1) ) ) ) ) ).
fof(d13_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v3_supinf_2(C,A,B)
<=> ( v1_supinf_2(C,A,B)
& v2_supinf_2(C,A,B) ) ) ) ) ) ).
fof(t39_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v3_supinf_2(C,A,B)
<=> ( ~ r1_supinf_1(k4_supinf_1,k8_supinf_2(A,B,C))
& ~ r1_supinf_1(k9_supinf_2(A,B,C),k5_supinf_1) ) ) ) ) ) ).
fof(t40_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v1_supinf_2(C,A,B)
<=> v2_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) ).
fof(t41_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_supinf_2(C,A,B)
<=> v1_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) ).
fof(t42_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v3_supinf_2(C,A,B)
<=> v3_supinf_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ) ) ).
fof(t43_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( r1_supinf_1(k5_supinf_1,k10_supinf_2(A,B,C,D))
& r1_supinf_1(k10_supinf_2(A,B,C,D),k4_supinf_1) ) ) ) ) ) ).
fof(t44_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( r1_tarski(B,k6_supinf_1)
=> ( ~ r1_supinf_1(k10_supinf_2(A,B,C,D),k5_supinf_1)
& ~ r1_supinf_1(k4_supinf_1,k10_supinf_2(A,B,C,D)) ) ) ) ) ) ) ).
fof(t45_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( r1_supinf_1(k9_supinf_2(A,B,C),k10_supinf_2(A,B,C,D))
& r1_supinf_1(k10_supinf_2(A,B,C,D),k8_supinf_2(A,B,C)) ) ) ) ) ) ).
fof(t46_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( r1_tarski(B,k6_supinf_1)
=> ( v1_supinf_2(C,A,B)
<=> r2_hidden(k8_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) ).
fof(t47_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( r1_tarski(B,k6_supinf_1)
=> ( v2_supinf_2(C,A,B)
<=> r2_hidden(k9_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) ).
fof(t48_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( r1_tarski(B,k6_supinf_1)
=> ( v3_supinf_2(C,A,B)
<=> ( r2_hidden(k9_supinf_2(A,B,C),k6_supinf_1)
& r2_hidden(k8_supinf_2(A,B,C),k6_supinf_1) ) ) ) ) ) ) ).
fof(t49_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ( ( r1_tarski(B,k6_supinf_1)
& r1_tarski(C,k6_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ( ( v1_supinf_2(D,A,B)
& v1_supinf_2(E,A,C) )
=> v1_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) ).
fof(t50_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ( ( r1_tarski(B,k6_supinf_1)
& r1_tarski(C,k6_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ( ( v2_supinf_2(D,A,B)
& v2_supinf_2(E,A,C) )
=> v2_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) ).
fof(t51_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1)) )
=> ( ( r1_tarski(B,k6_supinf_1)
& r1_tarski(C,k6_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ( ( v3_supinf_2(D,A,B)
& v3_supinf_2(E,A,C) )
=> v3_supinf_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ) ) ) ) ) ).
fof(t52_supinf_2,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1)
& v2_funct_1(A)
& k5_numbers = k2_relat_1(A)
& ~ v1_xboole_0(k2_relat_1(A))
& m1_subset_1(k2_relat_1(A),k1_zfmisc_1(k3_supinf_1)) ) ).
fof(d14_supinf_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_card_4(B)
<=> ~ ( ~ v1_xboole_0(B)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,A)
& m2_relset_1(C,k5_numbers,A) )
=> B != k2_relat_1(C) ) ) ) ) ) ).
fof(d15_supinf_2,axiom,
! [A] :
( v5_supinf_2(A)
<=> ! [B] :
( m1_subset_1(B,k3_supinf_1)
=> ( r2_hidden(B,A)
=> r1_supinf_1(k1_supinf_2,B) ) ) ) ).
fof(d16_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(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) )
=> ( m1_supinf_2(B,A)
<=> A = k2_relat_1(B) ) ) ) ).
fof(t53_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(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)
& k13_supinf_2(C,np__0) = k13_supinf_2(B,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,k3_supinf_1)
=> ( E = k13_supinf_2(C,D)
=> k13_supinf_2(C,k1_nat_1(D,np__1)) = k2_supinf_2(E,k13_supinf_2(B,k1_nat_1(D,np__1))) ) ) ) ) ) ) ).
fof(d17_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(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 = k14_supinf_2(A,B)
<=> ( k13_supinf_2(C,np__0) = k13_supinf_2(B,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,k3_supinf_1)
=> ( E = k13_supinf_2(C,D)
=> k13_supinf_2(C,k1_nat_1(D,np__1)) = k2_supinf_2(E,k13_supinf_2(B,k1_nat_1(D,np__1))) ) ) ) ) ) ) ) ) ).
fof(t54_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_supinf_1(k1_supinf_2,k13_supinf_2(B,C)) ) ) ) ).
fof(t55_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_supinf_1(k13_supinf_2(k14_supinf_2(A,B),C),k13_supinf_2(k14_supinf_2(A,B),k1_nat_1(C,np__1)))
& r1_supinf_1(k1_supinf_2,k13_supinf_2(k14_supinf_2(A,B),C)) ) ) ) ) ).
fof(t56_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_supinf_1(k13_supinf_2(k14_supinf_2(A,B),C),k13_supinf_2(k14_supinf_2(A,B),k1_nat_1(C,D))) ) ) ) ) ).
fof(d18_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> ( m2_supinf_2(B,A)
<=> ? [C] :
( m1_supinf_2(C,A)
& B = k2_relat_1(k14_supinf_2(A,C)) ) ) ) ) ).
fof(d19_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> k16_supinf_2(A,B) = k9_supinf_1(k15_supinf_2(k14_supinf_2(A,B))) ) ) ).
fof(d20_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> ( r1_supinf_2(A,B)
<=> r2_hidden(k16_supinf_2(A,B),k6_supinf_1) ) ) ) ).
fof(t57_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( ~ v1_xboole_0(k15_supinf_2(A))
& v1_card_4(k15_supinf_2(A))
& m1_subset_1(k15_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) ).
fof(d21_supinf_2,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) )
=> ( B = k18_supinf_2(A)
<=> ! [C] :
( m1_supinf_2(C,k17_supinf_2(A))
=> ( C = A
=> B = k14_supinf_2(k17_supinf_2(A),C) ) ) ) ) ) ).
fof(d22_supinf_2,axiom,
! [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)
<=> v5_supinf_2(k2_relat_1(B)) ) ) ).
fof(d23_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> k19_supinf_2(A) = k9_supinf_1(k17_supinf_2(k18_supinf_2(A))) ) ).
fof(t58_supinf_2,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,k8_funct_2(A,k3_supinf_1,B,C)) ) ) ) ) ).
fof(t59_supinf_2,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)
=> ( v6_supinf_2(A,k5_numbers)
=> ( r1_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,np__1)))
& r1_supinf_1(k1_supinf_2,k13_supinf_2(k18_supinf_2(A),B)) ) ) ) ) ).
fof(t60_supinf_2,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_supinf_1(k13_supinf_2(k18_supinf_2(A),B),k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,C))) ) ) ) ) ).
fof(t61_supinf_2,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(k13_supinf_2(A,C),k13_supinf_2(B,C)) ) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_supinf_1(k13_supinf_2(k18_supinf_2(A),C),k13_supinf_2(k18_supinf_2(B),C)) ) ) ) ) ).
fof(t62_supinf_2,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(k13_supinf_2(A,C),k13_supinf_2(B,C)) ) )
=> r1_supinf_1(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) ).
fof(t63_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( k13_supinf_2(k18_supinf_2(A),np__0) = k13_supinf_2(A,np__0)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ( C = k13_supinf_2(k18_supinf_2(A),B)
=> k13_supinf_2(k18_supinf_2(A),k1_nat_1(B,np__1)) = k2_supinf_2(C,k13_supinf_2(A,k1_nat_1(B,np__1))) ) ) ) ) ) ).
fof(t64_supinf_2,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)
=> k13_supinf_2(A,B) != k4_supinf_1 )
| k19_supinf_2(A) = k4_supinf_1 ) ) ) ).
fof(d24_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m2_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v7_supinf_2(A)
<=> r2_hidden(k19_supinf_2(A),k6_supinf_1) ) ) ).
fof(t65_supinf_2,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)
& k13_supinf_2(A,B) = k4_supinf_1 )
& v7_supinf_2(A) ) ) ).
fof(t66_supinf_2,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(k13_supinf_2(A,C),k13_supinf_2(B,C)) )
& v7_supinf_2(B) )
=> v7_supinf_2(A) ) ) ) ).
fof(t67_supinf_2,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)
=> k13_supinf_2(A,C) = k1_supinf_2 ) )
=> k19_supinf_2(A) = k13_supinf_2(k18_supinf_2(A),B) ) ) ) ) ).
fof(t68_supinf_2,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)
=> r2_hidden(k13_supinf_2(A,B),k6_supinf_1) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k13_supinf_2(k18_supinf_2(A),B),k6_supinf_1) ) ) ) ).
fof(t69_supinf_2,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)
=> k13_supinf_2(A,C) = k1_supinf_2 ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(C,B)
& k13_supinf_2(A,C) = k4_supinf_1 ) ) ) )
| v7_supinf_2(A) ) ) ) ).
fof(dt_m1_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m1_supinf_2(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_supinf_1)
& m2_relset_1(B,k5_numbers,k3_supinf_1) ) ) ) ).
fof(existence_m1_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ? [B] : m1_supinf_2(B,A) ) ).
fof(dt_m2_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ! [B] :
( m2_supinf_2(B,A)
=> ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) ) ) ) ).
fof(existence_m2_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> ? [B] : m2_supinf_2(B,A) ) ).
fof(redefinition_v4_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ( v4_supinf_2(B,A)
<=> v1_card_4(B) ) ) ).
fof(dt_k1_supinf_2,axiom,
m1_subset_1(k1_supinf_2,k3_supinf_1) ).
fof(dt_k2_supinf_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_supinf_1)
& m1_subset_1(B,k3_supinf_1) )
=> m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) ).
fof(commutativity_k2_supinf_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_supinf_1)
& m1_subset_1(B,k3_supinf_1) )
=> k2_supinf_2(A,B) = k2_supinf_2(B,A) ) ).
fof(dt_k3_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> m1_subset_1(k3_supinf_2(A),k3_supinf_1) ) ).
fof(involutiveness_k3_supinf_2,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> k3_supinf_2(k3_supinf_2(A)) = A ) ).
fof(dt_k4_supinf_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_supinf_1)
& m1_subset_1(B,k3_supinf_1) )
=> m1_subset_1(k4_supinf_2(A,B),k3_supinf_1) ) ).
fof(dt_k5_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
=> m1_subset_1(k5_supinf_2(A,B),k1_zfmisc_1(k3_supinf_1)) ) ).
fof(dt_k6_supinf_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
=> m1_subset_1(k6_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ).
fof(dt_k7_supinf_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ( ~ v1_xboole_0(k7_supinf_2(A,B,C))
& m1_subset_1(k7_supinf_2(A,B,C),k1_zfmisc_1(k3_supinf_1)) ) ) ).
fof(redefinition_k7_supinf_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k7_supinf_2(A,B,C) = k2_relat_1(C) ) ).
fof(dt_k8_supinf_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k8_supinf_2(A,B,C),k3_supinf_1) ) ).
fof(dt_k9_supinf_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k9_supinf_2(A,B,C),k3_supinf_1) ) ).
fof(dt_k10_supinf_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> m1_subset_1(k10_supinf_2(A,B,C,D),k3_supinf_1) ) ).
fof(redefinition_k10_supinf_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> k10_supinf_2(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k11_supinf_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B)
& v1_funct_1(E)
& v1_funct_2(E,A,C)
& m1_relset_1(E,A,C) )
=> ( v1_funct_1(k11_supinf_2(A,B,C,D,E))
& v1_funct_2(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C))
& m2_relset_1(k11_supinf_2(A,B,C,D,E),A,k5_supinf_2(B,C)) ) ) ).
fof(dt_k12_supinf_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k3_supinf_1))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ( v1_funct_1(k12_supinf_2(A,B,C))
& v1_funct_2(k12_supinf_2(A,B,C),A,k6_supinf_2(B))
& m2_relset_1(k12_supinf_2(A,B,C),A,k6_supinf_2(B)) ) ) ).
fof(dt_k13_supinf_2,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1)
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k13_supinf_2(A,B),k3_supinf_1) ) ).
fof(redefinition_k13_supinf_2,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1)
& m1_subset_1(B,k5_numbers) )
=> k13_supinf_2(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k14_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& m1_supinf_2(B,A) )
=> ( v1_funct_1(k14_supinf_2(A,B))
& v1_funct_2(k14_supinf_2(A,B),k5_numbers,k3_supinf_1)
& m2_relset_1(k14_supinf_2(A,B),k5_numbers,k3_supinf_1) ) ) ).
fof(dt_k15_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( ~ v1_xboole_0(k15_supinf_2(A))
& m1_subset_1(k15_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) ).
fof(redefinition_k15_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> k15_supinf_2(A) = k2_relat_1(A) ) ).
fof(dt_k16_supinf_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_card_4(A)
& v5_supinf_2(A)
& m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
& m1_supinf_2(B,A) )
=> m1_subset_1(k16_supinf_2(A,B),k3_supinf_1) ) ).
fof(dt_k17_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( ~ v1_xboole_0(k17_supinf_2(A))
& v1_card_4(k17_supinf_2(A))
& m1_subset_1(k17_supinf_2(A),k1_zfmisc_1(k3_supinf_1)) ) ) ).
fof(redefinition_k17_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> k17_supinf_2(A) = k2_relat_1(A) ) ).
fof(dt_k18_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> ( v1_funct_1(k18_supinf_2(A))
& v1_funct_2(k18_supinf_2(A),k5_numbers,k3_supinf_1)
& m2_relset_1(k18_supinf_2(A),k5_numbers,k3_supinf_1) ) ) ).
fof(dt_k19_supinf_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k3_supinf_1)
& m1_relset_1(A,k5_numbers,k3_supinf_1) )
=> m1_subset_1(k19_supinf_2(A),k3_supinf_1) ) ).
%------------------------------------------------------------------------------