SET007 Axioms: SET007+362.ax
%------------------------------------------------------------------------------
% File : SET007+362 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On a Mathematical Model of Programs
% 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 : ami_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 11 unt; 0 def)
% Number of atoms : 317 ( 98 equ)
% Maximal formula atoms : 57 ( 4 avg)
% Number of connectives : 269 ( 20 ~; 0 |; 109 &)
% ( 15 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 68 ( 68 usr; 25 con; 0-6 aty)
% Number of variables : 167 ( 119 !; 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(fc1_ami_2,axiom,
( ~ v1_xboole_0(k2_ami_2)
& v1_membered(k2_ami_2)
& v2_membered(k2_ami_2)
& v3_membered(k2_ami_2)
& v4_membered(k2_ami_2)
& v5_membered(k2_ami_2) ) ).
fof(fc2_ami_2,axiom,
( ~ v1_xboole_0(k3_ami_2)
& v1_membered(k3_ami_2)
& v2_membered(k3_ami_2)
& v3_membered(k3_ami_2)
& v4_membered(k3_ami_2)
& v5_membered(k3_ami_2) ) ).
fof(fc3_ami_2,axiom,
( v1_relat_1(k4_ami_2)
& ~ v1_xboole_0(k4_ami_2) ) ).
fof(fc4_ami_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k5_ami_2))
& m1_subset_1(B,k2_ami_2) )
=> ( v1_xreal_0(k1_funct_1(A,B))
& v1_int_1(k1_funct_1(A,B))
& v1_xcmplx_0(k1_funct_1(A,B)) ) ) ).
fof(d1_ami_2,axiom,
k1_ami_2 = np__0 ).
fof(t1_ami_2,axiom,
$true ).
fof(t2_ami_2,axiom,
r2_hidden(k4_tarski(np__0,k1_xboole_0),k4_ami_2) ).
fof(t3_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> r2_hidden(k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),np__6,k12_finseq_1(k3_ami_2,A)),k4_ami_2) ) ).
fof(t4_ami_2,axiom,
! [A,B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ( r2_hidden(A,k7_domain_1(k5_numbers,np__7,np__8))
=> r2_hidden(k4_tarski(A,k2_finseq_4(k5_numbers,B,C)),k4_ami_2) ) ) ) ).
fof(t5_ami_2,axiom,
! [A,B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ( r2_hidden(A,k10_domain_1(k5_numbers,np__1,np__2,np__3,np__4,np__5))
=> r2_hidden(k4_tarski(A,k2_finseq_4(k2_ami_2,B,C)),k4_ami_2) ) ) ) ).
fof(d5_ami_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)))
& m2_relset_1(A,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) )
=> ( A = k5_ami_2
<=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),A,np__0) = k3_ami_2
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),A,k1_nat_1(k2_nat_1(np__2,B),np__1)) = k4_numbers
& k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),A,k1_nat_1(k2_nat_1(np__2,B),np__2)) = k4_ami_2 ) ) ) ) ) ).
fof(t6_ami_2,axiom,
( k3_ami_2 != k4_numbers
& k4_ami_2 != k4_numbers
& k3_ami_2 != k4_ami_2 ) ).
fof(t7_ami_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k3_ami_2
<=> A = np__0 ) ) ).
fof(t8_ami_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_numbers
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) ) ) ) ).
fof(t9_ami_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_ami_2
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__2) ) ) ) ).
fof(t10_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_numbers ) ).
fof(t11_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_ami_2 ) ).
fof(t12_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> A != B ) ) ).
fof(t13_ami_2,axiom,
k5_card_3(np__0,k4_card_3(k5_ami_2)) = k3_ami_2 ).
fof(t14_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> k5_card_3(A,k4_card_3(k5_ami_2)) = k4_numbers ) ).
fof(t15_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k5_card_3(A,k4_card_3(k5_ami_2)) = k4_ami_2 ) ).
fof(d6_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> k6_ami_2(A) = k1_funct_1(A,np__0) ) ).
fof(d7_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> k7_ami_2(A,B) = k1_funct_4(A,k3_cqc_lang(np__0,B)) ) ) ).
fof(t16_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> k1_funct_1(k7_ami_2(A,B),np__0) = B ) ) ).
fof(t17_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> k1_funct_1(k7_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) ).
fof(t18_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> k1_funct_1(k7_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) ).
fof(d8_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k8_ami_2(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) ).
fof(t19_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k1_funct_1(k8_ami_2(A,B,C),np__0) = k1_funct_1(A,np__0) ) ) ) ).
fof(t20_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k1_funct_1(k8_ami_2(A,B,C),B) = C ) ) ) ).
fof(t21_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ( D != B
=> k1_funct_1(k8_ami_2(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ) ).
fof(t22_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k3_ami_2)
=> k1_funct_1(k8_ami_2(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ).
fof(d9_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),D,k2_finseq_4(k2_ami_2,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k9_ami_2(A)
<=> ? [C] :
( m2_finseq_1(C,k2_ami_2)
& C = k3_domain_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)),A)
& B = k4_finseq_4(k5_numbers,k2_ami_2,C,np__1) ) ) ) ) ) ).
fof(d10_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),D,k2_finseq_4(k2_ami_2,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k10_ami_2(A)
<=> ? [C] :
( m2_finseq_1(C,k2_ami_2)
& C = k3_domain_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)),A)
& B = k4_finseq_4(k5_numbers,k2_ami_2,C,np__2) ) ) ) ) ) ).
fof(t23_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
=> ( A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),D,k2_finseq_4(k2_ami_2,B,C))
=> ( k9_ami_2(A) = B
& k10_ami_2(A) = C ) ) ) ) ) ) ).
fof(d11_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k1_gr_cy_1(np__9))
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),C,k12_finseq_1(k3_ami_2,B)) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ( B = k11_ami_2(A)
<=> ? [C] :
( m2_finseq_1(C,k3_ami_2)
& C = k3_domain_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)),A)
& B = k4_finseq_4(k5_numbers,k3_ami_2,C,np__1) ) ) ) ) ) ).
fof(t24_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_gr_cy_1(np__9))
=> ( A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),C,k12_finseq_1(k3_ami_2,B))
=> k11_ami_2(A) = B ) ) ) ) ).
fof(d12_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),D,k2_finseq_4(k5_numbers,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ( B = k12_ami_2(A)
<=> ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& k2_finseq_4(k5_numbers,C,D) = k3_domain_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)),A)
& B = k4_finseq_4(k5_numbers,k5_numbers,k2_finseq_4(k5_numbers,C,D),np__1) ) ) ) ) ) ) ).
fof(d13_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),D,k2_finseq_4(k5_numbers,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k13_ami_2(A)
<=> ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& k2_finseq_4(k5_numbers,C,D) = k3_domain_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)),A)
& B = k4_finseq_4(k5_numbers,k5_numbers,k2_finseq_4(k5_numbers,C,D),np__2) ) ) ) ) ) ) ).
fof(t25_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__9))
=> ( A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),D,k2_finseq_4(k5_numbers,B,C))
=> ( k12_ami_2(A) = B
& k13_ami_2(A) = C ) ) ) ) ) ) ).
fof(d14_ami_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( ( ~ r1_xreal_0(B,C)
=> k14_ami_2(A,B,C,D,E) = D )
& ( r1_xreal_0(B,C)
=> k14_ami_2(A,B,C,D,E) = E ) ) ) ) ) ) ) ).
fof(d15_ami_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k15_ami_2(A) = k1_nat_1(A,np__2) ) ).
fof(d16_ami_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ! [B] :
( m1_subset_1(B,k4_card_3(k5_ami_2))
=> ( ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__1,k2_finseq_4(k2_ami_2,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k1_funct_1(B,k10_ami_2(A))),k15_ami_2(k6_ami_2(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__2,k2_finseq_4(k2_ami_2,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k2_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__3,k2_finseq_4(k2_ami_2,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k6_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__4,k2_finseq_4(k2_ami_2,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k3_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__5,k2_finseq_4(k2_ami_2,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(k8_ami_2(k8_ami_2(B,k9_ami_2(A),k5_int_1(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k10_ami_2(A),k6_int_1(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),np__6,k12_finseq_1(k3_ami_2,C)) )
=> k16_ami_2(A,B) = k7_ami_2(B,k11_ami_2(A)) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),np__7,k2_finseq_4(k5_numbers,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(B,k2_cqc_lang(k3_ami_2,k1_funct_1(B,k13_ami_2(A)),np__0,k12_ami_2(A),k15_ami_2(k6_ami_2(B)))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),np__8,k2_finseq_4(k5_numbers,C,D)) ) )
=> k16_ami_2(A,B) = k7_ami_2(B,k14_ami_2(k3_ami_2,k1_funct_1(B,k13_ami_2(A)),np__0,k12_ami_2(A),k15_ami_2(k6_ami_2(B)))) )
& ( ( ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__1,k2_finseq_4(k2_ami_2,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__2,k2_finseq_4(k2_ami_2,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__3,k2_finseq_4(k2_ami_2,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__4,k2_finseq_4(k2_ami_2,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),np__5,k2_finseq_4(k2_ami_2,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),np__6,k12_finseq_1(k3_ami_2,C)) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),np__7,k2_finseq_4(k5_numbers,C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),np__8,k2_finseq_4(k5_numbers,C,D)) ) ) )
=> k16_ami_2(A,B) = B ) ) ) ) ).
fof(d17_ami_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2)))
& m2_relset_1(A,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) )
=> ( A = k17_ami_2
<=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> ! [C] :
( m1_subset_1(C,k4_card_3(k5_ami_2))
=> k8_funct_2(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2),k1_cat_2(k4_ami_2,k4_card_3(k5_ami_2),k4_card_3(k5_ami_2),k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2)),A,B),C) = k16_ami_2(B,C) ) ) ) ) ).
fof(dt_k1_ami_2,axiom,
m2_subset_1(k1_ami_2,k5_numbers,k1_gr_cy_1(np__9)) ).
fof(dt_k2_ami_2,axiom,
m1_subset_1(k2_ami_2,k1_zfmisc_1(k5_numbers)) ).
fof(dt_k3_ami_2,axiom,
m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ).
fof(dt_k4_ami_2,axiom,
m1_subset_1(k4_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ).
fof(dt_k5_ami_2,axiom,
( v1_funct_1(k5_ami_2)
& v1_funct_2(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)))
& m2_relset_1(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) ) ).
fof(dt_k6_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k5_ami_2))
=> m2_subset_1(k6_ami_2(A),k5_numbers,k3_ami_2) ) ).
fof(dt_k7_ami_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k5_ami_2))
& m1_subset_1(B,k3_ami_2) )
=> m1_subset_1(k7_ami_2(A,B),k4_card_3(k5_ami_2)) ) ).
fof(dt_k8_ami_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(k5_ami_2))
& m1_subset_1(B,k2_ami_2)
& v1_int_1(C) )
=> m1_subset_1(k8_ami_2(A,B,C),k4_card_3(k5_ami_2)) ) ).
fof(dt_k9_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_ami_2)
=> m2_subset_1(k9_ami_2(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k10_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_ami_2)
=> m2_subset_1(k10_ami_2(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k11_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_ami_2)
=> m2_subset_1(k11_ami_2(A),k5_numbers,k3_ami_2) ) ).
fof(dt_k12_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_ami_2)
=> m2_subset_1(k12_ami_2(A),k5_numbers,k3_ami_2) ) ).
fof(dt_k13_ami_2,axiom,
! [A] :
( m1_subset_1(A,k4_ami_2)
=> m2_subset_1(k13_ami_2(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k14_ami_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> m1_subset_1(k14_ami_2(A,B,C,D,E),A) ) ).
fof(dt_k15_ami_2,axiom,
! [A] :
( m1_subset_1(A,k3_ami_2)
=> m2_subset_1(k15_ami_2(A),k5_numbers,k3_ami_2) ) ).
fof(dt_k16_ami_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_ami_2)
& m1_subset_1(B,k4_card_3(k5_ami_2)) )
=> m1_subset_1(k16_ami_2(A,B),k4_card_3(k5_ami_2)) ) ).
fof(dt_k17_ami_2,axiom,
( v1_funct_1(k17_ami_2)
& v1_funct_2(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2)))
& m2_relset_1(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) ) ).
fof(d2_ami_2,axiom,
k2_ami_2 = a_0_0_ami_2 ).
fof(d3_ami_2,axiom,
k3_ami_2 = a_0_1_ami_2 ).
fof(d4_ami_2,axiom,
k4_ami_2 = k2_xboole_0(k2_xboole_0(k2_xboole_0(k1_tarski(k4_tarski(k1_ami_2,k1_xboole_0)),a_0_2_ami_2),a_0_3_ami_2),a_0_4_ami_2) ).
fof(fraenkel_a_0_0_ami_2,axiom,
! [A] :
( r2_hidden(A,a_0_0_ami_2)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) ) ) ).
fof(fraenkel_a_0_1_ami_2,axiom,
! [A] :
( r2_hidden(A,a_0_1_ami_2)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_nat_1(np__2,B)
& ~ r1_xreal_0(B,np__0) ) ) ).
fof(fraenkel_a_0_2_ami_2,axiom,
! [A] :
( r2_hidden(A,a_0_2_ami_2)
<=> ? [B,C] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__9))
& m2_subset_1(C,k5_numbers,k3_ami_2)
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),B,k12_finseq_1(k3_ami_2,C))
& B = np__6 ) ) ).
fof(fraenkel_a_0_3_ami_2,axiom,
! [A] :
( r2_hidden(A,a_0_3_ami_2)
<=> ? [B,C,D] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__9))
& m2_subset_1(C,k5_numbers,k3_ami_2)
& m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),B,k2_finseq_4(k5_numbers,C,D))
& r2_hidden(B,k7_domain_1(k5_numbers,np__7,np__8)) ) ) ).
fof(fraenkel_a_0_4_ami_2,axiom,
! [A] :
( r2_hidden(A,a_0_4_ami_2)
<=> ? [B,C,D] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__9))
& m2_subset_1(C,k5_numbers,k2_ami_2)
& m2_subset_1(D,k5_numbers,k2_ami_2)
& A = k1_domain_1(k1_gr_cy_1(np__9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),B,k2_finseq_4(k2_ami_2,C,D))
& r2_hidden(B,k10_domain_1(k5_numbers,np__1,np__2,np__3,np__4,np__5)) ) ) ).
%------------------------------------------------------------------------------