SET007 Axioms: SET007+378.ax
%------------------------------------------------------------------------------
% File : SET007+378 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Remarks on the Simple Concrete Model of Computer
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 123 ( 17 unt; 0 def)
% Number of atoms : 659 ( 113 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 633 ( 97 ~; 1 |; 234 &)
% ( 16 <=>; 285 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-4 aty)
% Number of functors : 89 ( 89 usr; 26 con; 0-8 aty)
% Number of variables : 302 ( 295 !; 7 ?)
% 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_3,axiom,
( ~ v3_struct_0(k1_ami_3)
& v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(fc2_ami_3,axiom,
( ~ v3_struct_0(k1_ami_3)
& v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(fc3_ami_3,axiom,
( ~ v3_struct_0(k1_ami_3)
& v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v4_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(fc4_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ~ v1_xboole_0(k14_ami_1(A,B)) ) ).
fof(rc1_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_ami_3(C,A,B) ) ) ).
fof(fc5_ami_3,axiom,
( ~ v3_struct_0(k1_ami_3)
& v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v4_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v7_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v8_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(d1_ami_3,axiom,
k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,np__0,k3_ami_2,k1_gr_cy_1(np__9),k4_ami_2,k5_ami_2,k17_ami_2) ).
fof(t1_ami_3,axiom,
v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ).
fof(t2_ami_3,axiom,
v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ).
fof(d2_ami_3,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_ami_3))
=> ( m1_ami_3(A)
<=> r2_hidden(A,k2_ami_2) ) ) ).
fof(d3_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k3_ami_3(A,B) = k4_tarski(np__1,k10_finseq_1(A,B)) ) ) ).
fof(d4_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k4_ami_3(A,B) = k4_tarski(np__2,k10_finseq_1(A,B)) ) ) ).
fof(d5_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k5_ami_3(A,B) = k4_tarski(np__3,k10_finseq_1(A,B)) ) ) ).
fof(d6_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k6_ami_3(A,B) = k4_tarski(np__4,k10_finseq_1(A,B)) ) ) ).
fof(d7_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k7_ami_3(A,B) = k4_tarski(np__5,k10_finseq_1(A,B)) ) ) ).
fof(d8_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k8_ami_3(A) = k4_tarski(np__6,k12_finseq_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3),A)) ) ).
fof(d9_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_ami_3(B)
=> k9_ami_3(A,B) = k4_tarski(np__7,k10_finseq_1(A,B)) ) ) ).
fof(d10_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_ami_3(B)
=> k10_ami_3(A,B) = k4_tarski(np__8,k10_finseq_1(A,B)) ) ) ).
fof(t3_ami_3,axiom,
$true ).
fof(t4_ami_3,axiom,
k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) = np__0 ).
fof(t5_ami_3,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(k5_ami_2))
=> ( B = A
=> k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_2(B) ) ) ) ).
fof(d11_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( B = k11_ami_3(A)
<=> ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& C = A
& B = k15_ami_2(C) ) ) ) ) ).
fof(t6_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ( B = A
=> k15_ami_2(B) = k11_ami_3(A) ) ) ) ).
fof(t7_ami_3,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_ami_2)
=> ( C = A
=> ! [D] :
( m1_subset_1(D,k4_card_3(k5_ami_2))
=> ( D = B
=> k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B) = k16_ami_2(C,D) ) ) ) ) ) ) ).
fof(t8_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),A) = k2_ami_3(C,B)
& ! [D] :
( m1_ami_3(D)
=> ( D != A
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t9_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),A) = k2_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
& ! [D] :
( m1_ami_3(D)
=> ( D != A
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t10_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),A) = k6_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
& ! [D] :
( m1_ami_3(D)
=> ( D != A
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t11_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),A) = k3_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
& ! [D] :
( m1_ami_3(D)
=> ( D != A
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t12_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
& ( A != B
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),A) = k5_int_1(k2_ami_3(C,A),k2_ami_3(C,B)) )
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),B) = k6_int_1(k2_ami_3(C,A),k2_ami_3(C,B))
& ! [D] :
( m1_ami_3(D)
=> ~ ( D != A
& D != B
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),D) != k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t13_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = B
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),A) = k2_ami_3(C,A) ) ) ) ) ).
fof(t14_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( k2_ami_3(D,A) = np__0
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
& ( k2_ami_3(D,A) != np__0
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) ).
fof(t15_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( ~ r1_xreal_0(k2_ami_3(D,A),np__0)
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
& ( r1_xreal_0(k2_ami_3(D,A),np__0)
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) ).
fof(t16_ami_3,axiom,
$true ).
fof(t17_ami_3,axiom,
$true ).
fof(t18_ami_3,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> r1_int_1(k3_xcmplx_0(A,B),np__0,A) ) ) ).
fof(t19_ami_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ( ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> ( r2_hidden(k4_tarski(E,F),C)
<=> r2_hidden(k4_tarski(E,F),D) ) ) )
=> C = D ) ) ) ) ) ).
fof(t20_ami_3,axiom,
$true ).
fof(t21_ami_3,axiom,
$true ).
fof(t22_ami_3,axiom,
$true ).
fof(t23_ami_3,axiom,
$true ).
fof(t24_ami_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( k1_relat_1(A) = k1_relat_1(B)
& k1_funct_1(A,C) = k1_funct_1(B,C) )
=> k7_relat_1(A,k1_tarski(C)) = k7_relat_1(B,k1_tarski(C)) ) ) ) ).
fof(t25_ami_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( k1_relat_1(A) = k1_relat_1(B)
& k1_funct_1(A,C) = k1_funct_1(B,C)
& k1_funct_1(A,D) = k1_funct_1(B,D) )
=> k7_relat_1(A,k2_tarski(C,D)) = k7_relat_1(B,k2_tarski(C,D)) ) ) ) ).
fof(t26_ami_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D,E] :
( ( k1_relat_1(A) = k1_relat_1(B)
& k1_funct_1(A,C) = k1_funct_1(B,C)
& k1_funct_1(A,D) = k1_funct_1(B,D)
& k1_funct_1(A,E) = k1_funct_1(B,E) )
=> k7_relat_1(A,k1_enumset1(C,D,E)) = k7_relat_1(B,k1_enumset1(C,D,E)) ) ) ) ).
fof(t27_ami_3,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k1_relat_1(C))
& k1_funct_1(C,A) = B )
=> r1_tarski(k3_cqc_lang(A,B),C) ) ) ).
fof(t28_ami_3,axiom,
$true ).
fof(t29_ami_3,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r2_hidden(A,k1_relat_1(E))
& r2_hidden(C,k1_relat_1(E))
& k1_funct_1(E,A) = B
& k1_funct_1(E,C) = D )
=> r1_tarski(k4_funct_4(A,C,B,D),E) ) ) ).
fof(t30_ami_3,axiom,
$true ).
fof(t31_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> r2_hidden(C,k14_ami_1(A,B)) ) ) ).
fof(t32_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m2_subset_1(C,k7_ami_1(u5_ami_1(A,B)),k14_ami_1(A,B))
=> m1_ami_1(C,A,B) ) ) ).
fof(t33_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( ! [E] :
( m1_ami_1(E,A,B)
=> ! [F] :
( m1_ami_1(F,A,B)
=> ( r2_hidden(k4_tarski(E,F),C)
<=> r2_hidden(k4_tarski(E,F),D) ) ) )
=> C = D ) ) ) ) ).
fof(d12_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k12_ami_3(A,B,C) = k2_cat_3(u2_ami_1(A,B),k2_ami_1(A,B),C) ) ) ) ).
fof(t34_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k1_relat_1(k12_ami_3(A,B,C)) = k1_struct_0(B,k2_ami_1(A,B)) ) ) ) ).
fof(d13_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_ami_3(C,A,B)
<=> r1_tarski(k1_relat_1(C),u2_ami_1(A,B)) ) ) ) ).
fof(t35_ami_3,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> v1_ami_3(k17_ami_1(A,B,C,D),A,B) ) ) ) ).
fof(t36_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> k1_relat_1(C) = u1_struct_0(B) ) ) ) ).
fof(t37_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_tarski(k1_relat_1(C),u1_struct_0(B)) ) ) ) ).
fof(t38_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(C,D)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(C,k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) ).
fof(d14_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r1_ami_3(A,B,C,D)
<=> k6_ami_1(A,B,C) = D ) ) ) ) ) ).
fof(d15_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_ami_3(A,B,C,D)
<=> k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) ).
fof(t39_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ? [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
& r1_tarski(C,D) ) ) ) ) ).
fof(d16_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
=> k13_ami_3(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ) ).
fof(d17_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r3_ami_3(A,B,C,D)
<=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
& k13_ami_3(A,B,C) = D ) ) ) ) ) ) ).
fof(d18_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r4_ami_3(A,B,C,D)
<=> ( r2_hidden(D,k1_relat_1(C))
& k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) ) ).
fof(t40_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ( v9_ami_1(C,A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) ).
fof(t41_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_ami_1(D,A,B)
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> ( ( r1_tarski(D,C)
& r4_ami_3(A,B,D,E) )
=> r2_ami_3(A,B,C,E) ) ) ) ) ) ) ).
fof(t42_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v9_ami_1(C,A,B)
=> ( k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D)
<=> r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) ) ).
fof(t43_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( ( v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_tarski(D,C)
<=> r1_tarski(D,k11_ami_1(A,B,k10_ami_1(A,B,C),E)) ) ) ) ) ) ) ).
fof(t44_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)))
=> k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ).
fof(t45_ami_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( v1_setfam_1(C)
=> ( r1_xreal_0(A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v4_ami_1(D,C)
& v5_ami_1(D,C)
& v7_ami_1(D,C)
& v8_ami_1(D,C)
& l1_ami_1(D,C) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
=> ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
=> r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),B))) ) ) ) ) ) ) ) ).
fof(t46_ami_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( v1_setfam_1(C)
=> ( r1_xreal_0(A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v4_ami_1(D,C)
& v5_ami_1(D,C)
& v7_ami_1(D,C)
& v8_ami_1(D,C)
& l1_ami_1(D,C) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
=> ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
=> k11_ami_1(C,D,k10_ami_1(C,D,E),B) = k11_ami_1(C,D,k10_ami_1(C,D,E),A) ) ) ) ) ) ) ) ).
fof(t47_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ( ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k12_ami_1(A,B,C) = k12_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) ) ) ) ) ) ).
fof(t48_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_ami_3(A,B,C,D)
<=> r2_ami_3(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ) ).
fof(t49_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r3_ami_3(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(C,E)
=> r1_ami_3(A,B,E,D) ) ) ) ) ) ) ) ).
fof(t50_ami_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k1_funct_1(k12_ami_3(A,B,C),k2_ami_1(A,B)) = C ) ) ) ).
fof(t51_ami_3,axiom,
v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ).
fof(d19_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> k15_ami_3(A) = k2_xcmplx_0(k3_xcmplx_0(np__2,A),np__1) ) ).
fof(d20_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> k16_ami_3(A) = k2_xcmplx_0(k3_xcmplx_0(np__2,A),np__2) ) ).
fof(t52_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( A != B
& k15_ami_3(A) = k15_ami_3(B) ) ) ) ).
fof(t53_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( A != B
& k16_ami_3(A) = k16_ami_3(B) ) ) ) ).
fof(t54_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> k11_ami_3(k16_ami_3(A)) = k16_ami_3(k2_xcmplx_0(A,np__1)) ) ).
fof(t55_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> k3_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k4_numbers ) ).
fof(t56_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> k15_ami_3(A) != k16_ami_3(B) ) ) ).
fof(t57_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
& k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A) ) ) ).
fof(t58_ami_3,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( ? [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)) )
& v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t59_ami_3,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( A = k4_tarski(np__0,k1_xboole_0)
=> v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t60_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ~ v3_ami_1(k3_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t61_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ~ v3_ami_1(k4_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t62_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ~ v3_ami_1(k5_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t63_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ~ v3_ami_1(k6_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t64_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ~ v3_ami_1(k7_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t65_ami_3,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ v3_ami_1(k8_ami_3(A),k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(t66_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ v3_ami_1(k9_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t67_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ v3_ami_1(k10_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t68_ami_3,axiom,
m2_subset_1(k4_tarski(np__0,k1_xboole_0),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ).
fof(t69_ami_3,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
<=> ~ ( A != k4_tarski(np__0,k1_xboole_0)
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k3_ami_3(B,C) ) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k4_ami_3(B,C) ) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k5_ami_3(B,C) ) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k6_ami_3(B,C) ) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k7_ami_3(B,C) ) )
& ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> A != k8_ami_3(B) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> A != k9_ami_3(C,B) ) )
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> A != k10_ami_3(C,B) ) ) ) ) ).
fof(t70_ami_3,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t71_ami_3,axiom,
k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) = k4_tarski(np__0,k1_xboole_0) ).
fof(s1_ami_3,axiom,
( ( p1_s1_ami_3(np__0)
& ~ r1_xreal_0(f1_s1_ami_3,np__0)
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( p1_s1_ami_3(k2_nat_1(f1_s1_ami_3,A))
& r1_xreal_0(B,f1_s1_ami_3) )
=> ( B = np__0
| p1_s1_ami_3(k1_nat_1(k2_nat_1(f1_s1_ami_3,A),B)) ) ) ) ) )
=> p1_s1_ami_3(f2_s1_ami_3) ) ).
fof(s2_ami_3,axiom,
( ( ! [A] :
( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
=> ! [B] :
( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
=> ( r2_hidden(k4_tarski(A,B),f3_s2_ami_3)
<=> p1_s2_ami_3(A,B) ) ) )
& ! [A] :
( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
=> ! [B] :
( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
=> ( r2_hidden(k4_tarski(A,B),f4_s2_ami_3)
<=> p1_s2_ami_3(A,B) ) ) ) )
=> f3_s2_ami_3 = f4_s2_ami_3 ) ).
fof(dt_m1_ami_3,axiom,
! [A] :
( m1_ami_3(A)
=> m1_subset_1(A,u1_struct_0(k1_ami_3)) ) ).
fof(existence_m1_ami_3,axiom,
? [A] : m1_ami_3(A) ).
fof(dt_k1_ami_3,axiom,
( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(dt_k2_ami_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_ami_3(B) )
=> v1_int_1(k2_ami_3(A,B)) ) ).
fof(redefinition_k2_ami_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_ami_3(B) )
=> k2_ami_3(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k3_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& m1_ami_3(B) )
=> m2_subset_1(k3_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k4_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& m1_ami_3(B) )
=> m2_subset_1(k4_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k5_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& m1_ami_3(B) )
=> m2_subset_1(k5_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k6_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& m1_ami_3(B) )
=> m2_subset_1(k6_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k7_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& m1_ami_3(B) )
=> m2_subset_1(k7_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k8_ami_3,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> m2_subset_1(k8_ami_3(A),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k9_ami_3,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_ami_3(B) )
=> m2_subset_1(k9_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k10_ami_3,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_ami_3(B) )
=> m2_subset_1(k10_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k11_ami_3,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> m1_struct_0(k11_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k12_ami_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B)) )
=> m1_ami_1(k12_ami_3(A,B,C),A,B) ) ).
fof(dt_k13_ami_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> m1_struct_0(k13_ami_3(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(dt_k14_ami_3,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B))
& m1_subset_1(D,u4_ami_1(A,B)) )
=> ( v1_ami_3(k14_ami_3(A,B,C,D),A,B)
& m1_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ).
fof(redefinition_k14_ami_3,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B))
& m1_subset_1(D,u4_ami_1(A,B)) )
=> k14_ami_3(A,B,C,D) = k3_cqc_lang(C,D) ) ).
fof(dt_k15_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> m1_ami_3(k15_ami_3(A)) ) ).
fof(dt_k16_ami_3,axiom,
! [A] :
( v4_ordinal2(A)
=> m1_struct_0(k16_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k17_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& v1_int_1(B) )
=> m1_ami_1(k17_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(redefinition_k17_ami_3,axiom,
! [A,B] :
( ( m1_ami_3(A)
& v1_int_1(B) )
=> k17_ami_3(A,B) = k3_cqc_lang(A,B) ) ).
fof(dt_k18_ami_3,axiom,
! [A,B,C,D] :
( ( m1_ami_3(A)
& m1_ami_3(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m1_ami_1(k18_ami_3(A,B,C,D),k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(redefinition_k18_ami_3,axiom,
! [A,B,C,D] :
( ( m1_ami_3(A)
& m1_ami_3(B)
& v1_int_1(C)
& v1_int_1(D) )
=> k18_ami_3(A,B,C,D) = k4_funct_4(A,B,C,D) ) ).
%------------------------------------------------------------------------------