SET007 Axioms: SET007+355.ax
%------------------------------------------------------------------------------
% File : SET007+355 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Mathematical Model of CPU
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 173 ( 26 unt; 0 def)
% Number of atoms : 1181 ( 100 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1187 ( 179 ~; 0 |; 624 &)
% ( 29 <=>; 355 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-4 aty)
% Number of functors : 59 ( 59 usr; 6 con; 0-8 aty)
% Number of variables : 503 ( 478 !; 25 ?)
% 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(rc1_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& v1_ami_1(B,A) ) ).
fof(fc1_ami_1,axiom,
! [A] :
( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A) ) ).
fof(rc2_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A) ) ).
fof(fc2_ami_1,axiom,
! [A,B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ~ v1_xboole_0(u2_ami_1(A,B)) ) ).
fof(fc3_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> v1_fraenkel(k4_card_3(A)) ) ).
fof(fc4_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ( ~ v1_xboole_0(k4_card_3(C))
& v1_fraenkel(k4_card_3(C)) ) ) ).
fof(fc5_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v4_ami_1(k1_ami_1(A),A) ) ) ).
fof(rc3_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ? [B] :
( l1_ami_1(B,A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A) ) ) ).
fof(rc4_ami_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_subset_1(C,u4_ami_1(A,B))
& v3_ami_1(C,A,B) ) ) ).
fof(fc6_ami_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& l1_ami_1(B,A) )
=> v3_ami_1(k5_ami_1(A,B),A,B) ) ).
fof(fc7_ami_1,axiom,
! [A] :
( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v6_ami_1(k1_ami_1(A),A) ) ).
fof(fc8_ami_1,axiom,
! [A] :
( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v5_ami_1(k1_ami_1(A),A)
& v6_ami_1(k1_ami_1(A),A)
& v8_ami_1(k1_ami_1(A),A) ) ).
fof(fc9_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v4_ami_1(k1_ami_1(A),A)
& v5_ami_1(k1_ami_1(A),A)
& v6_ami_1(k1_ami_1(A),A)
& v7_ami_1(k1_ami_1(A),A)
& v8_ami_1(k1_ami_1(A),A) ) ) ).
fof(rc5_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& v1_ami_1(B,A)
& v6_ami_1(B,A) ) ).
fof(rc6_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& ~ v3_struct_0(B)
& v1_ami_1(B,A)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v6_ami_1(B,A)
& v8_ami_1(B,A) ) ).
fof(rc7_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ? [B] :
( l1_ami_1(B,A)
& ~ v3_struct_0(B)
& v1_ami_1(B,A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v6_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A) ) ) ).
fof(fc10_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ~ v1_xboole_0(k7_ami_1(A))
& v1_fraenkel(k7_ami_1(A)) ) ) ).
fof(fc11_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ~ v1_xboole_0(k3_ami_1(A,B,C)) ) ).
fof(fc12_ami_1,axiom,
! [A] :
( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v5_ami_1(k1_ami_1(A),A)
& v6_ami_1(k1_ami_1(A),A)
& v8_ami_1(k1_ami_1(A),A)
& v10_ami_1(k1_ami_1(A),A) ) ).
fof(fc13_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k1_ami_1(A))
& v1_ami_1(k1_ami_1(A),A)
& ~ v2_ami_1(k1_ami_1(A),A)
& v4_ami_1(k1_ami_1(A),A)
& v5_ami_1(k1_ami_1(A),A)
& v6_ami_1(k1_ami_1(A),A)
& v7_ami_1(k1_ami_1(A),A)
& v8_ami_1(k1_ami_1(A),A)
& v10_ami_1(k1_ami_1(A),A)
& v13_ami_1(k1_ami_1(A),A) ) ) ).
fof(rc8_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& v1_ami_1(B,A)
& v6_ami_1(B,A)
& v10_ami_1(B,A) ) ).
fof(rc9_ami_1,axiom,
! [A] :
? [B] :
( l1_ami_1(B,A)
& ~ v3_struct_0(B)
& v1_ami_1(B,A)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v6_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A) ) ).
fof(rc10_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ? [B] :
( l1_ami_1(B,A)
& ~ v3_struct_0(B)
& v1_ami_1(B,A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v6_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& v13_ami_1(B,A) ) ) ).
fof(rc11_ami_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v13_ami_1(B,A)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_ami_1(C,A,B)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v11_ami_1(C,A,B) ) ) ).
fof(rc12_ami_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v11_ami_1(C,A,B)
& v12_ami_1(C,A,B) ) ) ).
fof(t1_ami_1,axiom,
$true ).
fof(t2_ami_1,axiom,
! [A,B] : np__1 != k4_tarski(A,B) ).
fof(t3_ami_1,axiom,
! [A,B] : np__2 != k4_tarski(A,B) ).
fof(t4_ami_1,axiom,
$true ).
fof(t5_ami_1,axiom,
! [A,B,C,D] :
( A != B
=> k4_card_3(k4_funct_4(A,B,k1_tarski(C),k1_tarski(D))) = k1_tarski(k4_funct_4(A,B,C,D)) ) ).
fof(d1_ami_1,axiom,
$true ).
fof(d2_ami_1,axiom,
! [A,B] :
( ( v1_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( B = k1_ami_1(A)
<=> ( u1_struct_0(B) = k2_tarski(np__0,np__1)
& u1_ami_1(A,B) = np__0
& u2_ami_1(A,B) = k1_tarski(np__1)
& u3_ami_1(A,B) = k1_tarski(np__0)
& u4_ami_1(A,B) = k1_tarski(k4_tarski(np__0,k1_xboole_0))
& u5_ami_1(A,B) = k4_funct_4(np__0,np__1,k1_tarski(np__1),k1_tarski(k4_tarski(np__0,k1_xboole_0)))
& u6_ami_1(A,B) = k3_cqc_lang(k4_tarski(np__0,k1_xboole_0),k6_partfun1(k4_card_3(k4_funct_4(np__0,np__1,k1_tarski(np__1),k1_tarski(k4_tarski(np__0,k1_xboole_0)))))) ) ) ) ).
fof(d3_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v2_ami_1(B,A)
<=> v1_xboole_0(u2_ami_1(A,B)) ) ) ).
fof(d4_ami_1,axiom,
$true ).
fof(d5_ami_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> k2_ami_1(A,B) = u1_ami_1(A,B) ) ).
fof(d6_ami_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_ami_1(A,B,C) = k8_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),C) ) ) ).
fof(d7_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> k4_ami_1(A,B,C,D) = k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D) ) ) ) ) ).
fof(d8_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ( v3_ami_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> k4_ami_1(A,B,C,D) = D ) ) ) ) ) ).
fof(d9_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( v4_ami_1(B,A)
<=> ? [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
& v3_ami_1(C,A,B)
& ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ( v3_ami_1(D,A,B)
=> C = D ) ) ) ) ) ) ).
fof(t6_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> v4_ami_1(k1_ami_1(A),A) ) ).
fof(d10_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ( C = k5_ami_1(A,B)
<=> ( v3_ami_1(C,A,B)
& m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ) ) ) ) ).
fof(d11_ami_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ( v5_ami_1(B,A)
<=> k3_ami_1(A,B,k2_ami_1(A,B)) = u2_ami_1(A,B) ) ) ).
fof(d12_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v6_ami_1(B,A)
<=> r1_tarski(k3_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),k1_tarski(u4_ami_1(A,B))),u2_ami_1(A,B)) ) ) ).
fof(d13_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( v7_ami_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> k1_funct_1(k4_ami_1(A,B,D,C),E) = k1_funct_1(C,E) ) ) ) ) ) ) ).
fof(d14_ami_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( v8_ami_1(B,A)
<=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k3_ami_1(A,B,C) = u4_ami_1(A,B) ) ) ) ).
fof(t7_ami_1,axiom,
! [A] : v5_ami_1(k1_ami_1(A),A) ).
fof(t8_ami_1,axiom,
! [A] : v6_ami_1(k1_ami_1(A),A) ).
fof(t9_ami_1,axiom,
! [A,B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(A,k1_ami_1(A))))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,k1_ami_1(A))))
=> B = C ) ) ).
fof(t10_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> v7_ami_1(k1_ami_1(A),A) ) ).
fof(t11_ami_1,axiom,
! [A] : v8_ami_1(k1_ami_1(A),A) ).
fof(d15_ami_1,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)))
=> k6_ami_1(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ).
fof(t12_ami_1,axiom,
$true ).
fof(t13_ami_1,axiom,
$true ).
fof(t14_ami_1,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r1_partfun1(D,E)
& r2_hidden(k4_tarski(A,B),D)
& r2_hidden(k4_tarski(A,C),E) )
=> B = C ) ) ) ).
fof(t15_ami_1,axiom,
! [A] :
( ( ! [B] :
( r2_hidden(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) )
& ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r1_partfun1(B,C) ) ) ) )
=> ( v1_relat_1(k3_tarski(A))
& v1_funct_1(k3_tarski(A)) ) ) ).
fof(t16_ami_1,axiom,
$true ).
fof(t17_ami_1,axiom,
$true ).
fof(t18_ami_1,axiom,
! [A,B,C,D] : k4_funct_4(A,B,C,D) = k1_funct_4(k3_cqc_lang(A,C),k3_cqc_lang(B,D)) ).
fof(t19_ami_1,axiom,
! [A,B] : k3_cqc_lang(A,B) = k1_tarski(k4_tarski(A,B)) ).
fof(t20_ami_1,axiom,
! [A,B,C] : k4_funct_4(A,A,B,C) = k3_cqc_lang(A,C) ).
fof(t21_ami_1,axiom,
$true ).
fof(t22_ami_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(A,k4_card_3(B))
=> ( v1_relat_1(A)
& v1_funct_1(A) ) ) ) ).
fof(d16_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( B = k7_ami_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& C = D
& r1_tarski(k1_relat_1(D),k1_relat_1(A))
& ! [E] :
( r2_hidden(E,k1_relat_1(D))
=> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ).
fof(t23_ami_1,axiom,
$true ).
fof(t24_ami_1,axiom,
$true ).
fof(t25_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(A,k7_ami_1(B))
=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ).
fof(t26_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> r2_hidden(k1_xboole_0,k7_ami_1(A)) ) ).
fof(t27_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> r1_tarski(k4_card_3(A),k7_ami_1(A)) ) ).
fof(t28_ami_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(A,k7_ami_1(B))
=> ( v1_funct_1(A)
& m2_relset_1(A,k1_relat_1(B),k3_tarski(k2_relat_1(B))) ) ) ) ).
fof(t29_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k4_card_3(B))
& r2_hidden(C,k7_ami_1(B)) )
=> r2_hidden(k1_funct_4(A,C),k4_card_3(B)) ) ) ) ) ).
fof(t30_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k4_card_3(A) != k1_xboole_0
=> ( r2_hidden(B,k7_ami_1(A))
<=> ? [C] :
( v1_relat_1(C)
& v1_funct_1(C)
& r2_hidden(C,k4_card_3(A))
& r1_tarski(B,C) ) ) ) ) ) ).
fof(t31_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> r1_tarski(k7_ami_1(A),k4_partfun1(k1_relat_1(A),k3_tarski(k2_relat_1(A)))) ) ).
fof(t32_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(A,B)
=> r1_tarski(k7_ami_1(A),k7_ami_1(B)) ) ) ) ).
fof(t33_ami_1,axiom,
k7_ami_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ).
fof(t34_ami_1,axiom,
! [A,B] : k4_partfun1(A,B) = k7_ami_1(k2_funcop_1(A,B)) ).
fof(t36_ami_1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k1_relat_1(C))
& r2_hidden(B,k1_funct_1(C,A)) )
=> r2_hidden(k3_cqc_lang(A,B),k7_ami_1(C)) ) ) ).
fof(t37_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( k7_ami_1(A) = k1_tarski(k1_xboole_0)
<=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k1_xboole_0 ) ) ) ).
fof(t38_ami_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( r1_tarski(A,k7_ami_1(B))
& ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(C,A)
& r2_hidden(D,A) )
=> r1_partfun1(C,D) ) ) ) )
=> r2_hidden(k3_tarski(A),k7_ami_1(B)) ) ) ).
fof(t39_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_partfun1(A,B)
& r2_hidden(A,k7_ami_1(C))
& r2_hidden(B,k7_ami_1(C)) )
=> r2_hidden(k2_xboole_0(A,B),k7_ami_1(C)) ) ) ) ) ).
fof(t40_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_tarski(A,B)
& r2_hidden(B,k7_ami_1(C)) )
=> r2_hidden(A,k7_ami_1(C)) ) ) ) ) ).
fof(t41_ami_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(B,k7_ami_1(C))
=> r2_hidden(k7_relat_1(B,A),k7_ami_1(C)) ) ) ) ).
fof(t42_ami_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(B,k7_ami_1(C))
=> r2_hidden(k7_relat_1(B,A),k7_ami_1(k7_relat_1(C,A))) ) ) ) ).
fof(t43_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ~ ( r2_hidden(A,k7_ami_1(k1_funct_4(B,C)))
& ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ~ ( r2_hidden(D,k7_ami_1(B))
& r2_hidden(E,k7_ami_1(C))
& A = k1_funct_4(D,E) ) ) ) ) ) ) ) ).
fof(t44_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_xboole_0(k1_relat_1(A),k4_xboole_0(k1_relat_1(C),k1_relat_1(D)))
& r2_hidden(C,k7_ami_1(B))
& r2_hidden(D,k7_ami_1(A)) )
=> r2_hidden(k1_funct_4(C,D),k7_ami_1(k1_funct_4(B,A))) ) ) ) ) ) ).
fof(t45_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_xboole_0(k1_relat_1(C),k4_xboole_0(k1_relat_1(A),k1_relat_1(D)))
& r2_hidden(C,k7_ami_1(B))
& r2_hidden(D,k7_ami_1(A)) )
=> r2_hidden(k1_funct_4(C,D),k7_ami_1(k1_funct_4(B,A))) ) ) ) ) ) ).
fof(t46_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k7_ami_1(B))
& r2_hidden(C,k7_ami_1(B)) )
=> r2_hidden(k1_funct_4(A,C),k7_ami_1(B)) ) ) ) ) ).
fof(t47_ami_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(D,k1_funct_1(A,B))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(E,k1_funct_1(A,C)) )
=> r2_hidden(k4_funct_4(B,C,D,E),k7_ami_1(A)) ) ) ).
fof(d17_ami_1,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> k8_ami_1(A,B,C) = k1_funct_1(C,k6_ami_1(A,B,C)) ) ) ) ).
fof(d18_ami_1,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> k9_ami_1(A,B,C) = k4_ami_1(A,B,k8_ami_1(A,B,C),C) ) ) ) ).
fof(d19_ami_1,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) )
=> ( D = k10_ami_1(A,B,C)
<=> ( k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,np__0) = C
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,k1_nat_1(E,np__1)) = k9_ami_1(A,B,k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,E)) ) ) ) ) ) ) ) ).
fof(d20_ami_1,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_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)
& k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B) ) ) ) ) ) ).
fof(d21_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v10_ami_1(B,A)
<=> u4_ami_1(A,B) != u2_ami_1(A,B) ) ) ).
fof(t48_ami_1,axiom,
! [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) )
=> ( v10_ami_1(B,A)
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k2_ami_1(A,B) != C ) ) ) ).
fof(t49_ami_1,axiom,
$true ).
fof(t50_ami_1,axiom,
$true ).
fof(t51_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,A)
& v5_ami_1(C,A)
& v8_ami_1(C,A)
& l1_ami_1(C,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,C)))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k11_ami_1(A,C,k10_ami_1(A,C,D),k1_nat_1(B,E)) = k11_ami_1(A,C,k10_ami_1(A,C,k11_ami_1(A,C,k10_ami_1(A,C,D),B)),E) ) ) ) ) ) ).
fof(t52_ami_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> ! [C] :
( v1_setfam_1(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v4_ami_1(D,C)
& v5_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)))
=> ( k8_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)) = k5_ami_1(C,D)
=> 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(d22_ami_1,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ( v9_ami_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( D = k12_ami_1(A,B,C)
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = k11_ami_1(A,B,k10_ami_1(A,B,C),E)
& k8_ami_1(A,B,D) = k5_ami_1(A,B) ) ) ) ) ) ) ) ).
fof(t53_ami_1,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] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> k1_funct_1(C,D) = k1_funct_1(k9_ami_1(A,B,C),D) ) ) ) ) ).
fof(t54_ami_1,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] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k13_ami_1(A,B,C,D) = k13_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ).
fof(t55_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,A)
& v5_ami_1(C,A)
& v7_ami_1(C,A)
& v8_ami_1(C,A)
& l1_ami_1(C,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,C)))
=> k11_ami_1(A,C,k10_ami_1(A,C,D),k1_nat_1(B,np__1)) = k4_ami_1(A,C,k13_ami_1(A,C,D,k6_ami_1(A,C,k11_ami_1(A,C,k10_ami_1(A,C,D),B))),k11_ami_1(A,C,k10_ami_1(A,C,D),B)) ) ) ) ) ).
fof(t56_ami_1,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)
=> ( k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B)
=> k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ).
fof(t57_ami_1,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)
& k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B) )
=> ! [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(d24_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_subset_1(C,k7_ami_1(u5_ami_1(A,B)))
=> ( m1_ami_1(C,A,B)
<=> v1_finset_1(C) ) ) ) ).
fof(d25_ami_1,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)
=> ( v11_ami_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
=> ( ( r1_tarski(C,D)
& r1_tarski(C,E) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,D),F),k1_relat_1(C)) = k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,E),F),k1_relat_1(C)) ) ) ) ) ) ) ) ) ).
fof(d26_ami_1,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)
=> ( v12_ami_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(C,D)
=> v9_ami_1(D,A,B) ) ) ) ) ) ) ).
fof(d27_ami_1,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) )
=> ( v13_ami_1(B,A)
<=> ? [C] :
( m1_ami_1(C,A,B)
& ~ v1_xboole_0(C)
& v11_ami_1(C,A,B) ) ) ) ) ).
fof(t58_ami_1,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,D,E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( k3_ami_1(A,B,E) = C
& k3_ami_1(A,B,F) = D )
=> ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( m1_subset_1(H,D)
=> m1_ami_1(k4_funct_4(E,F,G,H),A,B) ) ) ) ) ) ) ) ).
fof(t59_ami_1,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,D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( k3_ami_1(A,B,D) = C
=> ! [E] :
( m1_subset_1(E,C)
=> m1_ami_1(k3_cqc_lang(D,E),A,B) ) ) ) ) ) ).
fof(t60_ami_1,axiom,
! [A] : v10_ami_1(k1_ami_1(A),A) ).
fof(t61_ami_1,axiom,
! [A] :
( v1_setfam_1(A)
=> v13_ami_1(k1_ami_1(A),A) ) ).
fof(t62_ami_1,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)))
=> ! [D] :
( m1_ami_1(D,A,B)
=> m1_ami_1(k7_relat_1(C,k1_relat_1(D)),A,B) ) ) ) ) ).
fof(t63_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> m1_ami_1(k1_xboole_0,A,B) ) ).
fof(t64_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
=> ( D = C
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,C))
=> ( E = k5_ami_1(A,B)
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),F)
=> k8_ami_1(A,B,F) = k5_ami_1(A,B) ) ) ) ) ) ) ) ) ) ).
fof(t65_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
=> ( D = C
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,C))
=> ( E = k5_ami_1(A,B)
=> v12_ami_1(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),A,B) ) ) ) ) ) ) ) ).
fof(t66_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
=> ( D = C
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,C))
=> ( E = k5_ami_1(A,B)
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),F)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k11_ami_1(A,B,k10_ami_1(A,B,F),G) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t67_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
=> ( D = C
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,C))
=> ( E = k5_ami_1(A,B)
=> v11_ami_1(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),A,B) ) ) ) ) ) ) ) ).
fof(d28_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( ( v11_ami_1(C,A,B)
& v12_ami_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( m1_ami_1(D,A,B)
=> ( D = k18_ami_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(C,E)
=> D = k7_relat_1(k12_ami_1(A,B,E),k1_relat_1(C)) ) ) ) ) ) ) ) ) ).
fof(d29_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r1_ami_1(A,B,C,D)
<=> ! [E] :
~ ( r2_hidden(E,k1_relat_1(D))
& ! [F] :
( m1_ami_1(F,A,B)
=> ~ ( E = F
& v11_ami_1(k17_ami_1(A,B,C,F),A,B)
& v12_ami_1(k17_ami_1(A,B,C,F),A,B)
& m1_ami_1(k17_ami_1(A,B,C,F),A,B)
& r1_tarski(k1_funct_1(D,F),k18_ami_1(A,B,k17_ami_1(A,B,C,F))) ) ) ) ) ) ) ) ) ).
fof(t68_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_ami_1(A,B,C,k1_xboole_0) ) ) ) ).
fof(t69_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( ( v11_ami_1(C,A,B)
& v12_ami_1(C,A,B)
& m1_ami_1(C,A,B) )
<=> r1_ami_1(A,B,C,k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))) ) ) ) ) ).
fof(t70_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( ( v11_ami_1(C,A,B)
& v12_ami_1(C,A,B)
& m1_ami_1(C,A,B) )
<=> r1_ami_1(A,B,C,k3_cqc_lang(k1_xboole_0,k1_xboole_0)) ) ) ) ) ).
fof(d30_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( v14_ami_1(C,A,B)
<=> ? [D] :
( m1_ami_1(D,A,B)
& r1_ami_1(A,B,D,C) ) ) ) ) ) ).
fof(t71_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( C = k1_xboole_0
=> v14_ami_1(C,A,B) ) ) ) ) ).
fof(t72_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( C = k3_cqc_lang(k1_xboole_0,k1_xboole_0)
=> v14_ami_1(C,A,B) ) ) ) ) ).
fof(t73_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v11_ami_1(C,A,B)
& v12_ami_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( D = k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))
=> v14_ami_1(D,A,B) ) ) ) ) ) ).
fof(d31_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( v14_ami_1(C,A,B)
=> ! [D] :
( m1_ami_1(D,A,B)
=> ( m2_ami_1(D,A,B,C)
<=> r1_ami_1(A,B,D,C) ) ) ) ) ) ) ).
fof(t74_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( C = k1_xboole_0
=> ! [D] :
( m1_ami_1(D,A,B)
=> m2_ami_1(D,A,B,C) ) ) ) ) ) ).
fof(t75_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( C = k3_cqc_lang(k1_xboole_0,k1_xboole_0)
=> ! [D] :
( ( v11_ami_1(D,A,B)
& v12_ami_1(D,A,B)
& m1_ami_1(D,A,B) )
=> m2_ami_1(D,A,B,C) ) ) ) ) ) ).
fof(t76_ami_1,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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v11_ami_1(C,A,B)
& v12_ami_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( D = k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))
=> m2_ami_1(C,A,B,D) ) ) ) ) ) ).
fof(dt_m1_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ).
fof(existence_m1_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ? [C] : m1_ami_1(C,A,B) ) ).
fof(dt_m2_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A)
& v1_funct_1(C)
& m1_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ! [D] :
( m2_ami_1(D,A,B,C)
=> m1_ami_1(D,A,B) ) ) ).
fof(existence_m2_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A)
& v1_funct_1(C)
& m1_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ? [D] : m2_ami_1(D,A,B,C) ) ).
fof(dt_l1_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> l1_struct_0(B) ) ).
fof(existence_l1_ami_1,axiom,
! [A] :
? [B] : l1_ami_1(B,A) ).
fof(abstractness_v1_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v1_ami_1(B,A)
=> B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ).
fof(dt_k1_ami_1,axiom,
! [A] :
( v1_ami_1(k1_ami_1(A),A)
& l1_ami_1(k1_ami_1(A),A) ) ).
fof(dt_k2_ami_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ).
fof(dt_k3_ami_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> m1_subset_1(k3_ami_1(A,B,C),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ).
fof(dt_k4_ami_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B))
& m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) )
=> m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ).
fof(dt_k5_ami_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& l1_ami_1(B,A) )
=> m2_subset_1(k5_ami_1(A,B),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ).
fof(dt_k6_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) )
=> m1_struct_0(k6_ami_1(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(dt_k7_ami_1,axiom,
$true ).
fof(dt_k8_ami_1,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,k4_card_3(u5_ami_1(A,B))) )
=> m2_subset_1(k8_ami_1(A,B,C),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ).
fof(dt_k9_ami_1,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,k4_card_3(u5_ami_1(A,B))) )
=> m1_subset_1(k9_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ).
fof(dt_k10_ami_1,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,k4_card_3(u5_ami_1(A,B))) )
=> ( v1_funct_1(k10_ami_1(A,B,C))
& v1_funct_2(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m2_relset_1(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) ) ) ).
fof(dt_k11_ami_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,k5_numbers) )
=> m1_subset_1(k11_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ).
fof(redefinition_k11_ami_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,k5_numbers) )
=> k11_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k12_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ 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)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) )
=> m1_subset_1(k12_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ).
fof(dt_k13_ami_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,u2_ami_1(A,B)) )
=> m2_subset_1(k13_ami_1(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ).
fof(redefinition_k13_ami_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,u2_ami_1(A,B)) )
=> k13_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k14_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> m1_subset_1(k14_ami_1(A,B),k1_zfmisc_1(k7_ami_1(u5_ami_1(A,B)))) ) ).
fof(dt_k15_ami_1,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,u1_struct_0(B))
& m1_subset_1(D,k3_ami_1(A,B,C)) )
=> m1_ami_1(k15_ami_1(A,B,C,D),A,B) ) ).
fof(redefinition_k15_ami_1,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,u1_struct_0(B))
& m1_subset_1(D,k3_ami_1(A,B,C)) )
=> k15_ami_1(A,B,C,D) = k3_cqc_lang(C,D) ) ).
fof(dt_k16_ami_1,axiom,
! [A,B,C,D,E,F] :
( ( 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,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k3_ami_1(A,B,C))
& m1_subset_1(F,k3_ami_1(A,B,D)) )
=> m1_ami_1(k16_ami_1(A,B,C,D,E,F),A,B) ) ).
fof(redefinition_k16_ami_1,axiom,
! [A,B,C,D,E,F] :
( ( 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,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k3_ami_1(A,B,C))
& m1_subset_1(F,k3_ami_1(A,B,D)) )
=> k16_ami_1(A,B,C,D,E,F) = k4_funct_4(C,D,E,F) ) ).
fof(dt_k17_ami_1,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& m1_ami_1(C,A,B)
& m1_ami_1(D,A,B) )
=> m1_ami_1(k17_ami_1(A,B,C,D),A,B) ) ).
fof(idempotence_k17_ami_1,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& m1_ami_1(C,A,B)
& m1_ami_1(D,A,B) )
=> k17_ami_1(A,B,C,C) = C ) ).
fof(redefinition_k17_ami_1,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& m1_ami_1(C,A,B)
& m1_ami_1(D,A,B) )
=> k17_ami_1(A,B,C,D) = k1_funct_4(C,D) ) ).
fof(dt_k18_ami_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> m1_ami_1(k18_ami_1(A,B,C),A,B) ) ).
fof(dt_u1_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ).
fof(dt_u2_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_u3_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ~ v1_xboole_0(u3_ami_1(A,B)) ) ).
fof(dt_u4_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( ~ v1_xboole_0(u4_ami_1(A,B))
& m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ).
fof(dt_u5_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v1_funct_1(u5_ami_1(A,B))
& v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))))
& m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ).
fof(dt_u6_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v1_funct_1(u6_ami_1(A,B))
& v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))))
& m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ).
fof(dt_g1_ami_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( m1_subset_1(C,B)
& m1_subset_1(D,k1_zfmisc_1(B))
& ~ v1_xboole_0(E)
& ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
& v1_funct_1(G)
& v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
& m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
& v1_funct_1(H)
& v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
& m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
=> ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A)
& l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ).
fof(free_g1_ami_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( m1_subset_1(C,B)
& m1_subset_1(D,k1_zfmisc_1(B))
& ~ v1_xboole_0(E)
& ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B)))))
& v1_funct_1(G)
& v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D)))
& m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D)))
& v1_funct_1(H)
& v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G)))
& m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) )
=> ! [I,J,K,L,M,N,O,P] :
( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P)
=> ( A = I
& B = J
& C = K
& D = L
& E = M
& F = N
& G = O
& H = P ) ) ) ).
fof(t35_ami_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> k7_ami_1(C) = k7_ami_1(k2_partfun1(A,B,C,a_3_0_ami_1(A,B,C))) ) ) ) ).
fof(d23_ami_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> k14_ami_1(A,B) = a_2_0_ami_1(A,B) ) ).
fof(fraenkel_a_3_0_ami_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,B,C)
& m2_relset_1(D,B,C) )
=> ( r2_hidden(A,a_3_0_ami_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& k8_funct_2(B,C,D,E) != k1_xboole_0 ) ) ) ).
fof(fraenkel_a_2_0_ami_1,axiom,
! [A,B,C] :
( l1_ami_1(C,B)
=> ( r2_hidden(A,a_2_0_ami_1(B,C))
<=> ? [D] :
( m1_subset_1(D,k7_ami_1(u5_ami_1(B,C)))
& A = D
& v1_finset_1(D) ) ) ) ).
%------------------------------------------------------------------------------