SET007 Axioms: SET007+646.ax
%------------------------------------------------------------------------------
% File : SET007+646 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Standard Ordering of Instruction Locations
% 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 : amistd_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 124 ( 3 unt; 0 def)
% Number of atoms : 1273 ( 80 equ)
% Maximal formula atoms : 25 ( 10 avg)
% Number of connectives : 1391 ( 242 ~; 5 |; 759 &)
% ( 30 <=>; 355 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 54 ( 52 usr; 1 prp; 0-4 aty)
% Number of functors : 73 ( 73 usr; 5 con; 0-4 aty)
% Number of variables : 400 ( 378 !; 22 ?)
% 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_amistd_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A) ) ).
fof(cc1_amistd_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_relat_1(A)
& v1_setfam_1(A) ) ) ).
fof(fc1_amistd_1,axiom,
! [A,B] :
( v1_finset_1(A)
=> v1_finset_1(k2_funcop_1(A,B)) ) ).
fof(fc2_amistd_1,axiom,
! [A,B] :
( ~ v1_xboole_0(k3_cqc_lang(A,B))
& v1_relat_1(k3_cqc_lang(A,B))
& v1_funct_1(k3_cqc_lang(A,B))
& v1_realset1(k3_cqc_lang(A,B))
& v1_setfam_1(k3_cqc_lang(A,B)) ) ).
fof(fc3_amistd_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ~ v1_xboole_0(k3_graph_2(A,B))
& v1_relat_1(k3_graph_2(A,B))
& v1_funct_1(k3_graph_2(A,B))
& v1_finset_1(k3_graph_2(A,B))
& v1_finseq_1(k3_graph_2(A,B))
& v1_setfam_1(k3_graph_2(A,B)) ) ) ).
fof(cc2_amistd_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_xboole_0(C)
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B) ) ) ) ) ).
fof(rc2_amistd_1,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v2_funct_1(C)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v1_membered(C)
& v2_membered(C)
& v3_membered(C)
& v4_membered(C)
& v5_membered(C) ) ) ).
fof(rc3_amistd_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)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_ami_1(C,A,B)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B) ) ) ).
fof(fc4_amistd_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))) )
=> ( v1_relat_1(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))
& v1_funct_1(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))
& v1_setfam_1(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(rc4_amistd_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ 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_ami_1(C,A,B)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v11_ami_1(C,A,B)
& v1_ami_3(C,A,B) ) ) ).
fof(cc3_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( l1_ami_1(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,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) ) ) ) ) ).
fof(fc5_amistd_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)
& v10_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B))
& m1_subset_1(D,u2_ami_1(A,B)) )
=> ~ v1_xboole_0(k1_amistd_1(A,B,D,C)) ) ).
fof(fc6_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v1_xboole_0(u2_ami_1(A,k4_amistd_1(A)))
& ~ v1_finset_1(u2_ami_1(A,k4_amistd_1(A)))
& ~ v1_realset1(u2_ami_1(A,k4_amistd_1(A))) ) ) ).
fof(fc7_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k4_amistd_1(A))
& v1_ami_1(k4_amistd_1(A),A)
& ~ v2_ami_1(k4_amistd_1(A),A) ) ) ).
fof(fc8_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k4_amistd_1(A))
& v1_ami_1(k4_amistd_1(A),A)
& ~ v2_ami_1(k4_amistd_1(A),A)
& v5_ami_1(k4_amistd_1(A),A)
& v6_ami_1(k4_amistd_1(A),A)
& v7_ami_1(k4_amistd_1(A),A)
& v8_ami_1(k4_amistd_1(A),A)
& v10_ami_1(k4_amistd_1(A),A)
& v13_ami_1(k4_amistd_1(A),A) ) ) ).
fof(fc9_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k4_amistd_1(A))
& v1_ami_1(k4_amistd_1(A),A)
& ~ v2_ami_1(k4_amistd_1(A),A)
& v5_ami_1(k4_amistd_1(A),A)
& v6_ami_1(k4_amistd_1(A),A)
& v7_ami_1(k4_amistd_1(A),A)
& v8_ami_1(k4_amistd_1(A),A)
& v10_ami_1(k4_amistd_1(A),A)
& v13_ami_1(k4_amistd_1(A),A)
& v4_amistd_1(k4_amistd_1(A),A) ) ) ).
fof(fc10_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( ~ v3_struct_0(k4_amistd_1(A))
& v1_ami_1(k4_amistd_1(A),A)
& ~ v2_ami_1(k4_amistd_1(A),A)
& v4_ami_1(k4_amistd_1(A),A)
& v5_ami_1(k4_amistd_1(A),A)
& v6_ami_1(k4_amistd_1(A),A)
& v7_ami_1(k4_amistd_1(A),A)
& v8_ami_1(k4_amistd_1(A),A)
& v10_ami_1(k4_amistd_1(A),A)
& v13_ami_1(k4_amistd_1(A),A)
& v4_amistd_1(k4_amistd_1(A),A) ) ) ).
fof(rc5_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ? [B] :
( l1_ami_1(B,A)
& ~ 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)
& v10_ami_1(B,A)
& v13_ami_1(B,A)
& v4_amistd_1(B,A) ) ) ).
fof(cc4_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( l1_ami_1(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A) )
=> ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v3_amistd_1(B,A) ) ) ) ) ).
fof(cc5_amistd_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)
& v10_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( v5_amistd_1(C,A,B)
=> ( ~ v1_xboole_0(C)
& ~ v3_ami_1(C,A,B) ) ) ) ) ).
fof(cc6_amistd_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)
& v10_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( v3_ami_1(C,A,B)
=> ( ~ v1_xboole_0(C)
& ~ v5_amistd_1(C,A,B) ) ) ) ) ).
fof(cc7_amistd_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ 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_ami_1(C,A,B)
=> ( v6_amistd_1(C,A,B)
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v7_amistd_1(C,A,B) ) ) ) ) ).
fof(cc8_amistd_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)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_xboole_0(C)
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v9_amistd_1(C,A,B) ) ) ) ) ).
fof(rc6_amistd_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)
& v4_amistd_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)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B) ) ) ).
fof(cc9_amistd_1,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v7_amistd_1(C,A,B)
& v9_amistd_1(C,A,B) )
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v8_amistd_1(C,A,B) ) ) ) ) ).
fof(rc7_amistd_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)
& v4_amistd_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)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& v10_amistd_1(C,A,B)
& v11_amistd_1(C,A,B) ) ) ).
fof(rc8_amistd_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)
& v4_amistd_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)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v6_amistd_1(C,A,B)
& v9_amistd_1(C,A,B) ) ) ).
fof(rc9_amistd_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)
& v4_amistd_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)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v6_amistd_1(C,A,B)
& v9_amistd_1(C,A,B)
& v10_amistd_1(C,A,B)
& v11_amistd_1(C,A,B) ) ) ).
fof(rc10_amistd_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)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& v4_amistd_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)
& v1_finset_1(C)
& v1_realset1(C)
& v1_setfam_1(C)
& v11_ami_1(C,A,B)
& v1_ami_3(C,A,B)
& v6_amistd_1(C,A,B)
& v7_amistd_1(C,A,B)
& v8_amistd_1(C,A,B)
& v9_amistd_1(C,A,B)
& v10_amistd_1(C,A,B)
& v11_amistd_1(C,A,B) ) ) ).
fof(rc11_amistd_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)
& v4_amistd_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)
& v1_finset_1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v6_amistd_1(C,A,B)
& v9_amistd_1(C,A,B)
& v10_amistd_1(C,A,B)
& v11_amistd_1(C,A,B) ) ) ).
fof(t1_amistd_1,axiom,
! [A] :
( v1_xreal_0(A)
=> k1_pre_circ(k1_tarski(A)) = A ) ).
fof(t2_amistd_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_pre_circ(k6_domain_1(k5_numbers,A)) = A ) ).
fof(t3_amistd_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_realset1(B)
& m2_finseq_1(B,A) )
=> ~ ( ~ v1_xboole_0(B)
& ! [C] :
( m1_subset_1(C,A)
=> B != k13_binarith(A,C) ) ) ) ) ).
fof(t4_amistd_1,axiom,
$true ).
fof(t5_amistd_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),np__1) = k4_finseq_4(k5_numbers,A,B,np__1) ) ) ) ).
fof(t6_amistd_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( ~ v1_realset1(C)
& m2_finseq_1(C,A) )
=> k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),k3_finseq_1(k4_graph_2(A,B,C))) = k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) ) ) ) ).
fof(t7_amistd_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k3_graph_2(A,k1_xboole_0) = A ) ).
fof(t8_amistd_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> k3_graph_2(B,k9_finseq_1(A)) = B ) ).
fof(t9_amistd_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),B) = k4_finseq_4(k5_numbers,A,C,B) ) ) ) ) ) ).
fof(t10_amistd_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(D),B)
| k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),k1_nat_1(k3_finseq_1(C),B)) = k4_finseq_4(k5_numbers,A,D,k1_nat_1(B,np__1)) ) ) ) ) ) ) ).
fof(t11_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_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)))
=> m1_subset_1(k1_funct_4(D,k2_pre_circ(u2_ami_1(A,B),C)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) ).
fof(t12_amistd_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_struct_0(C,B,u2_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))
=> v11_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ) ) ).
fof(t13_amistd_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) )
=> v13_ami_1(B,A) ) ) ).
fof(d1_amistd_1,axiom,
$true ).
fof(d2_amistd_1,axiom,
$true ).
fof(d3_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u3_ami_1(A,B))
=> ( v1_amistd_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m2_subset_1(F,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))
=> ( k1_ami_5(A,B,F) = C
=> ( E = k2_ami_1(A,B)
| k1_funct_1(k4_ami_1(A,B,F,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) ) ).
fof(d4_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(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))
=> ( v2_amistd_1(C,A,B)
<=> v1_amistd_1(k1_ami_5(A,B,C),A,B) ) ) ) ) ).
fof(t14_amistd_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] :
( 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_struct_0(D,B,u2_ami_1(A,B))
=> k1_amistd_1(A,B,D,C) = k1_struct_0(B,D) )
=> ( v1_realset1(u2_ami_1(A,B))
| v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) ) ).
fof(t15_amistd_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)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_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))
=> ( v3_ami_1(D,A,B)
=> k1_amistd_1(A,B,C,D) = k1_struct_0(B,C) ) ) ) ) ) ).
fof(d8_amistd_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_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r1_amistd_1(A,B,C,D)
<=> ? [E] :
( ~ v1_xboole_0(E)
& m2_finseq_1(E,u2_ami_1(A,B))
& k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,np__1) = C
& k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,k3_finseq_1(E)) = D
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,F)
=> ( r1_xreal_0(k3_finseq_1(E),F)
| r2_hidden(k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,k1_nat_1(F,np__1)),k3_amistd_1(A,B,k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,F))) ) ) ) ) ) ) ) ) ) ).
fof(t16_amistd_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_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> ( ( r1_amistd_1(A,B,C,D)
& r1_amistd_1(A,B,D,E) )
=> r1_amistd_1(A,B,C,E) ) ) ) ) ) ) ).
fof(d9_amistd_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) )
=> ( v3_amistd_1(B,A)
<=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( ( r1_amistd_1(A,B,C,D)
& r1_amistd_1(A,B,D,C) )
=> C = D ) ) ) ) ) ) ).
fof(d10_amistd_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) )
=> ( v4_amistd_1(B,A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(C,k5_numbers,u2_ami_1(A,B))
& v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
<=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E)) ) ) ) ) ) ) ) ).
fof(t17_amistd_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(C,k5_numbers,u2_ami_1(A,B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(D,k5_numbers,u2_ami_1(A,B)) )
=> ( ( v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,F)
<=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,F)) ) ) )
& v3_funct_2(D,k5_numbers,u2_ami_1(A,B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,F)
<=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),D,E),k8_funct_2(k5_numbers,u2_ami_1(A,B),D,F)) ) ) ) )
=> C = D ) ) ) ) ) ).
fof(t18_amistd_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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(C,k5_numbers,u2_ami_1(A,B)) )
=> ( v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
<=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E)) ) ) )
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,k1_nat_1(D,np__1)),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
=> r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) ).
fof(t19_amistd_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) )
=> ( v4_amistd_1(B,A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(C,k5_numbers,u2_ami_1(A,B))
& v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,k1_nat_1(D,np__1)),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
=> r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ).
fof(d11_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( v1_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( B = k4_amistd_1(A)
<=> ( u1_struct_0(B) = k2_xboole_0(k5_numbers,k6_domain_1(k1_zfmisc_1(k1_numbers),k5_numbers))
& u1_ami_1(A,B) = k5_numbers
& u2_ami_1(A,B) = k5_numbers
& u3_ami_1(A,B) = k7_domain_1(k5_numbers,np__0,np__1)
& u4_ami_1(A,B) = k7_domain_1(k2_zfmisc_1(k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0))
& u5_ami_1(A,B) = k1_funct_4(k2_pre_circ(k5_numbers,k7_domain_1(k2_zfmisc_1(k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0))),k3_cqc_lang(k5_numbers,k5_numbers))
& ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))
& m2_relset_1(C,k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))
& ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> k1_funct_1(C,D) = k1_funct_4(D,k3_cqc_lang(k5_numbers,k1_ordinal1(k1_funct_1(D,k5_numbers)))) )
& u6_ami_1(A,B) = k1_funct_4(k3_cqc_lang(k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),C),k3_cqc_lang(k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k6_partfun1(k4_card_3(u5_ami_1(A,B))))) ) ) ) ) ) ).
fof(t20_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> ( k1_ami_5(A,k4_amistd_1(A),B) = np__0
=> v3_ami_1(B,A,k4_amistd_1(A)) ) ) ) ).
fof(t21_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> ~ ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
& v3_ami_1(B,A,k4_amistd_1(A)) ) ) ) ).
fof(t22_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
| k1_ami_5(A,k4_amistd_1(A),B) = np__0 ) ) ) ).
fof(t23_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> v2_amistd_1(B,A,k4_amistd_1(A)) ) ) ).
fof(t24_amistd_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( m1_struct_0(C,k4_amistd_1(B),u2_ami_1(B,k4_amistd_1(B)))
=> ( C = A
=> k3_amistd_1(B,k4_amistd_1(B),C) = k2_tarski(A,k2_xcmplx_0(A,np__1)) ) ) ) ) ).
fof(d12_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( v4_ordinal2(C)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( D = k5_amistd_1(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u2_ami_1(A,B))
& m2_relset_1(E,k5_numbers,u2_ami_1(A,B))
& v3_funct_2(E,k5_numbers,u2_ami_1(A,B))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r1_xreal_0(F,G)
<=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),E,F),k8_funct_2(k5_numbers,u2_ami_1(A,B),E,G)) ) ) )
& D = k1_funct_1(E,C) ) ) ) ) ) ) ).
fof(t25_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( v4_ordinal2(C)
=> ! [D] :
( v4_ordinal2(D)
=> ( k5_amistd_1(A,B,C) = k5_amistd_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t26_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ? [D] :
( v4_ordinal2(D)
& C = k5_amistd_1(A,B,D) ) ) ) ) ).
fof(d13_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( v4_ordinal2(D)
=> ( D = k6_amistd_1(A,B,C)
<=> k5_amistd_1(A,B,D) = C ) ) ) ) ) ).
fof(t27_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( k7_amistd_1(A,B,C) = k7_amistd_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t28_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( v4_ordinal2(C)
=> ! [D] :
( v4_ordinal2(D)
=> ( r1_amistd_1(A,B,k5_amistd_1(A,B,C),k5_amistd_1(A,B,D))
<=> r1_xreal_0(C,D) ) ) ) ) ) ).
fof(t29_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r1_xreal_0(k7_amistd_1(A,B,C),k7_amistd_1(A,B,D))
<=> r1_amistd_1(A,B,C,D) ) ) ) ) ) ).
fof(t30_amistd_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) )
=> ( v4_amistd_1(B,A)
=> v3_amistd_1(B,A) ) ) ) ).
fof(d14_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( v4_ordinal2(D)
=> k8_amistd_1(A,B,C,D) = k5_amistd_1(A,B,k2_xcmplx_0(k7_amistd_1(A,B,C),D)) ) ) ) ) ).
fof(t31_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k8_amistd_1(A,B,C,np__0) = C ) ) ) ).
fof(t32_amistd_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( m1_struct_0(D,C,u2_ami_1(B,C))
=> ! [E] :
( m1_struct_0(E,C,u2_ami_1(B,C))
=> ( k8_amistd_1(B,C,D,A) = k8_amistd_1(B,C,E,A)
=> D = E ) ) ) ) ) ) ).
fof(t33_amistd_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( m1_struct_0(D,C,u2_ami_1(B,C))
=> k2_xcmplx_0(k7_amistd_1(B,C,D),A) = k7_amistd_1(B,C,k8_amistd_1(B,C,D,A)) ) ) ) ) ).
fof(d15_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k9_amistd_1(A,B,C) = k8_amistd_1(A,B,C,np__1) ) ) ) ).
fof(t34_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k9_amistd_1(A,B,C) = k5_amistd_1(A,B,k1_nat_1(k7_amistd_1(A,B,C),np__1)) ) ) ) ).
fof(t35_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> C != k9_amistd_1(A,B,C) ) ) ) ).
fof(t36_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( k9_amistd_1(A,B,C) = k9_amistd_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t37_amistd_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> k5_amistd_1(B,k4_amistd_1(B),A) = A ) ) ).
fof(t38_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,k4_amistd_1(A))))
=> ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
=> k1_funct_1(k4_ami_1(A,k4_amistd_1(A),B,C),k2_ami_1(A,k4_amistd_1(A))) = k9_amistd_1(A,k4_amistd_1(A),k6_ami_1(A,k4_amistd_1(A),C)) ) ) ) ) ).
fof(t39_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m1_struct_0(B,k4_amistd_1(A),u2_ami_1(A,k4_amistd_1(A)))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
=> ( k1_ami_5(A,k4_amistd_1(A),C) = np__1
=> k1_amistd_1(A,k4_amistd_1(A),B,C) = k1_struct_0(k4_amistd_1(A),k9_amistd_1(A,k4_amistd_1(A),B)) ) ) ) ) ).
fof(t40_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m1_struct_0(B,k4_amistd_1(A),u2_ami_1(A,k4_amistd_1(A)))
=> k3_amistd_1(A,k4_amistd_1(A),B) = k2_struct_0(k4_amistd_1(A),B,k9_amistd_1(A,k4_amistd_1(A),B)) ) ) ).
fof(d16_amistd_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)
& v4_amistd_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))
=> ( v5_amistd_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> k1_funct_1(k4_ami_1(A,B,C,D),k2_ami_1(A,B)) = k9_amistd_1(A,B,k6_ami_1(A,B,D)) ) ) ) ) ) ).
fof(t41_amistd_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)
& v10_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_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))
=> ( v5_amistd_1(D,A,B)
=> k1_amistd_1(A,B,C,D) = k1_struct_0(B,k9_amistd_1(A,B,C)) ) ) ) ) ) ).
fof(t42_amistd_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)
& v10_ami_1(B,A)
& v4_amistd_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))
=> ~ ( v5_amistd_1(C,A,B)
& v3_ami_1(C,A,B) ) ) ) ) ).
fof(t43_amistd_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)
& v4_amistd_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))
=> ~ ( ~ v1_xboole_0(k2_amistd_1(A,B,C))
& v5_amistd_1(C,A,B) ) ) ) ) ).
fof(d17_amistd_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)
=> ( v6_amistd_1(C,A,B)
<=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_hidden(D,k1_relat_1(C))
=> r1_tarski(k1_amistd_1(A,B,D,k5_ami_5(A,B,C,D)),k1_relat_1(C)) ) ) ) ) ) ) ).
fof(d18_amistd_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)
=> ( v7_amistd_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( ( r1_tarski(C,D)
& r2_hidden(k6_ami_1(A,B,D),k1_relat_1(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,D),E)),k1_relat_1(C)) ) ) ) ) ) ) ) ).
fof(d19_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v8_amistd_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( ( r1_tarski(C,D)
& k6_ami_1(A,B,D) = k5_amistd_1(A,B,np__0) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,D),E)),k1_relat_1(C)) ) ) ) ) ) ) ) ).
fof(t44_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( ( v7_amistd_1(C,A,B)
& r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(C)) )
=> v8_amistd_1(C,A,B) ) ) ) ) ).
fof(t45_amistd_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_ami_1(C,A,B)
=> ( v6_amistd_1(C,A,B)
=> v7_amistd_1(C,A,B) ) ) ) ) ).
fof(t46_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> v6_amistd_1(k14_ami_3(A,B,k5_amistd_1(A,B,np__0),k5_ami_1(A,B)),A,B) ) ) ).
fof(d20_amistd_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)
=> ( v9_amistd_1(C,A,B)
<=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_hidden(D,k1_relat_1(C))
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> ( r1_amistd_1(A,B,E,D)
=> r2_hidden(E,k1_relat_1(C)) ) ) ) ) ) ) ) ) ).
fof(t47_amistd_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] :
( ( v1_xboole_0(C)
& m1_ami_1(C,A,B) )
=> v9_amistd_1(C,A,B) ) ) ) ).
fof(t48_amistd_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)
& v4_amistd_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))
=> v9_amistd_1(k14_ami_3(A,B,k5_amistd_1(A,B,np__0),C),A,B) ) ) ) ).
fof(t49_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(C)) ) ) ) ).
fof(t50_amistd_1,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( ( v1_ami_3(D,B,C)
& v9_amistd_1(D,B,C)
& m1_ami_1(D,B,C) )
=> ( ~ r1_xreal_0(k4_card_1(D),A)
<=> r2_hidden(k5_amistd_1(B,C,A),k1_relat_1(D)) ) ) ) ) ) ).
fof(t51_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> r2_hidden(k10_amistd_1(A,B,C),k1_relat_1(C)) ) ) ) ).
fof(t52_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( r1_tarski(C,D)
=> r1_amistd_1(A,B,k10_amistd_1(A,B,C),k10_amistd_1(A,B,D)) ) ) ) ) ) ).
fof(t53_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_hidden(D,k1_relat_1(C))
=> r1_amistd_1(A,B,D,k10_amistd_1(A,B,C)) ) ) ) ) ) ).
fof(t54_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( ( r1_tarski(C,D)
& k10_amistd_1(A,B,C) = k10_amistd_1(A,B,D) )
=> C = D ) ) ) ) ) ).
fof(t55_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> k10_amistd_1(A,B,C) = k5_amistd_1(A,B,k5_binarith(k4_card_1(C),np__1)) ) ) ) ).
fof(d22_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ( v10_amistd_1(C,A,B)
<=> k1_funct_1(C,k10_amistd_1(A,B,C)) = k5_ami_1(A,B) ) ) ) ) ).
fof(d23_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ( v11_amistd_1(C,A,B)
<=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( ( k1_funct_1(C,D) = k5_ami_1(A,B)
& r2_hidden(D,k1_relat_1(C)) )
=> D = k10_amistd_1(A,B,C) ) ) ) ) ) ) ).
fof(reflexivity_r1_amistd_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,u2_ami_1(A,B))
& m1_subset_1(D,u2_ami_1(A,B)) )
=> r1_amistd_1(A,B,C,C) ) ).
fof(dt_k1_amistd_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,u2_ami_1(A,B))
& m1_subset_1(D,u4_ami_1(A,B)) )
=> m1_subset_1(k1_amistd_1(A,B,C,D),k1_zfmisc_1(u2_ami_1(A,B))) ) ).
fof(dt_k2_amistd_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,u4_ami_1(A,B)) )
=> m1_subset_1(k2_amistd_1(A,B,C),k1_zfmisc_1(u2_ami_1(A,B))) ) ).
fof(dt_k3_amistd_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,u2_ami_1(A,B)) )
=> m1_subset_1(k3_amistd_1(A,B,C),k1_zfmisc_1(u2_ami_1(A,B))) ) ).
fof(dt_k4_amistd_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ( v1_ami_1(k4_amistd_1(A),A)
& l1_ami_1(k4_amistd_1(A),A) ) ) ).
fof(dt_k5_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& v4_ordinal2(C) )
=> m1_struct_0(k5_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(dt_k6_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B)) )
=> v4_ordinal2(k6_amistd_1(A,B,C)) ) ).
fof(dt_k7_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B)) )
=> m2_subset_1(k7_amistd_1(A,B,C),k1_numbers,k5_numbers) ) ).
fof(redefinition_k7_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B)) )
=> k7_amistd_1(A,B,C) = k6_amistd_1(A,B,C) ) ).
fof(dt_k8_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B))
& v4_ordinal2(D) )
=> m1_struct_0(k8_amistd_1(A,B,C,D),B,u2_ami_1(A,B)) ) ).
fof(dt_k9_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u2_ami_1(A,B)) )
=> m1_struct_0(k9_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(dt_k10_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> m1_struct_0(k10_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(d5_amistd_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_struct_0(C,B,u2_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))
=> k1_amistd_1(A,B,C,D) = a_4_0_amistd_1(A,B,C,D) ) ) ) ) ).
fof(d6_amistd_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] :
( 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))
=> k2_amistd_1(A,B,C) = k1_setfam_1(a_3_0_amistd_1(A,B,C)) ) ) ) ).
fof(d7_amistd_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_struct_0(C,B,u2_ami_1(A,B))
=> k3_amistd_1(A,B,C) = k3_tarski(a_3_1_amistd_1(A,B,C)) ) ) ) ).
fof(d21_amistd_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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( D = k10_amistd_1(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& v1_finset_1(E)
& v5_membered(E)
& E = a_3_2_amistd_1(A,B,C)
& D = k5_amistd_1(A,B,k1_pre_circ(E)) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_amistd_1,axiom,
! [A,B,C,D,E] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& l1_ami_1(C,B)
& m1_struct_0(D,C,u2_ami_1(B,C))
& m2_subset_1(E,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C)) )
=> ( r2_hidden(A,a_4_0_amistd_1(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(B,C)))
& A = k6_ami_1(B,C,k9_ami_1(B,C,F))
& k6_ami_1(B,C,F) = D
& k13_ami_1(B,C,F,D) = E ) ) ) ).
fof(fraenkel_a_3_0_amistd_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& l1_ami_1(C,B)
& m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C)) )
=> ( r2_hidden(A,a_3_0_amistd_1(B,C,D))
<=> ? [E] :
( m1_struct_0(E,C,u2_ami_1(B,C))
& A = k1_amistd_1(B,C,E,D) ) ) ) ).
fof(fraenkel_a_3_1_amistd_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& l1_ami_1(C,B)
& m1_struct_0(D,C,u2_ami_1(B,C)) )
=> ( r2_hidden(A,a_3_1_amistd_1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
& A = k6_subset_1(u2_ami_1(B,C),k1_amistd_1(B,C,D,E),k2_amistd_1(B,C,E)) ) ) ) ).
fof(fraenkel_a_3_2_amistd_1,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,B,C)
& m1_ami_1(D,B,C) )
=> ( r2_hidden(A,a_3_2_amistd_1(B,C,D))
<=> ? [E] :
( m1_struct_0(E,C,u2_ami_1(B,C))
& A = k7_amistd_1(B,C,E)
& r2_hidden(E,k1_relat_1(D)) ) ) ) ).
%------------------------------------------------------------------------------