SET007 Axioms: SET007+647.ax
%------------------------------------------------------------------------------
% File : SET007+647 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Composition of Macro Instructions of Standard Computers
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 160 ( 2 unt; 0 def)
% Number of atoms : 1868 ( 96 equ)
% Maximal formula atoms : 33 ( 11 avg)
% Number of connectives : 2036 ( 328 ~; 1 |;1294 &)
% ( 25 <=>; 388 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 64 ( 62 usr; 1 prp; 0-3 aty)
% Number of functors : 68 ( 68 usr; 5 con; 0-6 aty)
% Number of variables : 514 ( 499 !; 15 ?)
% 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_amistd_2,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B) )
=> ( v1_relat_1(k1_funct_4(A,B))
& v1_funct_1(k1_funct_4(A,B))
& ~ v1_xboole_0(k1_funct_4(A,B))
& v1_setfam_1(k1_funct_4(A,B)) ) ) ).
fof(fc2_amistd_2,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B) )
=> ( v1_relat_1(k1_funct_4(B,A))
& v1_funct_1(k1_funct_4(B,A))
& ~ v1_xboole_0(k1_funct_4(B,A))
& v1_setfam_1(k1_funct_4(B,A)) ) ) ).
fof(fc3_amistd_2,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B) )
=> ( v1_relat_1(k1_funct_4(A,B))
& v1_funct_1(k1_funct_4(A,B))
& v1_finset_1(k1_funct_4(A,B))
& v1_setfam_1(k1_funct_4(A,B)) ) ) ).
fof(fc4_amistd_2,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k4_xboole_0(A,B))
& v1_funct_1(k4_xboole_0(A,B))
& v1_setfam_1(k4_xboole_0(A,B)) ) ) ).
fof(fc5_amistd_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_fraenkel(k4_card_3(A))
& v1_amistd_2(k4_card_3(A)) ) ) ).
fof(cc1_amistd_2,axiom,
! [A] :
( v1_amistd_2(A)
=> ( v1_fraenkel(A)
& v1_pralg_2(A) ) ) ).
fof(rc1_amistd_2,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_pralg_2(A)
& v1_amistd_2(A) ) ).
fof(cc2_amistd_2,axiom,
! [A,B] :
( m1_finseq_2(B,A)
=> v1_fraenkel(B) ) ).
fof(fc6_amistd_2,axiom,
! [A,B] :
( m1_subset_1(A,k5_numbers)
=> ( v1_fraenkel(k4_finseq_2(A,B))
& v1_pralg_2(k4_finseq_2(A,B)) ) ) ).
fof(fc7_amistd_2,axiom,
! [A,B] :
( m1_subset_1(A,k5_numbers)
=> ( v1_fraenkel(k4_finseq_2(A,B))
& v1_pralg_2(k4_finseq_2(A,B))
& v1_amistd_2(k4_finseq_2(A,B)) ) ) ).
fof(rc2_amistd_2,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))
& ~ v1_xboole_0(C)
& v3_ami_1(C,A,B) ) ) ).
fof(fc8_amistd_2,axiom,
! [A,B,C] :
( ( l1_ami_1(B,A)
& m1_subset_1(C,u3_ami_1(A,B)) )
=> v1_fraenkel(k5_amistd_2(A,B,C)) ) ).
fof(cc3_amistd_2,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)
& v7_amistd_2(B,A) ) ) ) ) ).
fof(rc3_amistd_2,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)
& v3_amistd_1(B,A)
& v4_amistd_1(B,A)
& v7_amistd_2(B,A) ) ) ).
fof(fc9_amistd_2,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& v7_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ~ v1_realset1(u2_ami_1(A,B)) ) ).
fof(fc10_amistd_2,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& m1_subset_1(B,u4_ami_1(A,k4_amistd_1(A))) )
=> ( v1_relat_1(k2_amistd_1(A,k4_amistd_1(A),B))
& v1_xboole_0(k2_amistd_1(A,k4_amistd_1(A),B))
& v1_finset_1(k2_amistd_1(A,k4_amistd_1(A),B))
& v1_setfam_1(k2_amistd_1(A,k4_amistd_1(A),B))
& v1_membered(k2_amistd_1(A,k4_amistd_1(A),B))
& v2_membered(k2_amistd_1(A,k4_amistd_1(A),B))
& v3_membered(k2_amistd_1(A,k4_amistd_1(A),B))
& v4_membered(k2_amistd_1(A,k4_amistd_1(A),B))
& v5_membered(k2_amistd_1(A,k4_amistd_1(A),B)) ) ) ).
fof(cc4_amistd_2,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v8_amistd_2(B,A)
=> v2_amistd_2(B,A) ) ) ).
fof(fc11_amistd_2,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)
& v3_amistd_1(k4_amistd_1(A),A)
& v4_amistd_1(k4_amistd_1(A),A)
& v2_amistd_2(k4_amistd_1(A),A)
& v5_amistd_2(k4_amistd_1(A),A)
& v6_amistd_2(k4_amistd_1(A),A)
& v7_amistd_2(k4_amistd_1(A),A)
& v8_amistd_2(k4_amistd_1(A),A) ) ) ).
fof(rc4_amistd_2,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)
& v3_amistd_1(B,A)
& v4_amistd_1(B,A)
& v2_amistd_2(B,A)
& v5_amistd_2(B,A)
& v6_amistd_2(B,A)
& v7_amistd_2(B,A)
& v8_amistd_2(B,A) ) ) ).
fof(fc12_amistd_2,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u3_ami_1(A,B)) )
=> ( v1_fraenkel(k5_amistd_2(A,B,C))
& v1_pralg_2(k5_amistd_2(A,B,C))
& v1_amistd_2(k5_amistd_2(A,B,C)) ) ) ).
fof(fc13_amistd_2,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& v2_amistd_2(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u3_ami_1(A,B)) )
=> ( v1_fraenkel(k5_amistd_2(A,B,C))
& v1_pralg_2(k5_amistd_2(A,B,C)) ) ) ).
fof(cc5_amistd_2,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)
& v5_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( ~ v1_xboole_0(C)
& v3_amistd_2(C,A,B) ) ) ) ).
fof(cc6_amistd_2,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)
& v6_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( ~ v1_xboole_0(C)
& v4_amistd_2(C,A,B) ) ) ) ).
fof(fc14_amistd_2,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)
& v7_amistd_2(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> ( v1_relat_1(k2_amistd_1(A,B,C))
& v1_xboole_0(k2_amistd_1(A,B,C))
& v1_finset_1(k2_amistd_1(A,B,C))
& v1_setfam_1(k2_amistd_1(A,B,C))
& v1_membered(k2_amistd_1(A,B,C))
& v2_membered(k2_amistd_1(A,B,C))
& v3_membered(k2_amistd_1(A,B,C))
& v4_membered(k2_amistd_1(A,B,C))
& v5_membered(k2_amistd_1(A,B,C)) ) ) ).
fof(rc5_amistd_2,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)
& v7_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& ~ v1_realset1(C) ) ) ).
fof(cc7_amistd_2,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_ami_3(C,A,B)
& v1_realset1(C) )
=> ( v1_relat_1(C)
& v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_finset_1(C)
& v1_setfam_1(C)
& v1_ami_3(C,A,B)
& v11_amistd_1(C,A,B) ) ) ) ) ).
fof(cc8_amistd_2,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)
& v6_amistd_2(B,A)
& v7_amistd_2(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)
& v4_amistd_2(C,A,B)
& v9_amistd_2(C,A,B) ) ) ) ) ).
fof(cc9_amistd_2,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)
& v6_amistd_2(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)
& v4_amistd_2(C,A,B)
& v9_amistd_2(C,A,B) ) ) ) ) ).
fof(fc15_amistd_2,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) )
=> ( v1_relat_1(k6_amistd_2(A,B))
& v1_funct_1(k6_amistd_2(A,B))
& ~ v1_xboole_0(k6_amistd_2(A,B))
& v1_finset_1(k6_amistd_2(A,B))
& v1_setfam_1(k6_amistd_2(A,B))
& v1_ami_3(k6_amistd_2(A,B),A,B)
& v9_amistd_1(k6_amistd_2(A,B),A,B)
& v11_amistd_1(k6_amistd_2(A,B),A,B)
& v1_realset1(k6_amistd_2(A,B)) ) ) ).
fof(fc16_amistd_2,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) )
=> ( v1_relat_1(k6_amistd_2(A,B))
& v1_funct_1(k6_amistd_2(A,B))
& ~ v1_xboole_0(k6_amistd_2(A,B))
& v1_finset_1(k6_amistd_2(A,B))
& v1_setfam_1(k6_amistd_2(A,B))
& v1_ami_3(k6_amistd_2(A,B),A,B)
& v6_amistd_1(k6_amistd_2(A,B),A,B)
& v9_amistd_1(k6_amistd_2(A,B),A,B)
& v11_amistd_1(k6_amistd_2(A,B),A,B)
& v1_realset1(k6_amistd_2(A,B)) ) ) ).
fof(fc17_amistd_2,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ( v1_relat_1(k6_amistd_2(A,B))
& v1_funct_1(k6_amistd_2(A,B))
& ~ v1_xboole_0(k6_amistd_2(A,B))
& v1_finset_1(k6_amistd_2(A,B))
& v1_setfam_1(k6_amistd_2(A,B))
& v11_ami_1(k6_amistd_2(A,B),A,B)
& v1_ami_3(k6_amistd_2(A,B),A,B)
& v9_amistd_1(k6_amistd_2(A,B),A,B)
& v11_amistd_1(k6_amistd_2(A,B),A,B)
& v1_realset1(k6_amistd_2(A,B)) ) ) ).
fof(fc18_amistd_2,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) )
=> ( v1_relat_1(k6_amistd_2(A,B))
& v1_funct_1(k6_amistd_2(A,B))
& ~ v1_xboole_0(k6_amistd_2(A,B))
& v1_finset_1(k6_amistd_2(A,B))
& v1_setfam_1(k6_amistd_2(A,B))
& v1_ami_3(k6_amistd_2(A,B),A,B)
& v9_amistd_1(k6_amistd_2(A,B),A,B)
& v10_amistd_1(k6_amistd_2(A,B),A,B)
& v11_amistd_1(k6_amistd_2(A,B),A,B)
& v1_realset1(k6_amistd_2(A,B)) ) ) ).
fof(fc19_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B))
& v4_ordinal2(D) )
=> ( ~ v1_xboole_0(k8_amistd_2(A,B,C,D))
& v3_ami_1(k8_amistd_2(A,B,C,D),A,B)
& ~ v5_amistd_1(k8_amistd_2(A,B,C,D),A,B)
& v4_amistd_2(k8_amistd_2(A,B,C,D),A,B)
& v9_amistd_2(k8_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc20_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k9_amistd_2(A,B,C,D))
& v1_funct_1(k9_amistd_2(A,B,C,D))
& v1_finset_1(k9_amistd_2(A,B,C,D))
& v1_setfam_1(k9_amistd_2(A,B,C,D))
& v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc21_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k9_amistd_2(A,B,C,D))
& v1_funct_1(k9_amistd_2(A,B,C,D))
& v1_xboole_0(k9_amistd_2(A,B,C,D))
& v1_finset_1(k9_amistd_2(A,B,C,D))
& v1_setfam_1(k9_amistd_2(A,B,C,D))
& v1_ami_3(k9_amistd_2(A,B,C,D),A,B)
& v1_membered(k9_amistd_2(A,B,C,D))
& v2_membered(k9_amistd_2(A,B,C,D))
& v3_membered(k9_amistd_2(A,B,C,D))
& v4_membered(k9_amistd_2(A,B,C,D))
& v5_membered(k9_amistd_2(A,B,C,D))
& v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc22_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k9_amistd_2(A,B,C,D))
& v1_funct_1(k9_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k9_amistd_2(A,B,C,D))
& v1_finset_1(k9_amistd_2(A,B,C,D))
& v1_setfam_1(k9_amistd_2(A,B,C,D))
& v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc23_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k9_amistd_2(A,B,C,D))
& v1_funct_1(k9_amistd_2(A,B,C,D))
& v1_finset_1(k9_amistd_2(A,B,C,D))
& v1_setfam_1(k9_amistd_2(A,B,C,D))
& v1_ami_3(k9_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc24_amistd_2,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_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k10_amistd_2(A,B,C,D))
& v1_funct_1(k10_amistd_2(A,B,C,D))
& v1_finset_1(k10_amistd_2(A,B,C,D))
& v1_setfam_1(k10_amistd_2(A,B,C,D))
& v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc25_amistd_2,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)
& v1_xboole_0(C)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k10_amistd_2(A,B,C,D))
& v1_funct_1(k10_amistd_2(A,B,C,D))
& v1_xboole_0(k10_amistd_2(A,B,C,D))
& v1_finset_1(k10_amistd_2(A,B,C,D))
& v1_setfam_1(k10_amistd_2(A,B,C,D))
& v1_ami_3(k10_amistd_2(A,B,C,D),A,B)
& v1_membered(k10_amistd_2(A,B,C,D))
& v2_membered(k10_amistd_2(A,B,C,D))
& v3_membered(k10_amistd_2(A,B,C,D))
& v4_membered(k10_amistd_2(A,B,C,D))
& v5_membered(k10_amistd_2(A,B,C,D))
& v9_amistd_1(k10_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc26_amistd_2,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)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> ( v1_relat_1(k10_amistd_2(A,B,C,D))
& v1_funct_1(k10_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k10_amistd_2(A,B,C,D))
& v1_finset_1(k10_amistd_2(A,B,C,D))
& v1_setfam_1(k10_amistd_2(A,B,C,D))
& v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ).
fof(cc10_amistd_2,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)
& v6_amistd_2(B,A)
& v8_amistd_2(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)
& v4_amistd_2(C,A,B)
& v10_amistd_2(C,A,B) ) ) ) ) ).
fof(cc11_amistd_2,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)
& v6_amistd_2(B,A)
& v8_amistd_2(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)
& v4_amistd_2(C,A,B)
& v10_amistd_2(C,A,B) ) ) ) ) ).
fof(cc12_amistd_2,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v2_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)
=> ( ~ v1_xboole_0(C)
& v12_amistd_2(C,A,B) ) ) ) ) ).
fof(fc27_amistd_2,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)
& v3_amistd_1(k4_amistd_1(A),A)
& v4_amistd_1(k4_amistd_1(A),A)
& v2_amistd_2(k4_amistd_1(A),A)
& v5_amistd_2(k4_amistd_1(A),A)
& v6_amistd_2(k4_amistd_1(A),A)
& v7_amistd_2(k4_amistd_1(A),A)
& v8_amistd_2(k4_amistd_1(A),A)
& v11_amistd_2(k4_amistd_1(A),A)
& v13_amistd_2(k4_amistd_1(A),A) ) ) ).
fof(rc6_amistd_2,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)
& v3_amistd_1(B,A)
& v4_amistd_1(B,A)
& v2_amistd_2(B,A)
& v5_amistd_2(B,A)
& v6_amistd_2(B,A)
& v7_amistd_2(B,A)
& v8_amistd_2(B,A)
& v11_amistd_2(B,A)
& v13_amistd_2(B,A) ) ) ).
fof(cc13_amistd_2,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)
& v8_amistd_2(B,A)
& v11_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( ~ v1_xboole_0(C)
& v10_amistd_2(C,A,B) ) ) ) ).
fof(cc14_amistd_2,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& v13_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> ( ~ v1_xboole_0(C)
& v12_amistd_2(C,A,B) ) ) ) ).
fof(fc28_amistd_2,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)
& v1_realset1(C)
& m1_ami_1(C,A,B) )
=> ( v1_relat_1(k11_amistd_2(A,B,C))
& v1_funct_1(k11_amistd_2(A,B,C))
& v1_xboole_0(k11_amistd_2(A,B,C))
& v1_finset_1(k11_amistd_2(A,B,C))
& v1_setfam_1(k11_amistd_2(A,B,C))
& v1_ami_3(k11_amistd_2(A,B,C),A,B)
& v1_membered(k11_amistd_2(A,B,C))
& v2_membered(k11_amistd_2(A,B,C))
& v3_membered(k11_amistd_2(A,B,C))
& v4_membered(k11_amistd_2(A,B,C))
& v5_membered(k11_amistd_2(A,B,C))
& v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) ).
fof(fc29_amistd_2,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) )
=> ( v1_relat_1(k11_amistd_2(A,B,C))
& v1_funct_1(k11_amistd_2(A,B,C))
& v1_finset_1(k11_amistd_2(A,B,C))
& v1_setfam_1(k11_amistd_2(A,B,C))
& v1_ami_3(k11_amistd_2(A,B,C),A,B) ) ) ).
fof(fc30_amistd_2,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)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ( v1_relat_1(k11_amistd_2(A,B,C))
& v1_funct_1(k11_amistd_2(A,B,C))
& v1_finset_1(k11_amistd_2(A,B,C))
& v1_setfam_1(k11_amistd_2(A,B,C))
& v1_ami_3(k11_amistd_2(A,B,C),A,B)
& v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) ).
fof(fc31_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_relat_1(k12_amistd_2(A,B,C,D))
& v1_funct_1(k12_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
& v1_finset_1(k12_amistd_2(A,B,C,D))
& v1_setfam_1(k12_amistd_2(A,B,C,D))
& v1_ami_3(k12_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc32_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_relat_1(k12_amistd_2(A,B,C,D))
& v1_funct_1(k12_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
& v1_finset_1(k12_amistd_2(A,B,C,D))
& v1_setfam_1(k12_amistd_2(A,B,C,D))
& v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc33_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& v10_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_relat_1(k12_amistd_2(A,B,C,D))
& v1_funct_1(k12_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
& v1_finset_1(k12_amistd_2(A,B,C,D))
& v1_setfam_1(k12_amistd_2(A,B,C,D))
& v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v10_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc34_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(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)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& v10_amistd_1(D,A,B)
& v11_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_relat_1(k12_amistd_2(A,B,C,D))
& v1_funct_1(k12_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
& v1_finset_1(k12_amistd_2(A,B,C,D))
& v1_setfam_1(k12_amistd_2(A,B,C,D))
& v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v10_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v11_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) ).
fof(fc35_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v8_amistd_2(B,A)
& v11_amistd_2(B,A)
& v13_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v6_amistd_1(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v6_amistd_1(D,A,B)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_relat_1(k12_amistd_2(A,B,C,D))
& v1_funct_1(k12_amistd_2(A,B,C,D))
& ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
& v1_finset_1(k12_amistd_2(A,B,C,D))
& v1_setfam_1(k12_amistd_2(A,B,C,D))
& v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
& v6_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v7_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v8_amistd_1(k12_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) ).
fof(t1_amistd_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_tarski(k1_relat_1(A),k1_relat_1(B))
<=> r2_tarski(A,B) ) ) ) ).
fof(t2_amistd_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B) )
=> ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
=> k4_card_1(k1_funct_4(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) ).
fof(t3_amistd_2,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(A,k4_xboole_0(k1_relat_1(B),k1_relat_1(C)))
=> k1_funct_1(k4_xboole_0(B,C),A) = k1_funct_1(B,A) ) ) ) ).
fof(t4_amistd_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> k6_xcmplx_0(k4_card_1(A),np__1) = k5_binarith(k4_card_1(A),np__1) ) ).
fof(d1_amistd_2,axiom,
! [A] :
( v1_fraenkel(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( ~ v1_xboole_0(A)
=> ( B = k1_amistd_2(A)
<=> ( ! [C] :
( r2_hidden(C,k1_relat_1(B))
<=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,A)
=> r2_hidden(C,k1_relat_1(D)) ) ) )
& ! [C] :
( r2_hidden(C,k1_relat_1(B))
=> k1_funct_1(B,C) = k5_card_3(C,A) ) ) ) )
& ( v1_xboole_0(A)
=> ( B = k1_amistd_2(A)
<=> B = k1_xboole_0 ) ) ) ) ) ).
fof(d2_amistd_2,axiom,
! [A] :
( v1_amistd_2(A)
<=> ? [B] :
( v1_relat_1(B)
& v1_funct_1(B)
& A = k4_card_3(B) ) ) ).
fof(t7_amistd_2,axiom,
! [A] :
( ( v1_fraenkel(A)
& v1_pralg_2(A) )
=> k1_relat_1(k1_amistd_2(A)) = k1_pralg_2(A) ) ).
fof(t8_amistd_2,axiom,
! [A] :
( v1_fraenkel(A)
=> ! [B] :
( r2_hidden(B,k1_relat_1(k1_amistd_2(A)))
=> k1_funct_1(k1_amistd_2(A),B) = k5_card_3(B,A) ) ) ).
fof(t9_amistd_2,axiom,
! [A] :
( ( v1_fraenkel(A)
& v1_pralg_2(A) )
=> r1_tarski(A,k4_card_3(k1_amistd_2(A))) ) ).
fof(t10_amistd_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_amistd_2(A) )
=> A = k4_card_3(k1_amistd_2(A)) ) ).
fof(t11_amistd_2,axiom,
! [A,B,C] :
( l1_ami_1(C,B)
=> ! [D] :
( m1_ami_1(D,B,C)
=> m1_ami_1(k4_xboole_0(D,A),B,C) ) ) ).
fof(t12_amistd_2,axiom,
! [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)
& l1_ami_1(C,B) )
=> ! [D] :
( ( v1_ami_3(D,B,C)
& m1_ami_1(D,B,C) )
=> ( v1_ami_3(k4_xboole_0(D,A),B,C)
& m1_ami_1(k4_xboole_0(D,A),B,C) ) ) ) ) ).
fof(t13_amistd_2,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_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( k1_relat_1(C) = k1_relat_1(D)
=> v9_amistd_1(D,A,B) ) ) ) ) ) ).
fof(t14_amistd_2,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_ami_3(C,A,B)
& v9_amistd_1(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_xreal_0(k4_card_1(C),k7_amistd_1(A,B,D)) ) ) ) ) ) ).
fof(d3_amistd_2,axiom,
! [A,B] :
( 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))
=> k3_amistd_2(A,B,C) = k3_domain_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B))),C) ) ) ).
fof(t16_amistd_2,axiom,
! [A,B] :
( 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] :
( 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_ami_5(A,B,C) = k1_ami_5(A,B,D)
& k4_amistd_2(A,B,C) = k4_amistd_2(A,B,D) )
=> C = D ) ) ) ) ).
fof(d4_amistd_2,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v2_amistd_2(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] :
( 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_ami_5(A,B,C) = k1_ami_5(A,B,D)
=> k4_finseq_1(k4_amistd_2(A,B,C)) = k4_finseq_1(k4_amistd_2(A,B,D)) ) ) ) ) ) ).
fof(t17_amistd_2,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)))
=> k4_amistd_2(A,k4_amistd_1(A),B) = np__0 ) ) ).
fof(d6_amistd_2,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))
=> ( v3_amistd_2(C,A,B)
<=> ! [D] :
~ ( r2_hidden(D,k2_amistd_1(A,B,C))
& ! [E] :
~ ( r2_hidden(E,k4_finseq_1(k4_amistd_2(A,B,C)))
& D = k1_funct_1(k4_amistd_2(A,B,C),E)
& k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),E) = u2_ami_1(A,B) ) ) ) ) ) ) ).
fof(d7_amistd_2,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))
=> ( v4_amistd_2(C,A,B)
<=> ! [D] :
( ? [E] :
( r2_hidden(E,k4_finseq_1(k4_amistd_2(A,B,C)))
& D = k1_funct_1(k4_amistd_2(A,B,C),E)
& k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),E) = u2_ami_1(A,B) )
=> r2_hidden(D,k2_amistd_1(A,B,C)) ) ) ) ) ) ).
fof(d8_amistd_2,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) )
=> ( v5_amistd_2(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_amistd_2(C,A,B) ) ) ) ) ).
fof(d9_amistd_2,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) )
=> ( v6_amistd_2(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))
=> v4_amistd_2(C,A,B) ) ) ) ) ).
fof(d10_amistd_2,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v7_amistd_2(B,A)
<=> ~ v1_realset1(u2_ami_1(A,B)) ) ) ).
fof(t18_amistd_2,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))
=> ( ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> k1_amistd_1(A,B,D,C) = k1_struct_0(B,k9_amistd_1(A,B,D)) )
=> v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) ).
fof(d11_amistd_2,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v8_amistd_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u3_ami_1(A,B))
=> v1_amistd_2(k5_amistd_2(A,B,C)) ) ) ) ).
fof(t19_amistd_2,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u3_ami_1(A,k4_amistd_1(A)))
=> k5_amistd_2(A,k4_amistd_1(A),B) = k6_domain_1(k5_numbers,np__0) ) ) ).
fof(t20_amistd_2,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v2_amistd_2(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] :
( ( r2_hidden(D,k4_finseq_1(k4_amistd_2(A,B,C)))
& k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),D) = u2_ami_1(A,B) )
=> m1_struct_0(k1_funct_1(k4_amistd_2(A,B,C),D),B,u2_ami_1(A,B)) ) ) ) ) ).
fof(t21_amistd_2,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)
& v7_amistd_2(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)
=> v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) ).
fof(d12_amistd_2,axiom,
! [A,B] :
( 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_2(C,A,B)
<=> ! [D] :
~ ( r2_hidden(D,k4_finseq_1(k4_amistd_2(A,B,C)))
& k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),D) = u2_ami_1(A,B) ) ) ) ) ).
fof(t22_amistd_2,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)
& v5_amistd_2(B,A)
& v7_amistd_2(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_2(C,A,B)
=> v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) ).
fof(t23_amistd_2,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)
& v6_amistd_2(B,A)
& v7_amistd_2(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)
=> v9_amistd_2(C,A,B) ) ) ) ) ).
fof(t24_amistd_2,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)
& v6_amistd_2(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)
=> v9_amistd_2(C,A,B) ) ) ) ) ).
fof(d13_amistd_2,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) )
=> k6_amistd_2(A,B) = k14_ami_3(A,B,k5_amistd_1(A,B,np__0),k5_ami_1(A,B)) ) ) ).
fof(t25_amistd_2,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) )
=> k4_card_1(k6_amistd_2(A,B)) = np__1 ) ) ).
fof(t26_amistd_2,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)
& v9_amistd_1(C,A,B)
& v10_amistd_1(C,A,B)
& v11_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> ( k4_card_1(C) = np__1
=> C = k6_amistd_2(A,B) ) ) ) ) ).
fof(t27_amistd_2,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) )
=> k10_amistd_1(A,B,k6_amistd_2(A,B)) = k5_amistd_1(A,B,np__0) ) ) ).
fof(d14_amistd_2,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)
& v8_amistd_2(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] :
( v4_ordinal2(D)
=> ! [E] :
( m2_subset_1(E,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 = k8_amistd_2(A,B,C,D)
<=> ( k1_ami_5(A,B,E) = k1_ami_5(A,B,C)
& k4_finseq_1(k4_amistd_2(A,B,E)) = k4_finseq_1(k4_amistd_2(A,B,C))
& ! [F] :
( r2_hidden(F,k4_finseq_1(k4_amistd_2(A,B,C)))
=> ( ~ ( k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),F) = u2_ami_1(A,B)
& ! [G] :
( m1_struct_0(G,B,u2_ami_1(A,B))
=> ~ ( G = k1_funct_1(k4_amistd_2(A,B,C),F)
& k1_funct_1(k4_amistd_2(A,B,E),F) = k5_amistd_1(A,B,k2_xcmplx_0(D,k7_amistd_1(A,B,G))) ) ) )
& ( k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),F) != u2_ami_1(A,B)
=> k1_funct_1(k4_amistd_2(A,B,E),F) = k1_funct_1(k4_amistd_2(A,B,C),F) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_amistd_2,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)
& v8_amistd_2(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))
=> k8_amistd_2(A,B,C,np__0) = C ) ) ) ).
fof(t29_amistd_2,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)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> ( v9_amistd_2(D,B,C)
=> k8_amistd_2(B,C,D,A) = D ) ) ) ) ) ).
fof(t30_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v4_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v10_ami_1(C,B)
& v4_amistd_1(C,B)
& v6_amistd_2(C,B)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> k8_amistd_2(B,C,k5_ami_1(B,C),A) = k5_ami_1(B,C) ) ) ) ).
fof(t31_amistd_2,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)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> k5_amistd_2(B,C,k1_ami_5(B,C,D)) = k5_amistd_2(B,C,k1_ami_5(B,C,k8_amistd_2(B,C,D,A))) ) ) ) ) ).
fof(t32_amistd_2,axiom,
! [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)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> ! [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))
=> ( k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,D))),A) = u2_ami_1(B,C)
=> ( ! [F] :
( v4_ordinal2(F)
=> k8_amistd_2(B,C,D,F) != k8_amistd_2(B,C,E,F) )
| k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,E))),A) = u2_ami_1(B,C) ) ) ) ) ) ) ).
fof(t33_amistd_2,axiom,
! [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)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> ! [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))
=> ~ ( ? [F] :
( v4_ordinal2(F)
& k8_amistd_2(B,C,D,F) = k8_amistd_2(B,C,E,F) )
& k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,D))),A) != u2_ami_1(B,C)
& k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,E))),A) = u2_ami_1(B,C) ) ) ) ) ) ).
fof(t34_amistd_2,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)
& v8_amistd_2(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] :
( 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] :
( v4_ordinal2(E)
& k8_amistd_2(A,B,C,E) = k8_amistd_2(A,B,D,E) )
=> C = D ) ) ) ) ) ).
fof(t35_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v4_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v10_ami_1(C,B)
& v4_amistd_1(C,B)
& v6_amistd_2(C,B)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> ( k8_amistd_2(B,C,D,A) = k5_ami_1(B,C)
=> D = k5_ami_1(B,C) ) ) ) ) ) ).
fof(t36_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v4_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v10_ami_1(C,B)
& v4_amistd_1(C,B)
& v6_amistd_2(C,B)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( 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))
=> ( v5_amistd_1(D,B,C)
=> v5_amistd_1(k8_amistd_2(B,C,D,A),B,C) ) ) ) ) ) ).
fof(t37_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v1_setfam_1(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v5_ami_1(D,C)
& v8_ami_1(D,C)
& v4_amistd_1(D,C)
& v8_amistd_2(D,C)
& l1_ami_1(D,C) )
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(C,D),k13_finseq_1(k2_xboole_0(k3_tarski(C),u1_struct_0(D)))),u4_ami_1(C,D))
=> k8_amistd_2(C,D,k8_amistd_2(C,D,E,A),B) = k8_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(d15_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( m1_ami_1(E,A,B)
=> ( E = k9_amistd_2(A,B,C,D)
<=> ( k1_relat_1(E) = k1_relat_1(C)
& ! [F] :
( v4_ordinal2(F)
=> ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C))
=> k1_funct_1(E,k5_amistd_1(A,B,F)) = k8_amistd_2(A,B,k5_ami_5(A,B,C,k5_amistd_1(A,B,F)),D) ) ) ) ) ) ) ) ) ) ).
fof(t38_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> k9_amistd_2(A,B,C,np__0) = C ) ) ) ).
fof(t39_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v1_setfam_1(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v5_ami_1(D,C)
& v8_ami_1(D,C)
& v4_amistd_1(D,C)
& v8_amistd_2(D,C)
& l1_ami_1(D,C) )
=> ! [E] :
( ( v1_ami_3(E,C,D)
& v9_amistd_1(E,C,D)
& m1_ami_1(E,C,D) )
=> k9_amistd_2(C,D,k9_amistd_2(C,D,E,A),B) = k9_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t40_amistd_2,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_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> k10_amistd_2(A,B,C,np__0) = C ) ) ) ).
fof(t41_amistd_2,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)
=> ! [D] :
( v4_ordinal2(D)
=> ~ ( ~ r1_xreal_0(D,np__0)
& r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(k10_amistd_2(A,B,C,D))) ) ) ) ) ) ).
fof(t42_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v1_setfam_1(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& ~ v2_ami_1(D,C)
& v5_ami_1(D,C)
& v8_ami_1(D,C)
& v4_amistd_1(D,C)
& l1_ami_1(D,C) )
=> ! [E] :
( m1_ami_1(E,C,D)
=> k10_amistd_2(C,D,k10_amistd_2(C,D,E,A),B) = k10_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t43_amistd_2,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)
& m1_ami_1(D,B,C) )
=> r2_tarski(k1_relat_1(D),k1_relat_1(k10_amistd_2(B,C,D,A))) ) ) ) ) ).
fof(d17_amistd_2,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)
& v8_amistd_2(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))
=> ( v10_amistd_2(C,A,B)
<=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> ( F = k1_funct_4(E,k3_cqc_lang(k2_ami_1(A,B),k8_amistd_1(A,B,k6_ami_1(A,B,E),D)))
=> k8_amistd_1(A,B,k6_ami_1(A,B,k4_ami_1(A,B,C,E)),D) = k6_ami_1(A,B,k4_ami_1(A,B,k8_amistd_2(A,B,C,D),F)) ) ) ) ) ) ) ) ) ).
fof(d18_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ( v11_amistd_2(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))
=> v10_amistd_2(C,A,B) ) ) ) ) ).
fof(d19_amistd_2,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))
=> ( v12_amistd_2(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_funct_7(D,E,u2_ami_1(A,B))
=> r1_funct_7(k4_ami_1(A,B,C,D),k4_ami_1(A,B,C,E),u2_ami_1(A,B)) ) ) ) ) ) ) ) ).
fof(d20_amistd_2,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v2_ami_1(B,A)
& l1_ami_1(B,A) )
=> ( v13_amistd_2(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))
=> v12_amistd_2(C,A,B) ) ) ) ) ).
fof(t44_amistd_2,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)
& v6_amistd_2(B,A)
& v8_amistd_2(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)
=> v10_amistd_2(C,A,B) ) ) ) ) ).
fof(t45_amistd_2,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)
& v6_amistd_2(B,A)
& v8_amistd_2(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)
=> v10_amistd_2(C,A,B) ) ) ) ) ).
fof(t46_amistd_2,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)
=> v12_amistd_2(C,A,B) ) ) ) ) ).
fof(d21_amistd_2,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) )
=> k11_amistd_2(A,B,C) = k4_xboole_0(C,k3_cqc_lang(k10_amistd_1(A,B,C),k1_funct_1(C,k10_amistd_1(A,B,C)))) ) ) ) ).
fof(t47_amistd_2,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) )
=> k1_relat_1(k11_amistd_2(A,B,C)) = k4_xboole_0(k1_relat_1(C),k1_struct_0(B,k10_amistd_1(A,B,C))) ) ) ) ).
fof(t48_amistd_2,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) )
=> k1_relat_1(C) = k2_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_struct_0(B,k10_amistd_1(A,B,C))) ) ) ) ).
fof(t49_amistd_2,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) )
=> k4_card_1(k11_amistd_2(A,B,C)) = k6_xcmplx_0(k4_card_1(C),np__1) ) ) ) ).
fof(t50_amistd_2,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)
& v8_amistd_2(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_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_relat_1(k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_binarith(k4_card_1(C),np__1)))) ) ) ) ) ).
fof(t51_amistd_2,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)
& v9_amistd_1(C,A,B)
& v11_amistd_1(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(k11_amistd_2(A,B,C)))
& k1_funct_1(k11_amistd_2(A,B,C),D) = k5_ami_1(A,B) ) ) ) ) ) ).
fof(d22_amistd_2,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)
& v8_amistd_2(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) )
=> k12_amistd_2(A,B,C,D) = k1_scmfsa_4(A,B,k11_amistd_2(A,B,C),k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_binarith(k4_card_1(C),np__1))) ) ) ) ) ).
fof(t52_amistd_2,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)
& v8_amistd_2(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) )
=> ( k4_card_1(k12_amistd_2(A,B,C,D)) = k6_xcmplx_0(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__1)
& k4_card_1(k12_amistd_2(A,B,C,D)) = k5_binarith(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__1) ) ) ) ) ) ).
fof(t53_amistd_2,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)
& v8_amistd_2(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)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> r1_tarski(k1_relat_1(C),k1_relat_1(k12_amistd_2(A,B,C,D))) ) ) ) ) ).
fof(t54_amistd_2,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)
& v8_amistd_2(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)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> r1_tarski(k11_amistd_2(A,B,C),k11_amistd_2(A,B,k12_amistd_2(A,B,C,D))) ) ) ) ) ).
fof(t55_amistd_2,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)
& v8_amistd_2(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)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> k1_funct_1(k12_amistd_2(A,B,C,D),k10_amistd_1(A,B,C)) = k1_funct_1(k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_amistd_1(A,B,np__0)) ) ) ) ) ).
fof(t56_amistd_2,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)
& v8_amistd_2(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)
& v9_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> ( ~ r1_xreal_0(k6_xcmplx_0(k4_card_1(C),np__1),k7_amistd_1(A,B,E))
=> k1_funct_1(k9_amistd_2(A,B,C,k5_binarith(k4_card_1(C),np__1)),E) = k1_funct_1(k9_amistd_2(A,B,k12_amistd_2(A,B,C,D),k5_binarith(k4_card_1(C),np__1)),E) ) ) ) ) ) ) ).
fof(t57_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v4_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v10_ami_1(C,B)
& v4_amistd_1(C,B)
& v6_amistd_2(C,B)
& v8_amistd_2(C,B)
& l1_ami_1(C,B) )
=> k9_amistd_2(B,C,k7_amistd_2(B,C),A) = k7_amistd_2(B,C) ) ) ) ).
fof(t58_amistd_2,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v4_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> k10_amistd_2(B,C,k7_amistd_2(B,C),A) = k14_ami_3(B,C,k5_amistd_1(B,C,A),k5_ami_1(B,C)) ) ) ) ).
fof(t59_amistd_2,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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(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)
& m1_ami_1(C,A,B) )
=> k12_amistd_2(A,B,C,k7_amistd_2(A,B)) = C ) ) ) ).
fof(t60_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(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)
& m1_ami_1(C,A,B) )
=> k12_amistd_2(A,B,k7_amistd_2(A,B),C) = C ) ) ) ).
fof(t61_amistd_2,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)
& v10_ami_1(B,A)
& v4_amistd_1(B,A)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(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)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& v10_amistd_1(D,A,B)
& v11_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v1_ami_3(E,A,B)
& v9_amistd_1(E,A,B)
& v10_amistd_1(E,A,B)
& v11_amistd_1(E,A,B)
& m1_ami_1(E,A,B) )
=> k13_amistd_2(A,B,k13_amistd_2(A,B,C,D),E) = k13_amistd_2(A,B,C,k13_amistd_2(A,B,D,E)) ) ) ) ) ) ).
fof(dt_k1_amistd_2,axiom,
! [A] :
( v1_fraenkel(A)
=> ( v1_relat_1(k1_amistd_2(A))
& v1_funct_1(k1_amistd_2(A)) ) ) ).
fof(dt_k2_amistd_2,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,u2_ami_1(A,B))
& m1_subset_1(D,u2_ami_1(A,B))
& m1_subset_1(E,u4_ami_1(A,B))
& m1_subset_1(F,u4_ami_1(A,B)) )
=> m1_ami_1(k2_amistd_2(A,B,C,D,E,F),A,B) ) ).
fof(redefinition_k2_amistd_2,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,u2_ami_1(A,B))
& m1_subset_1(D,u2_ami_1(A,B))
& m1_subset_1(E,u4_ami_1(A,B))
& m1_subset_1(F,u4_ami_1(A,B)) )
=> k2_amistd_2(A,B,C,D,E,F) = k4_funct_4(C,D,E,F) ) ).
fof(dt_k3_amistd_2,axiom,
$true ).
fof(dt_k4_amistd_2,axiom,
! [A,B,C] :
( ( l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> m2_finseq_1(k4_amistd_2(A,B,C),k2_xboole_0(k3_tarski(A),u1_struct_0(B))) ) ).
fof(redefinition_k4_amistd_2,axiom,
! [A,B,C] :
( ( l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> k4_amistd_2(A,B,C) = k3_amistd_2(A,B,C) ) ).
fof(dt_k5_amistd_2,axiom,
$true ).
fof(dt_k6_amistd_2,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) )
=> m1_ami_1(k6_amistd_2(A,B),A,B) ) ).
fof(dt_k7_amistd_2,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) )
=> ( ~ v1_xboole_0(k7_amistd_2(A,B))
& v1_ami_3(k7_amistd_2(A,B),A,B)
& v9_amistd_1(k7_amistd_2(A,B),A,B)
& v10_amistd_1(k7_amistd_2(A,B),A,B)
& v11_amistd_1(k7_amistd_2(A,B),A,B)
& m1_ami_1(k7_amistd_2(A,B),A,B) ) ) ).
fof(redefinition_k7_amistd_2,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) )
=> k7_amistd_2(A,B) = k6_amistd_2(A,B) ) ).
fof(dt_k8_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B))
& v4_ordinal2(D) )
=> m2_subset_1(k8_amistd_2(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(dt_k9_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v4_ordinal2(D) )
=> m1_ami_1(k9_amistd_2(A,B,C,D),A,B) ) ).
fof(dt_k10_amistd_2,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_ami_1(C,A,B)
& v4_ordinal2(D) )
=> m1_ami_1(k10_amistd_2(A,B,C,D),A,B) ) ).
fof(dt_k11_amistd_2,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_ami_1(k11_amistd_2(A,B,C),A,B) ) ).
fof(dt_k12_amistd_2,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)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> m1_ami_1(k12_amistd_2(A,B,C,D),A,B) ) ).
fof(dt_k13_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(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)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& v10_amistd_1(D,A,B)
& v11_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> ( ~ v1_xboole_0(k13_amistd_2(A,B,C,D))
& v1_ami_3(k13_amistd_2(A,B,C,D),A,B)
& v9_amistd_1(k13_amistd_2(A,B,C,D),A,B)
& v10_amistd_1(k13_amistd_2(A,B,C,D),A,B)
& v11_amistd_1(k13_amistd_2(A,B,C,D),A,B)
& m1_ami_1(k13_amistd_2(A,B,C,D),A,B) ) ) ).
fof(redefinition_k13_amistd_2,axiom,
! [A,B,C,D] :
( ( 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)
& v6_amistd_2(B,A)
& v8_amistd_2(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(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)
& m1_ami_1(C,A,B)
& ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& v9_amistd_1(D,A,B)
& v10_amistd_1(D,A,B)
& v11_amistd_1(D,A,B)
& m1_ami_1(D,A,B) )
=> k13_amistd_2(A,B,C,D) = k12_amistd_2(A,B,C,D) ) ).
fof(t5_amistd_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A) )
=> k1_relat_1(k1_amistd_2(A)) = k1_setfam_1(a_1_0_amistd_2(A)) ) ).
fof(t6_amistd_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(k1_amistd_2(A)))
=> k1_funct_1(k1_amistd_2(A),B) = a_2_0_amistd_2(A,B) ) ) ).
fof(t15_amistd_2,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_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> k1_relat_1(C) = a_3_0_amistd_2(A,B,C) ) ) ) ).
fof(d5_amistd_2,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_subset_1(C,u3_ami_1(A,B))
=> k5_amistd_2(A,B,C) = a_3_1_amistd_2(A,B,C) ) ) ).
fof(d16_amistd_2,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)
=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( m1_ami_1(E,A,B)
=> ( E = k10_amistd_2(A,B,C,D)
<=> ( k1_relat_1(E) = a_4_0_amistd_2(A,B,C,D)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C))
=> k1_funct_1(E,k5_amistd_1(A,B,k2_xcmplx_0(F,D))) = k1_funct_1(C,k5_amistd_1(A,B,F)) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_1_0_amistd_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_fraenkel(B) )
=> ( r2_hidden(A,a_1_0_amistd_2(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k1_relat_1(C) ) ) ) ).
fof(fraenkel_a_2_0_amistd_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_fraenkel(B) )
=> ( r2_hidden(A,a_2_0_amistd_2(B,C))
<=> ? [D] :
( m1_subset_1(D,B)
& A = k1_funct_1(D,C) ) ) ) ).
fof(fraenkel_a_3_0_amistd_2,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_ami_3(D,B,C)
& v9_amistd_1(D,B,C)
& m1_ami_1(D,B,C) )
=> ( r2_hidden(A,a_3_0_amistd_2(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k5_amistd_1(B,C,E)
& ~ r1_xreal_0(k4_card_1(D),E) ) ) ) ).
fof(fraenkel_a_3_1_amistd_2,axiom,
! [A,B,C,D] :
( ( l1_ami_1(C,B)
& m1_subset_1(D,u3_ami_1(B,C)) )
=> ( r2_hidden(A,a_3_1_amistd_2(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 = k4_amistd_2(B,C,E)
& k1_ami_5(B,C,E) = D ) ) ) ).
fof(fraenkel_a_4_0_amistd_2,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)
& v4_amistd_1(C,B)
& l1_ami_1(C,B)
& m1_ami_1(D,B,C)
& v4_ordinal2(E) )
=> ( r2_hidden(A,a_4_0_amistd_2(B,C,D,E))
<=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& A = k5_amistd_1(B,C,k2_xcmplx_0(F,E))
& r2_hidden(k5_amistd_1(B,C,F),k1_relat_1(D)) ) ) ) ).
%------------------------------------------------------------------------------