SET007 Axioms: SET007+688.ax
%------------------------------------------------------------------------------
% File : SET007+688 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Input and Output of Instructions
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : ami_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 98 ( 0 unt; 0 def)
% Number of atoms : 670 ( 78 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 703 ( 131 ~; 2 |; 305 &)
% ( 9 <=>; 256 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 40 ( 39 usr; 0 prp; 1-3 aty)
% Number of functors : 47 ( 47 usr; 3 con; 0-5 aty)
% Number of variables : 272 ( 271 !; 1 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_ami_7,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)
& v2_ami_7(k4_amistd_1(A),A) ) ) ).
fof(rc1_ami_7,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)
& v1_ami_7(B,A)
& v2_ami_7(B,A) ) ) ).
fof(cc1_ami_7,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( l1_ami_1(B,A)
=> ( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& v2_ami_7(B,A) )
=> ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& v1_ami_7(B,A) ) ) ) ) ).
fof(cc2_ami_7,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( l1_ami_1(B,A)
=> ( ( ~ v3_struct_0(B)
& v5_ami_1(B,A)
& v2_ami_7(B,A) )
=> ( ~ v3_struct_0(B)
& v5_ami_1(B,A)
& v7_amistd_2(B,A) ) ) ) ) ).
fof(fc2_ami_7,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& v2_ami_7(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u1_struct_0(B)) )
=> ~ v1_realset1(k3_ami_1(A,B,C)) ) ).
fof(fc3_ami_7,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& v1_ami_7(B,A)
& l1_ami_1(B,A) )
=> ( ~ v1_xboole_0(u4_ami_1(A,B))
& v1_relat_1(u4_ami_1(A,B))
& v1_setfam_1(u4_ami_1(A,B))
& ~ v1_realset1(u4_ami_1(A,B)) ) ) ).
fof(fc4_ami_7,axiom,
! [A,B] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& v5_ami_1(B,A)
& v7_amistd_2(B,A)
& l1_ami_1(B,A) )
=> ~ v1_realset1(k3_ami_1(A,B,k2_ami_1(A,B))) ) ).
fof(fc5_ami_7,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> v1_xboole_0(k5_ami_7(A,B,C)) ) ).
fof(fc6_ami_7,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> v1_xboole_0(k2_ami_7(A,B,C)) ) ).
fof(fc7_ami_7,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> v1_xboole_0(k4_ami_7(A,B,C)) ) ).
fof(fc8_ami_7,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)
& v2_ami_7(B,A)
& l1_ami_1(B,A)
& v3_ami_1(C,A,B)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> v1_xboole_0(k3_ami_7(A,B,C)) ) ).
fof(fc9_ami_7,axiom,
( ~ v3_struct_0(k1_ami_3)
& v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v4_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v7_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v8_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v10_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v13_ami_1(k1_ami_3,k1_tarski(k4_numbers))
& v3_amistd_1(k1_ami_3,k1_tarski(k4_numbers))
& v4_amistd_1(k1_ami_3,k1_tarski(k4_numbers))
& v2_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v5_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v6_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v7_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v8_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v11_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v13_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
& v1_ami_7(k1_ami_3,k1_tarski(k4_numbers))
& v2_ami_7(k1_ami_3,k1_tarski(k4_numbers)) ) ).
fof(t1_ami_7,axiom,
! [A,B,C] :
~ ( A != B
& A != C
& k4_xboole_0(k1_enumset1(A,B,C),k1_tarski(A)) != k2_tarski(B,C) ) ).
fof(t2_ami_7,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,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r2_hidden(k1_funct_1(C,D),k3_ami_1(A,B,D)) ) ) ) ) ).
fof(t3_ami_7,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,k2_ami_1(A,B)))
=> k1_funct_1(k2_funct_7(C,k2_ami_1(A,B),E),D) = k13_ami_1(A,B,C,D) ) ) ) ) ) ).
fof(t4_ami_7,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,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))
=> ! [G] :
( m1_subset_1(G,k3_ami_1(A,B,D))
=> ( E != D
=> k13_ami_1(A,B,k4_ami_1(A,B,F,C),E) = k13_ami_1(A,B,k4_ami_1(A,B,F,k1_ami_7(A,B,C,D,G)),E) ) ) ) ) ) ) ) ) ).
fof(t5_ami_7,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,k3_ami_1(A,B,D))
=> ( D != k2_ami_1(A,B)
=> k6_ami_1(A,B,C) = k6_ami_1(A,B,k1_ami_7(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t6_ami_7,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k3_ami_1(A,B,E))
=> ( v5_amistd_1(C,A,B)
=> ( E = k2_ami_1(A,B)
| k6_ami_1(A,B,k4_ami_1(A,B,C,D)) = k6_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F))) ) ) ) ) ) ) ) ) ).
fof(t7_ami_7,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k3_ami_1(A,B,E))
=> ( v5_amistd_1(C,A,B)
=> ( E = k2_ami_1(A,B)
| k6_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F))) = k6_ami_1(A,B,k1_ami_7(A,B,k4_ami_1(A,B,C,D),E,F)) ) ) ) ) ) ) ) ) ).
fof(t8_ami_7,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] :
( 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)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k3_ami_1(A,B,E))
=> ! [G] :
( m1_struct_0(G,B,u2_ami_1(A,B))
=> k13_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F)),G) = k13_ami_1(A,B,k1_ami_7(A,B,k4_ami_1(A,B,C,D),E,F),G) ) ) ) ) ) ) ) ).
fof(d1_ami_7,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ( v1_ami_7(B,A)
<=> ~ v1_realset1(u4_ami_1(A,B)) ) ) ).
fof(d2_ami_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ( v2_ami_7(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ~ v1_realset1(k3_ami_1(A,B,C)) ) ) ) ).
fof(d3_ami_7,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))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( D = k2_ami_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,D)
<=> ~ ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> k1_funct_1(F,E) = k1_funct_1(k4_ami_1(A,B,C,F),E) ) ) ) ) ) ) ) ) ).
fof(d4_ami_7,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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( D = k3_ami_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,D)
<=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> ! [G] :
( m1_subset_1(G,k3_ami_1(A,B,E))
=> k4_ami_1(A,B,C,F) = k4_ami_1(A,B,C,k1_ami_7(A,B,F,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d5_ami_7,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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( D = k4_ami_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,D)
<=> ~ ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
=> ! [G] :
( m1_subset_1(G,k3_ami_1(A,B,E))
=> k4_ami_1(A,B,C,k1_ami_7(A,B,F,E,G)) = k1_ami_7(A,B,k4_ami_1(A,B,C,F),E,G) ) ) ) ) ) ) ) ) ) ).
fof(d6_ami_7,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))
=> k5_ami_7(A,B,C) = k6_subset_1(u1_struct_0(B),k4_ami_7(A,B,C),k3_ami_7(A,B,C)) ) ) ) ).
fof(t9_ami_7,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))
=> r1_xboole_0(k3_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) ).
fof(t10_ami_7,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)
& v2_ami_7(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))
=> r1_tarski(k3_ami_7(A,B,C),k2_ami_7(A,B,C)) ) ) ) ).
fof(t11_ami_7,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))
=> r1_tarski(k2_ami_7(A,B,C),k4_ami_7(A,B,C)) ) ) ) ).
fof(t12_ami_7,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))
=> r1_tarski(k5_ami_7(A,B,C),k4_ami_7(A,B,C)) ) ) ) ).
fof(t13_ami_7,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)
& v2_ami_7(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))
=> k3_ami_7(A,B,C) = k6_subset_1(u1_struct_0(B),k2_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) ).
fof(t14_ami_7,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)
& v2_ami_7(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))
=> k4_ami_7(A,B,C) = k4_subset_1(u1_struct_0(B),k2_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) ).
fof(t15_ami_7,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_subset_1(D,u1_struct_0(B))
=> ~ ( v1_realset1(k3_ami_1(A,B,D))
& r2_hidden(D,k4_ami_7(A,B,C)) ) ) ) ) ) ).
fof(t16_ami_7,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_subset_1(D,u1_struct_0(B))
=> ~ ( v1_realset1(k3_ami_1(A,B,D))
& r2_hidden(D,k5_ami_7(A,B,C)) ) ) ) ) ) ).
fof(t17_ami_7,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_subset_1(D,u1_struct_0(B))
=> ~ ( v1_realset1(k3_ami_1(A,B,D))
& r2_hidden(D,k2_ami_7(A,B,C)) ) ) ) ) ) ).
fof(t18_ami_7,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_ami_1(C,A,B)
<=> v1_xboole_0(k2_ami_7(A,B,C)) ) ) ) ) ).
fof(t19_ami_7,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)
& v2_ami_7(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(k3_ami_7(A,B,C)) ) ) ) ) ).
fof(t20_ami_7,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_ami_1(C,A,B)
=> v1_xboole_0(k4_ami_7(A,B,C)) ) ) ) ) ).
fof(t21_ami_7,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_ami_1(C,A,B)
=> v1_xboole_0(k5_ami_7(A,B,C)) ) ) ) ) ).
fof(t22_ami_7,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)
& v1_ami_7(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))
=> ~ r2_hidden(C,k3_ami_7(A,B,D)) ) ) ) ) ).
fof(t23_ami_7,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)
& r2_hidden(k2_ami_1(A,B),k3_ami_7(A,B,C)) ) ) ) ) ).
fof(t24_ami_7,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_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)) = k6_ami_1(A,B,D) )
=> r2_hidden(k2_ami_1(A,B),k2_ami_7(A,B,C)) ) ) ) ) ).
fof(t25_ami_7,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)
=> r2_hidden(k2_ami_1(A,B),k2_ami_7(A,B,C)) ) ) ) ) ).
fof(t26_ami_7,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_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)) = k6_ami_1(A,B,D) )
=> r2_hidden(k2_ami_1(A,B),k4_ami_7(A,B,C)) ) ) ) ) ).
fof(t27_ami_7,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)
=> r2_hidden(k2_ami_1(A,B),k4_ami_7(A,B,C)) ) ) ) ) ).
fof(t28_ami_7,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))
=> ~ ( ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
=> ! [F] :
( ( v1_ami_3(F,A,B)
& m1_ami_1(F,A,B) )
=> k4_ami_1(A,B,D,k8_ami_5(A,B,E,F)) = k8_ami_5(A,B,k4_ami_1(A,B,D,E),F) ) )
& r2_hidden(C,k4_ami_7(A,B,D)) ) ) ) ) ) ).
fof(t29_ami_7,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_subset_1(D,u1_struct_0(B))
=> ( ( v2_amistd_1(C,A,B)
& r2_hidden(D,k2_ami_7(A,B,C)) )
=> D = k2_ami_1(A,B) ) ) ) ) ) ).
fof(t30_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k3_ami_1(k1_tarski(k4_numbers),k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> k2_ami_3(k1_ami_7(k1_tarski(k4_numbers),k1_ami_3,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),C),A) = k2_ami_3(B,A) ) ) ) ).
fof(t31_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> A != k11_ami_3(A) ) ).
fof(t32_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_xboole_0 ) ).
fof(t33_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k1_struct_0(k1_ami_3,A) ) ) ) ).
fof(t34_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_xboole_0 ) ) ).
fof(t35_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,A)) = k1_struct_0(k1_ami_3,A) ) ).
fof(t36_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_xboole_0 ) ) ) ).
fof(t37_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_xboole_0 ) ) ).
fof(t38_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A)) = k1_struct_0(k1_ami_3,A) ) ).
fof(t39_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_xboole_0 ) ) ) ).
fof(t40_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t41_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k1_xboole_0 ) ) ).
fof(t42_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k1_xboole_0 ) ) ).
fof(t43_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t44_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) ).
fof(t45_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t46_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t47_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t48_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t49_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t50_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t51_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t52_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ r2_hidden(A,k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,B)) ) ) ).
fof(t53_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t54_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) ).
fof(t55_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t56_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t57_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t58_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t59_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t60_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t61_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t62_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t63_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k2_struct_0(k1_ami_3,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) ).
fof(t64_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t65_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t66_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) ).
fof(t67_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t68_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(t69_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> ( A != B
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) ).
fof(t70_ami_7,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_xboole_0 ) ).
fof(t71_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(t72_ami_7,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(dt_k1_ami_7,axiom,
! [A,B,C,D,E] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k3_ami_1(A,B,D)) )
=> m1_subset_1(k1_ami_7(A,B,C,D,E),k4_card_3(u5_ami_1(A,B))) ) ).
fof(redefinition_k1_ami_7,axiom,
! [A,B,C,D,E] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k3_ami_1(A,B,D)) )
=> k1_ami_7(A,B,C,D,E) = k2_funct_7(C,D,E) ) ).
fof(dt_k2_ami_7,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> m1_subset_1(k2_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k3_ami_7,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(k3_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k4_ami_7,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(k4_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k5_ami_7,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(k5_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k6_ami_7,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_ami_3(B)
& v1_int_1(C) )
=> m1_subset_1(k6_ami_7(A,B,C),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ).
fof(redefinition_k6_ami_7,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_ami_3(B)
& v1_int_1(C) )
=> k6_ami_7(A,B,C) = k2_funct_7(A,B,C) ) ).
%------------------------------------------------------------------------------