SET007 Axioms: SET007+404.ax
%------------------------------------------------------------------------------
% File : SET007+404 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Relocatability
% 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 : reloc [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 55 ( 0 unt; 0 def)
% Number of atoms : 295 ( 72 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 251 ( 11 ~; 1 |; 66 &)
% ( 12 <=>; 161 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 0 prp; 1-4 aty)
% Number of functors : 74 ( 74 usr; 15 con; 0-4 aty)
% Number of variables : 154 ( 149 !; 5 ?)
% 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(d1_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( C = k1_reloc(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k16_ami_3(D)
& C = k16_ami_3(k1_nat_1(D,B)) ) ) ) ) ) ).
fof(d2_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( C = k2_reloc(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k16_ami_3(D)
& C = k16_ami_3(k5_binarith(D,B)) ) ) ) ) ) ).
fof(t1_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_reloc(k1_reloc(A,B),B) = A ) ) ).
fof(t2_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(B,C))
<=> k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,A) = k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,B) ) ) ) ) ).
fof(t3_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,A) = k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,B)
=> k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k2_reloc(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k2_reloc(B,C)) ) ) ) ) ).
fof(d3_reloc,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__6
=> k3_reloc(A,B) = k8_ami_3(k1_reloc(k3_ami_5(k11_ami_2(k2_ami_5(A))),B)) )
& ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__7
=> k3_reloc(A,B) = k9_ami_3(k1_reloc(k3_ami_5(k12_ami_2(k2_ami_5(A))),B),k4_ami_5(k13_ami_2(k2_ami_5(A)))) )
& ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__8
=> k3_reloc(A,B) = k10_ami_3(k1_reloc(k3_ami_5(k12_ami_2(k2_ami_5(A))),B),k4_ami_5(k13_ami_2(k2_ami_5(A)))) )
& ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != np__6
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != np__7
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != np__8
& k3_reloc(A,B) != A ) ) ) ) ).
fof(t4_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_reloc(k5_ami_1(k1_tarski(k4_numbers),k1_ami_3),A) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(t5_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k3_ami_3(B,C),A) = k3_ami_3(B,C) ) ) ) ).
fof(t6_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k4_ami_3(B,C),A) = k4_ami_3(B,C) ) ) ) ).
fof(t7_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k5_ami_3(B,C),A) = k5_ami_3(B,C) ) ) ) ).
fof(t8_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k6_ami_3(B,C),A) = k6_ami_3(B,C) ) ) ) ).
fof(t9_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k7_ami_3(B,C),A) = k7_ami_3(B,C) ) ) ) ).
fof(t10_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k3_reloc(k8_ami_3(B),A) = k8_ami_3(k1_reloc(B,A)) ) ) ).
fof(t11_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k9_ami_3(B,C),A) = k9_ami_3(k1_reloc(B,A),C) ) ) ) ).
fof(t12_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_ami_3(C)
=> k3_reloc(k10_ami_3(B,C),A) = k10_ami_3(k1_reloc(B,A),C) ) ) ) ).
fof(t13_reloc,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k3_reloc(A,B)) = k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) ) ) ).
fof(t14_reloc,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( 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))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k3_reloc(A,C) = B
=> ( ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__0
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__1
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__2
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__3
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__4
& k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,B) != np__5 )
| A = B ) ) ) ) ) ).
fof(t15_reloc,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(A,k1_relat_1(C))
=> k1_funct_1(k4_reloc(C,B),k1_reloc(A,B)) = k1_funct_1(C,A) ) ) ) ) ).
fof(t17_reloc,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k1_relat_1(k4_reloc(A,B)),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ).
fof(d5_reloc,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
=> ( C = k5_reloc(A,B)
<=> ( k1_relat_1(C) = k1_relat_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k16_ami_3(D),k1_relat_1(A))
=> k1_funct_1(C,k16_ami_3(D)) = k3_reloc(k5_ami_5(k1_tarski(k4_numbers),k1_ami_3,A,k16_ami_3(D)),B) ) ) ) ) ) ) ) ).
fof(t18_reloc,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(k5_reloc(A,B),C) = k3_reloc(k5_ami_5(k1_tarski(k4_numbers),k1_ami_3,A,C),B) ) ) ) ) ).
fof(t19_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> k4_reloc(k5_reloc(B,A),A) = k5_reloc(k4_reloc(B,A),A) ) ) ).
fof(d6_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_reloc(A,B) = k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),B)),k5_reloc(k4_reloc(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),B),B)),k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) ) ) ).
fof(t20_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
=> r1_tarski(k1_relat_1(k5_reloc(k4_reloc(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,B),A),A)),k3_ami_2) ) ) ).
fof(t21_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(A,B)) = k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) ) ) ).
fof(t22_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(A,B)) = k5_reloc(k4_reloc(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),B),B) ) ) ).
fof(t24_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( r2_hidden(C,k1_relat_1(A))
<=> r2_hidden(k1_reloc(C,B),k1_relat_1(k6_reloc(A,B))) ) ) ) ) ).
fof(t25_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(k6_reloc(A,B))) ) ) ).
fof(t26_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(A,B)) = k1_reloc(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),B) ) ) ).
fof(t27_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [D] :
( m2_subset_1(D,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(C,k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)))
& D = k1_funct_1(A,C) )
=> k3_reloc(D,B) = k1_funct_1(k6_reloc(A,B),k1_reloc(C,B)) ) ) ) ) ) ).
fof(t28_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),B)),k6_reloc(A,B)) ) ) ).
fof(t29_reloc,axiom,
! [A] :
( ( v1_ami_5(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
=> k6_reloc(k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,A),C) = k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,C),A) ) ) ) ) ).
fof(t30_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v11_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(B,C)
& r1_tarski(k6_reloc(B,A),D) )
=> r1_tarski(B,k1_funct_4(C,k7_relat_1(D,k2_ami_2))) ) ) ) ) ) ).
fof(t31_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_reloc(k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),A),k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,B,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),A)))) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k9_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)),A))) ) ) ).
fof(t32_reloc,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B) = k16_ami_3(k1_nat_1(C,D))
=> k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,B,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k2_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_reloc(A,D),B),k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k2_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_reloc(A,D),B)),D))) ) ) ) ) ) ).
fof(t33_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v11_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( r1_tarski(B,C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,C,k6_reloc(B,A))),D) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)),A))),k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A))) ) ) ) ) ) ) ).
fof(t34_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v11_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
& r1_tarski(B,C)
& r1_tarski(k6_reloc(B,A),D)
& E = k1_funct_4(C,k7_relat_1(D,k2_ami_2)) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k1_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),F)),A) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F))
& k3_reloc(k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),F)),A) = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F))
& k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),F),k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,B))) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F),k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A))))
& k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),F),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F),k2_ami_2) ) ) ) ) ) ) ) ) ).
fof(t35_reloc,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
=> ( v12_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
<=> v12_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ).
fof(t36_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v11_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( r1_tarski(k6_reloc(B,A),C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k1_funct_4(k1_funct_4(k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,C,B)),D),k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,C,B)),D)),A))),k7_relat_1(C,k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,B)))),k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A))) ) ) ) ) ) ) ).
fof(t37_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(B,C)
& v11_ami_1(k6_reloc(B,A),k1_tarski(k4_numbers),k1_ami_3) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k1_funct_4(k1_funct_4(k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,C,k6_reloc(B,A))),D),k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k2_reloc(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,C,k6_reloc(B,A))),D)),A))),k7_relat_1(C,k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A))))),k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,B)) ) ) ) ) ) ) ).
fof(t38_reloc,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
<=> v11_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ).
fof(t39_reloc,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& v12_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k18_ami_1(k1_tarski(k4_numbers),k1_ami_3,A)) = k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k18_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(A,B))) ) ) ) ).
fof(t40_reloc,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k14_ami_1(k1_tarski(k4_numbers),k1_ami_3),k14_ami_1(k1_tarski(k4_numbers),k1_ami_3)) )
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
=> ( ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B))
& v2_ami_5(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,A)
<=> r1_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,C),A) ) ) ) ) ) ).
fof(dt_k1_reloc,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k1_reloc(A,B),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k2_reloc,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k2_reloc(A,B),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k3_reloc,axiom,
! [A,B] :
( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k3_reloc(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k4_reloc,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_subset_1(B,k5_numbers) )
=> ( v1_ami_3(k4_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(k4_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(dt_k5_reloc,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_subset_1(B,k5_numbers) )
=> ( v1_ami_3(k5_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(k5_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(dt_k6_reloc,axiom,
! [A,B] :
( ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_subset_1(B,k5_numbers) )
=> m1_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(d4_reloc,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
=> ( C = k4_reloc(A,B)
<=> ( k1_relat_1(C) = a_2_0_reloc(A,B)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k16_ami_3(D),k1_relat_1(A))
=> k1_funct_1(C,k16_ami_3(k1_nat_1(D,B))) = k1_funct_1(A,k16_ami_3(D)) ) ) ) ) ) ) ) ).
fof(t16_reloc,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_relat_1(k4_reloc(A,B)) = a_2_1_reloc(A,B) ) ) ).
fof(t23_reloc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
=> k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A))) = a_2_2_reloc(A,B) ) ) ).
fof(fraenkel_a_2_0_reloc,axiom,
! [A,B,C] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_reloc(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k16_ami_3(k1_nat_1(D,C))
& r2_hidden(k16_ami_3(D),k1_relat_1(B)) ) ) ) ).
fof(fraenkel_a_2_1_reloc,axiom,
! [A,B,C] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_reloc(B,C))
<=> ? [D] :
( m1_struct_0(D,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& A = k1_reloc(D,C)
& r2_hidden(D,k1_relat_1(B)) ) ) ) ).
fof(fraenkel_a_2_2_reloc,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(A,a_2_2_reloc(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k16_ami_3(k1_nat_1(D,B))
& r2_hidden(k16_ami_3(D),k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,C))) ) ) ) ).
%------------------------------------------------------------------------------