SET007 Axioms: SET007+404.ax


%------------------------------------------------------------------------------
% File     : SET007+404 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  295 (  72 equality)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :  251 (  11 ~  ;   1  |;  66  &)
%                                         (  12 <=>; 161 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   16 (   0 propositional; 1-4 arity)
%            Number of functors    :   74 (  15 constant; 0-4 arity)
%            Number of variables   :  154 (   0 singleton; 149 !;   5 ?)
%            Maximal term depth    :   11 (   2 average)
% 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))) ) ) ) )).
%------------------------------------------------------------------------------