SET007 Axioms: SET007+605.ax


%------------------------------------------------------------------------------
% File     : SET007+605 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The SCMPDS Computer and the Basic Semantics of its 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    : scmpds_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  146 (  15 unit)
%            Number of atoms       :  684 ( 172 equality)
%            Maximal formula depth :   26 (   7 average)
%            Number of connectives :  632 (  94 ~  ;   0  |; 135  &)
%                                         (   5 <=>; 398 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   1 propositional; 0-3 arity)
%            Number of functors    :   91 (  26 constant; 0-8 arity)
%            Number of variables   :  415 (   0 singleton; 407 !;   8 ?)
%            Maximal term depth    :    8 (   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(fc1_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(fc2_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(fc3_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & ~ v3_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) )).

fof(fc4_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(fc5_scmpds_2,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(d1_scmpds_2,axiom,(
    k1_scmpds_2 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,np__0,k3_ami_2,k1_gr_cy_1(np__14),k5_scmpds_1,k6_scmpds_1,k29_scmpds_1) )).

fof(t1_scmpds_2,axiom,(
    ! [A] :
      ( ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k1_nat_1(k2_nat_1(np__2,B),np__2) )
    <=> r2_hidden(A,k3_ami_2) ) )).

fof(t2_scmpds_2,axiom,(
    v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(t3_scmpds_2,axiom,(
    v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(t4_scmpds_2,axiom,
    ( u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k4_numbers
    & u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k4_numbers
    & u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) )).

fof(t5_scmpds_2,axiom,(
    k5_numbers = k2_xboole_0(k2_xboole_0(k1_tarski(np__0),k2_ami_2),k3_ami_2) )).

fof(t6_scmpds_2,axiom,(
    k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) = np__0 )).

fof(t7_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k6_scmpds_1))
         => ( B = A
           => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k7_scmpds_1(B) ) ) ) )).

fof(d2_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k1_scmpds_2))
     => ( m1_scmpds_2(A)
      <=> r2_hidden(A,k2_ami_2) ) ) )).

fof(t8_scmpds_2,axiom,(
    $true )).

fof(t9_scmpds_2,axiom,(
    ! [A] :
      ( r2_hidden(A,k2_ami_2)
     => m1_scmpds_2(A) ) )).

fof(t10_scmpds_2,axiom,(
    r1_subset_1(k2_ami_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )).

fof(t11_scmpds_2,axiom,(
    ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )).

fof(t12_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => m1_ami_3(A) ) )).

fof(t13_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => k3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k4_numbers ) )).

fof(t14_scmpds_2,axiom,(
    ! [A] :
      ( r2_hidden(A,k3_ami_2)
     => m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(t15_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),np__13) ) )).

fof(d3_scmpds_2,axiom,(
    $true )).

fof(d4_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => k3_scmpds_2(A,B) = k1_nat_1(k2_nat_1(np__2,k1_int_2(k2_xcmplx_0(A,B))),np__1) ) ) )).

fof(t16_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => r2_hidden(k4_tarski(np__0,k9_finseq_1(A)),k5_scmpds_1) ) )).

fof(t17_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k2_ami_2)
     => r2_hidden(k4_tarski(np__1,k12_finseq_1(k2_ami_2,A)),k5_scmpds_1) ) )).

fof(t18_scmpds_2,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_numbers,k2_ami_2)
     => ! [C] :
          ( v1_int_1(C)
         => ( r2_hidden(A,k2_tarski(np__2,np__3))
           => r2_hidden(k4_tarski(A,k13_scmpds_1(B,C)),k5_scmpds_1) ) ) ) )).

fof(t19_scmpds_2,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_numbers,k2_ami_2)
     => ! [C] :
          ( v1_int_1(C)
         => ! [D] :
              ( v1_int_1(D)
             => ( r2_hidden(A,k3_enumset1(np__4,np__5,np__6,np__7,np__8))
               => r2_hidden(k4_tarski(A,k11_finseq_1(B,C,D)),k5_scmpds_1) ) ) ) ) )).

fof(t20_scmpds_2,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_numbers,k2_ami_2)
     => ! [C] :
          ( m2_subset_1(C,k5_numbers,k2_ami_2)
         => ! [D] :
              ( v1_int_1(D)
             => ! [E] :
                  ( v1_int_1(E)
                 => ( r2_hidden(A,k3_enumset1(np__9,np__10,np__11,np__12,np__13))
                   => r2_hidden(k4_tarski(A,k1_scmpds_1(B,C,D,E)),k5_scmpds_1) ) ) ) ) ) )).

fof(d5_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k4_scmpds_2(A) = k4_tarski(np__0,k9_finseq_1(A)) ) )).

fof(d6_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => k5_scmpds_2(A) = k4_tarski(np__1,k12_finseq_1(u1_struct_0(k1_scmpds_2),A)) ) )).

fof(d7_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => k6_scmpds_2(A,B) = k4_tarski(np__2,k10_finseq_1(A,B)) ) ) )).

fof(d8_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => k7_scmpds_2(A,B) = k4_tarski(np__3,k10_finseq_1(A,B)) ) ) )).

fof(d9_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k8_scmpds_2(A,B,C) = k4_tarski(np__4,k11_finseq_1(A,B,C)) ) ) ) )).

fof(d10_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k9_scmpds_2(A,B,C) = k4_tarski(np__5,k11_finseq_1(A,B,C)) ) ) ) )).

fof(d11_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k10_scmpds_2(A,B,C) = k4_tarski(np__6,k11_finseq_1(A,B,C)) ) ) ) )).

fof(d12_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k11_scmpds_2(A,B,C) = k4_tarski(np__7,k11_finseq_1(A,B,C)) ) ) ) )).

fof(d13_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k12_scmpds_2(A,B,C) = k4_tarski(np__8,k11_finseq_1(A,B,C)) ) ) ) )).

fof(d14_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k13_scmpds_2(A,B,C,D) = k4_tarski(np__9,k1_scmpds_1(A,B,C,D)) ) ) ) ) )).

fof(d15_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k14_scmpds_2(A,B,C,D) = k4_tarski(np__10,k1_scmpds_1(A,B,C,D)) ) ) ) ) )).

fof(d16_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k15_scmpds_2(A,B,C,D) = k4_tarski(np__11,k1_scmpds_1(A,B,C,D)) ) ) ) ) )).

fof(d17_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k16_scmpds_2(A,B,C,D) = k4_tarski(np__12,k1_scmpds_1(A,B,C,D)) ) ) ) ) )).

fof(d18_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k17_scmpds_2(A,B,C,D) = k4_tarski(np__13,k1_scmpds_1(A,B,C,D)) ) ) ) ) )).

fof(t21_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)) = np__0 ) )).

fof(t22_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)) = np__1 ) )).

fof(t23_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(B,A)) = np__2 ) ) )).

fof(t24_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(B,A)) = np__3 ) ) )).

fof(t25_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(C,A,B)) = np__4 ) ) ) )).

fof(t26_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(C,A,B)) = np__5 ) ) ) )).

fof(t27_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(C,A,B)) = np__6 ) ) ) )).

fof(t28_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(C,A,B)) = np__7 ) ) ) )).

fof(t29_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(C,A,B)) = np__8 ) ) ) )).

fof(t30_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(C,D,A,B)) = np__9 ) ) ) ) )).

fof(t31_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(C,D,A,B)) = np__10 ) ) ) ) )).

fof(t32_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(C,D,A,B)) = np__11 ) ) ) ) )).

fof(t33_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,D,A,B)) = np__12 ) ) ) ) )).

fof(t34_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(C,D,A,B)) = np__13 ) ) ) ) )).

fof(t35_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__0
          & ! [B] :
              ( v1_int_1(B)
             => A != k4_scmpds_2(B) ) ) ) )).

fof(t36_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__1
          & ! [B] :
              ( m1_scmpds_2(B)
             => A != k5_scmpds_2(B) ) ) ) )).

fof(t37_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__2
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => A != k6_scmpds_2(B,C) ) ) ) ) )).

fof(t38_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__3
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => A != k7_scmpds_2(B,C) ) ) ) ) )).

fof(t39_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__4
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k8_scmpds_2(B,C,D) ) ) ) ) ) )).

fof(t40_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__5
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k9_scmpds_2(B,C,D) ) ) ) ) ) )).

fof(t41_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__6
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k10_scmpds_2(B,C,D) ) ) ) ) ) )).

fof(t42_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__7
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k11_scmpds_2(B,C,D) ) ) ) ) ) )).

fof(t43_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__8
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k12_scmpds_2(B,C,D) ) ) ) ) ) )).

fof(t44_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__9
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k13_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t45_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__10
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k14_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t46_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__11
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k15_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t47_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__12
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k16_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t48_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__13
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k17_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t49_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_scmpds_2(B)
         => r2_hidden(B,k1_relat_1(A)) ) ) )).

fof(t50_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => r1_tarski(k2_ami_2,k1_relat_1(A)) ) )).

fof(t51_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k1_relat_1(k7_relat_1(A,k2_ami_2)) = k2_ami_2 ) )).

fof(t52_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => A != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(t53_scmpds_2,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_scmpds_2(B)
         => A != B ) ) )).

fof(t54_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
              & ! [C] :
                  ( m1_scmpds_2(C)
                 => k2_scmpds_2(A,C) = k2_scmpds_2(B,C) )
              & ! [C] :
                  ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                 => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) ) )
           => A = B ) ) ) )).

fof(d19_scmpds_2,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ( B = k18_scmpds_2(A)
          <=> ? [C] :
                ( m2_subset_1(C,k5_numbers,k3_ami_2)
                & C = A
                & B = k15_ami_2(C) ) ) ) ) )).

fof(t55_scmpds_2,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ( B = A
           => k15_ami_2(B) = k18_scmpds_2(A) ) ) ) )).

fof(t56_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( m1_subset_1(C,k5_scmpds_1)
             => ( C = B
               => ! [D] :
                    ( m1_subset_1(D,k4_card_3(k6_scmpds_1))
                   => ( D = A
                     => k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k28_scmpds_1(C,D) ) ) ) ) ) ) )).

fof(t57_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),C) = B
                & ! [D] :
                    ( m1_scmpds_2(D)
                   => ( D != C
                     => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t58_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                    & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = C
                    & ! [E] :
                        ( m1_scmpds_2(E)
                       => ( E != k3_scmpds_2(k2_scmpds_2(A,D),B)
                         => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ) )).

fof(t59_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C))
                        & ! [F] :
                            ( m1_scmpds_2(F)
                           => ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
                             => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) )).

fof(t60_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                    & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),C)
                    & ! [E] :
                        ( m1_scmpds_2(E)
                       => ( E != k3_scmpds_2(k2_scmpds_2(A,D),B)
                         => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ) )).

fof(t61_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
                        & ! [F] :
                            ( m1_scmpds_2(F)
                           => ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
                             => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) )).

fof(t62_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k6_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
                        & ! [F] :
                            ( m1_scmpds_2(F)
                           => ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
                             => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) )).

fof(t63_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k3_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
                        & ! [F] :
                            ( m1_scmpds_2(F)
                           => ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
                             => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) )).

fof(t64_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                        & ( k3_scmpds_2(k2_scmpds_2(A,D),B) != k3_scmpds_2(k2_scmpds_2(A,E),C)
                         => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k5_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C))) )
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,E),C)) = k6_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
                        & ! [F] :
                            ( m1_scmpds_2(F)
                           => ~ ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
                                & F != k3_scmpds_2(k2_scmpds_2(A,E),C)
                                & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),F) != k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) )).

fof(t65_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),k3_scmpds_2(k2_scmpds_2(A,C),B)) = k6_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),B)))
                & ! [D] :
                    ( m1_scmpds_2(D)
                   => ( D != k3_scmpds_2(k2_scmpds_2(A,C),B)
                     => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(d20_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( C = k19_scmpds_2(A,B)
              <=> ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & D = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
                    & C = k1_nat_1(k1_int_2(k2_xcmplx_0(k6_xcmplx_0(D,np__2),k3_xcmplx_0(np__2,B))),np__2) ) ) ) ) ) )).

fof(t66_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,B)
            & ! [C] :
                ( m1_scmpds_2(C)
               => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(B),A),C) = k2_scmpds_2(A,C) ) ) ) ) )).

fof(t67_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)) != np__0
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
                        & ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)) = np__0
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) )).

fof(t68_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),np__0)
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
                        & ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),np__0)
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) )).

fof(t69_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)))
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
                        & ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)))
                         => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
                        & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) )).

fof(t70_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_scmpds_2(B)
         => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k1_nat_1(k2_nat_1(np__2,k3_nat_1(k1_int_2(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,B),k27_scmpds_1))),np__2)),np__4)
            & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),B) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,B),k26_scmpds_1))
            & ! [C] :
                ( m1_scmpds_2(C)
               => ( B != C
                 => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),C) = k2_scmpds_2(A,C) ) ) ) ) ) )).

fof(t71_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),k3_scmpds_2(k2_scmpds_2(A,C),B)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
                & ! [D] :
                    ( m1_scmpds_2(D)
                   => ( k3_scmpds_2(k2_scmpds_2(A,C),B) != D
                     => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t72_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k2_ami_2,k4_numbers)
          & m2_relset_1(B,k2_ami_2,k4_numbers)
          & ! [C] :
              ( m2_subset_1(C,k5_numbers,k2_ami_2)
             => k8_funct_2(k2_ami_2,k4_numbers,B,C) = A ) ) ) )).

fof(t73_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ? [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
          & ! [C] :
              ( m1_scmpds_2(C)
             => k2_scmpds_2(B,C) = A ) ) ) )).

fof(t74_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ? [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
              & k1_funct_1(C,np__0) = B
              & ! [D] :
                  ( m1_scmpds_2(D)
                 => k2_scmpds_2(C,D) = A ) ) ) ) )).

fof(t75_scmpds_2,axiom,(
    v3_ami_1(k4_scmpds_2(np__0),k1_tarski(k4_numbers),k1_scmpds_2) )).

fof(t76_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ ( ? [B] :
              ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
              & k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)) )
          & v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t77_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ~ v3_ami_1(k6_scmpds_2(B,A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t78_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ~ v3_ami_1(k11_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t79_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ~ v3_ami_1(k17_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t80_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ~ v3_ami_1(k12_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t81_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ~ v3_ami_1(k13_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t82_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ~ v3_ami_1(k14_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t83_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ~ v3_ami_1(k15_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t84_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ~ v3_ami_1(k16_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t85_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ~ ( A != np__0
          & v3_ami_1(k4_scmpds_2(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t86_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ~ v3_ami_1(k8_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t87_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ~ v3_ami_1(k9_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t88_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scmpds_2(C)
             => ~ v3_ami_1(k10_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t89_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ~ v3_ami_1(k5_scmpds_2(A),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(t90_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ~ v3_ami_1(k7_scmpds_2(B,A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t91_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
    <=> ~ ( ! [B] :
              ( v1_int_1(B)
             => A != k4_scmpds_2(B) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => A != k5_scmpds_2(B) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => A != k7_scmpds_2(B,C) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => A != k6_scmpds_2(B,C) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k11_scmpds_2(B,C,D) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k8_scmpds_2(B,C,D) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k9_scmpds_2(B,C,D) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( v1_int_1(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => A != k10_scmpds_2(B,C,D) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k12_scmpds_2(B,D,E) ) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k13_scmpds_2(B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k14_scmpds_2(B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k15_scmpds_2(B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k16_scmpds_2(B,C,D,E) ) ) ) )
          & ! [B] :
              ( m1_scmpds_2(B)
             => ! [C] :
                  ( m1_scmpds_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ! [E] :
                          ( v1_int_1(E)
                         => A != k17_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).

fof(t92_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t93_scmpds_2,axiom,(
    k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) = k4_scmpds_2(np__0) )).

fof(t94_scmpds_2,axiom,(
    $true )).

fof(t95_scmpds_2,axiom,(
    $true )).

fof(t96_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) ) ) ) )).

fof(t97_scmpds_2,axiom,(
    v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(t98_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k15_ami_3(A)
        & k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k16_ami_3(A) ) ) )).

fof(t99_scmpds_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( A = k4_scmpds_2(np__0)
       => v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_m1_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) )).

fof(existence_m1_scmpds_2,axiom,(
    ? [A] : m1_scmpds_2(A) )).

fof(dt_k1_scmpds_2,axiom,
    ( v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & l1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(dt_k2_scmpds_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
        & m1_scmpds_2(B) )
     => v1_int_1(k2_scmpds_2(A,B)) ) )).

fof(redefinition_k2_scmpds_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
        & m1_scmpds_2(B) )
     => k2_scmpds_2(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k3_scmpds_2,axiom,(
    ! [A,B] :
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => m1_scmpds_2(k3_scmpds_2(A,B)) ) )).

fof(dt_k4_scmpds_2,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => m2_subset_1(k4_scmpds_2(A),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k5_scmpds_2,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => m2_subset_1(k5_scmpds_2(A),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k6_scmpds_2,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => m2_subset_1(k6_scmpds_2(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k7_scmpds_2,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => m2_subset_1(k7_scmpds_2(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k8_scmpds_2,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k8_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k9_scmpds_2,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k9_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k10_scmpds_2,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k10_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k11_scmpds_2,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k11_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k12_scmpds_2,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => m2_subset_1(k12_scmpds_2(A,B,C),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k13_scmpds_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m2_subset_1(k13_scmpds_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k14_scmpds_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m2_subset_1(k14_scmpds_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k15_scmpds_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m2_subset_1(k15_scmpds_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k16_scmpds_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m2_subset_1(k16_scmpds_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k17_scmpds_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m2_subset_1(k17_scmpds_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k18_scmpds_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => m1_struct_0(k18_scmpds_2(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k19_scmpds_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
        & v1_int_1(B) )
     => m1_struct_0(k19_scmpds_2(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).
%------------------------------------------------------------------------------