SET007 Axioms: SET007+595.ax


%------------------------------------------------------------------------------
% File     : SET007+595 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Insert Sort on SCMFSA
% 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    : scmisort [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (   5 unit)
%            Number of atoms       :  471 (  80 equality)
%            Maximal formula depth :   20 (   9 average)
%            Number of connectives :  467 (  55 ~  ;  12  |; 206  &)
%                                         (   1 <=>; 193 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   46 (   1 propositional; 0-4 arity)
%            Number of functors    :   94 (  22 constant; 0-7 arity)
%            Number of variables   :  165 (   0 singleton; 163 !;   2 ?)
%            Maximal term depth    :   12 (   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_scmisort,axiom,(
    ! [A] :
      ( ( v4_scm_halt(A)
        & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( v1_relat_1(k2_scmfsa6a(A))
        & v1_funct_1(k2_scmfsa6a(A))
        & v1_finset_1(k2_scmfsa6a(A))
        & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa6a(A))
        & v1_scmfsa7b(k2_scmfsa6a(A)) ) ) )).

fof(fc2_scmisort,axiom,(
    ! [A,B] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A)
        & m1_scmfsa_2(B) )
     => ( v1_scmfsa6c(k9_scmfsa_2(A,B))
        & v2_scmfsa6c(k9_scmfsa_2(A,B))
        & v4_scm_halt(k9_scmfsa_2(A,B)) ) ) )).

fof(t1_scmisort,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r2_hidden(B,k1_relat_1(A))
         => k1_relat_1(A) = k1_relat_1(k1_funct_4(A,k3_cqc_lang(B,C))) ) ) )).

fof(t2_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ( r2_hidden(B,k1_relat_1(A))
               => ( ! [D] :
                      ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                     => ~ ( D = k1_funct_1(A,B)
                          & k1_sf_mastr(D) = k1_sf_mastr(C) ) )
                  | k2_sf_mastr(A) = k2_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C))) ) ) ) ) ) )).

fof(t3_scmisort,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k1_funct_1(k2_scmfsa8b(A,k4_scmfsa6a(B,k2_scmfsa8a(k5_scmfsa_2(np__0))),k5_scmfsa_4),k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__4))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__4))) ) ) )).

fof(t4_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ( r2_hidden(B,k1_relat_1(A))
               => ( ! [D] :
                      ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                     => ~ ( D = k1_funct_1(A,B)
                          & k3_sf_mastr(D) = k3_sf_mastr(C) ) )
                  | k4_sf_mastr(A) = k4_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C))) ) ) ) ) ) )).

fof(t5_scmisort,axiom,(
    $true )).

fof(t6_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
              & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0) )
           => k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)) ) ) ) )).

fof(t7_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( r4_scmfsa7b(A,C)
               => r4_scmfsa7b(k2_scmfsa_9(B,A),C) ) ) ) ) )).

fof(t8_scmisort,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(A,np__11)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6
          & A != np__7
          & A != np__8
          & A != np__9
          & A != np__10
          & A != np__11 ) ) )).

fof(t9_scmisort,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,k3_finseq_1(A))
                      & r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(A))
                      & B = k3_funct_7(k4_numbers,k3_funct_7(k4_numbers,A,C,k4_finseq_4(k5_numbers,k4_numbers,A,D)),D,k4_finseq_4(k5_numbers,k4_numbers,A,C)) )
                   => ( k2_seq_1(k5_numbers,k4_numbers,A,C) = k2_seq_1(k5_numbers,k4_numbers,B,D)
                      & k2_seq_1(k5_numbers,k4_numbers,A,D) = k2_seq_1(k5_numbers,k4_numbers,B,C)
                      & ! [E] :
                          ( r2_hidden(E,k4_finseq_1(A))
                         => ( E = C
                            | E = D
                            | k2_seq_1(k5_numbers,k4_numbers,A,E) = k2_seq_1(k5_numbers,k4_numbers,B,E) ) )
                      & r1_rfinseq(A,B) ) ) ) ) ) ) )).

fof(t10_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r6_scmfsa7b(B,k1_scmfsa6c(A))
           => ! [C] :
                ( m1_scmfsa_2(C)
               => k20_scmfsa_2(k3_scmfsa6b(B,A),C) = k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),C) ) ) ) ) )).

fof(t11_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scm_halt(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_tarski(k3_scmfsa6a(C),A)
                  & r1_tarski(k3_scmfsa6a(C),B)
                  & r1_funct_7(A,B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_funct_7(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),D),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                      & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D)) = k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),D)) ) ) ) ) ) ) )).

fof(t12_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scm_halt(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_tarski(k3_scmfsa6a(C),A)
                  & r1_tarski(k3_scmfsa6a(C),B)
                  & r1_funct_7(A,B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
               => ( k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)
                  & r1_funct_7(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ) )).

fof(t13_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ~ r2_hidden(B,k1_relat_1(A)) ) ) )).

fof(t14_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ~ r2_hidden(B,k1_relat_1(A)) ) ) )).

fof(t15_scmisort,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_setfam_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(B,C)))
                 => ( ( r1_xreal_0(k2_scm_1(B,C,D),A)
                      & v9_ami_1(D,B,C) )
                   => k11_ami_1(B,C,k10_ami_1(B,C,D),A) = k11_ami_1(B,C,k10_ami_1(B,C,D),k2_scm_1(B,C,D)) ) ) ) ) ) )).

fof(t16_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
               => ( r2_scm_halt(k2_scmfsa_9(C,B),A)
                  & r1_scm_halt(k2_scmfsa_9(C,B),A) ) ) ) ) ) )).

fof(t17_scmisort,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_scm_halt(B,C)
                      & r2_scm_halt(B,C)
                      & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(np__1,D))) = k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),D)),np__4)
                      & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(np__1,D)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) )
                   => ( r1_xreal_0(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),D)
                      | ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(k1_nat_1(np__1,D),np__1))) = k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),k1_nat_1(D,np__1))),np__4)
                        & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(k1_nat_1(np__1,D),np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) )).

fof(t18_scmisort,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r1_scm_halt(B,C)
                  & r2_scm_halt(B,C)
                  & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(np__1,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B)))))) = k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B))))),np__4) )
               => k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(A,B)))),k1_nat_1(np__1,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(B)))))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__4))) ) ) ) ) )).

fof(t19_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( ( r1_scm_halt(B,A)
                  & r2_scm_halt(B,A) )
               => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
                  | ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3))) = k5_scmfsa_2(np__0)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(D,k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3))
                         => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))),D)),k1_relat_1(k2_scmfsa_9(C,B))) ) ) ) ) ) ) ) ) )).

fof(t20_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( ( r1_scm_halt(B,A)
                  & r2_scm_halt(B,A) )
               => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(D,k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3))
                       => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))),D)),k1_relat_1(k2_scmfsa_9(C,B))) ) ) ) ) ) ) ) )).

fof(t21_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( ( r1_scm_halt(B,A)
                  & r2_scm_halt(B,A) )
               => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
                  | ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3))) = k5_scmfsa_2(np__0)
                    & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t22_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & v2_scm_halt(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ~ ( ~ r1_xreal_0(k20_scmfsa_2(A,C),np__0)
                  & ! [D] :
                      ( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( D = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k2_scmfsa_9(C,B)))
                              & E = k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__3)
                              & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E)) = k5_scmfsa_2(np__0)
                              & ! [F] :
                                  ( m1_scmfsa_2(F)
                                 => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E),F) = k20_scmfsa_2(k3_scmfsa6b(B,A),F) )
                              & ! [F] :
                                  ( m2_scmfsa_2(F)
                                 => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E),F) = k21_scmfsa_2(k3_scmfsa6b(B,A),F) ) ) ) ) ) ) ) ) )).

fof(d1_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                    & m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) )
                 => ( D = k1_scmisort(A,B,C)
                  <=> ( k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,np__0) = A
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k1_nat_1(E,np__1)) = k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,E),k3_scmfsa6a(k2_scmfsa_9(C,B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,E),k3_scmfsa6a(B))),np__3)) ) ) ) ) ) ) ) )).

fof(t23_scmisort,axiom,(
    $true )).

fof(t24_scmisort,axiom,(
    $true )).

fof(t25_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(A,B,C),k1_nat_1(D,np__1)) = k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(A,B,C),D),B,C),np__1) ) ) ) ) )).

fof(t26_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),k1_nat_1(np__0,np__1)) = k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(B,A)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(A))),np__3)) ) ) ) )).

fof(t27_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D)) = k5_scmfsa_2(np__0)
                          & k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D) = k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(B,A)))),E)
                          & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D),k4_scmfsa_2(np__0)) = np__1 )
                       => ( k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D),k3_scmfsa6a(k2_scmfsa_9(B,A)))
                          & k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),k1_nat_1(D,np__1)) = k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k2_scmfsa_9(B,A)))),k1_nat_1(E,k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),D),k3_scmfsa6a(A))),np__3))) ) ) ) ) ) ) ) )).

fof(t28_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E)) != np__0
                           => ( ~ r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),k1_nat_1(E,np__1))))
                              & r1_scm_halt(A,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E))
                              & r2_scm_halt(A,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E)) ) )
                          & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),k1_nat_1(E,np__1)),k4_scmfsa_2(np__0)) = np__1
                          & ( k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E)) = np__0
                           => r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E),B),np__0) )
                          & ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E),B),np__0)
                           => k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmisort(C,A,B),E)) = np__0 ) ) ) )
               => ( r2_scm_halt(k2_scmfsa_9(B,A),C)
                  & r1_scm_halt(k2_scmfsa_9(B,A),C) ) ) ) ) ) )).

fof(t29_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & v2_scm_halt(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ( ! [C] :
                ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
               => ~ ( ~ r1_xreal_0(k20_scmfsa_2(C,B),np__0)
                    & r1_xreal_0(k20_scmfsa_2(C,B),k20_scmfsa_2(k3_scmfsa6b(A,C),B)) ) )
           => v2_scm_halt(k2_scmfsa_9(B,A)) ) ) ) )).

fof(t30_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & v2_scm_halt(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ( ! [C] :
                ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
               => ~ ( r1_xreal_0(k20_scmfsa_2(C,B),k20_scmfsa_2(k3_scmfsa6b(A,C),B))
                    & ~ r1_xreal_0(k20_scmfsa_2(k3_scmfsa6b(A,C),B),np__0) ) )
           => v2_scm_halt(k2_scmfsa_9(B,A)) ) ) ) )).

fof(t31_scmisort,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & v2_scm_halt(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ( ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k4_numbers)
                & m2_relset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k4_numbers)
                & ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                       => ( ~ ( ~ r1_xreal_0(k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,D),np__0)
                              & r1_xreal_0(k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,D),k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,k3_scmfsa6b(A,D))) )
                          & ( k7_relat_1(D,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(E,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
                           => k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,D) = k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,E) )
                          & ( r1_xreal_0(k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,D),np__0)
                           => r1_xreal_0(k20_scmfsa_2(D,B),np__0) )
                          & ( r1_xreal_0(k20_scmfsa_2(D,B),np__0)
                           => r1_xreal_0(k2_scmisort(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),C,D),np__0) ) ) ) ) )
           => v2_scm_halt(k2_scmfsa_9(B,A)) ) ) ) )).

fof(t32_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
               => k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(C,B),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k1_scmfsa6c(A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t33_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & v1_scmfsa7b(B)
            & v2_scm_halt(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( v2_scm_halt(k2_scmfsa_9(C,B))
               => ( r1_xreal_0(k20_scmfsa_2(A,C),np__0)
                  | k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(C,B),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(C,B),k3_scmfsa6b(B,A)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t34_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( ( ~ v1_sf_mastr(D)
                    & m1_scmfsa_2(D) )
                 => ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
                   => k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),A),C) = k21_scmfsa_2(A,C) ) ) ) ) ) )).

fof(t35_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( ( ~ v1_sf_mastr(D)
                    & m1_scmfsa_2(D) )
                 => ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
                   => k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),A),C) = k20_scmfsa_2(k1_scmfsa6c(A),C) ) ) ) ) ) )).

fof(t36_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & v1_scmfsa7b(B)
            & v2_scm_halt(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( ( ~ v1_sf_mastr(D)
                    & m1_scmfsa_2(D) )
                 => ( v2_scm_halt(k2_scmfsa_9(D,B))
                   => ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
                      | k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),A),C) = k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),k3_scmfsa6b(B,A)),C) ) ) ) ) ) ) )).

fof(t37_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & v1_scmfsa7b(B)
            & v2_scm_halt(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( ( ~ v1_sf_mastr(D)
                    & m1_scmfsa_2(D) )
                 => ( v2_scm_halt(k2_scmfsa_9(D,B))
                   => ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
                      | k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),A),C) = k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_9(D,B),k3_scmfsa6b(B,A)),C) ) ) ) ) ) ) )).

fof(d2_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => k3_scmisort(A) = k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__0)),k8_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__4),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__0))),k18_scmfsa_2(k4_scmfsa_2(np__1),A)),k10_scmfsa_2(k4_scmfsa_2(np__1),k4_scmfsa_2(np__0))),k2_scmfsa8c(k4_scmfsa_2(np__1),k4_scmfsa6a(k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k18_scmfsa_2(k4_scmfsa_2(np__2),A),k10_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__1))),k8_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__2))),k9_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__0))),k16_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__3),A)),k10_scmfsa_2(k4_scmfsa_2(np__4),k4_scmfsa_2(np__4))),k2_scmfsa_9(k4_scmfsa_2(np__2),k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__2),A),k10_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__6))),k2_scmfsa8b(k4_scmfsa_2(np__5),k2_scmfsa6a(k10_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__2))),k7_scmfsa6a(k9_scmfsa_2(k4_scmfsa_2(np__4),k4_scmfsa_2(np__0)),k10_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__0))))))),k2_scmfsa8c(k4_scmfsa_2(np__4),k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__3)),k10_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__0))),k16_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__2),A)),k16_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__3),A)),k17_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__2),A)),k17_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__3),A)))))) ) )).

fof(d3_scmisort,axiom,(
    k4_scmisort = k3_scmisort(k6_scmfsa_2(np__0)) )).

fof(t38_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => k2_sf_mastr(k3_scmisort(A)) = k5_enumset1(k4_scmfsa_2(np__0),k4_scmfsa_2(np__1),k4_scmfsa_2(np__2),k4_scmfsa_2(np__3),k4_scmfsa_2(np__4),k4_scmfsa_2(np__5),k4_scmfsa_2(np__6)) ) )).

fof(t39_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => k4_sf_mastr(k3_scmisort(A)) = k1_struct_0(k1_scmfsa_2,A) ) )).

fof(t40_scmisort,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                 => k4_card_1(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(A,B),C),D)) = np__8 ) ) ) ) )).

fof(t41_scmisort,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                     => k4_card_1(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(A,B),C),D),E)) = np__10 ) ) ) ) ) )).

fof(t42_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => k4_card_1(k3_scmisort(A)) = np__82 ) )).

fof(t43_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(np__82,B)
           => r2_hidden(k5_scmfsa_2(B),k1_relat_1(k3_scmisort(A))) ) ) ) )).

fof(t44_scmisort,axiom,
    ( v3_scm_halt(k3_scmisort(k6_scmfsa_2(np__0)))
    & v2_scm_halt(k3_scmisort(k6_scmfsa_2(np__0))) )).

fof(t45_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( r1_rfinseq(k21_scmfsa_2(A,k6_scmfsa_2(np__0)),k21_scmfsa_2(k3_scmfsa6b(k3_scmisort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)))
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r1_xreal_0(np__1,B)
                    & r1_xreal_0(C,k3_finseq_1(k21_scmfsa_2(A,k6_scmfsa_2(np__0)))) )
                 => ( r1_xreal_0(C,B)
                    | ! [D] :
                        ( v1_int_1(D)
                       => ! [E] :
                            ( v1_int_1(E)
                           => ( ( D = k2_seq_1(k5_numbers,k4_numbers,k21_scmfsa_2(k3_scmfsa6b(k3_scmisort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)),B)
                                & E = k2_seq_1(k5_numbers,k4_numbers,k21_scmfsa_2(k3_scmfsa6b(k3_scmisort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)),C) )
                             => r1_xreal_0(E,D) ) ) ) ) ) ) ) ) ) )).

fof(t46_scmisort,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k4_scmisort),k1_scmbsort(k6_scmfsa_2(np__0),C)),B)
               => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),A)),k1_relat_1(k4_scmisort)) ) ) ) ) )).

fof(t47_scmisort,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ~ ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k4_scmisort),k1_scmbsort(k6_scmfsa_2(np__0),B)),A)
              & ! [C] :
                  ( m2_finseq_1(C,k1_numbers)
                 => ~ ( r1_rfinseq(B,C)
                      & v1_rfinseq(C)
                      & m2_finseq_1(C,k4_numbers)
                      & k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k6_scmfsa_2(np__0)) = C ) ) ) ) ) )).

fof(t48_scmisort,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => v11_ami_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k4_scmisort),k1_scmbsort(k6_scmfsa_2(np__0),A)),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) )).

fof(t49_scmisort,axiom,(
    r1_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k4_scmisort),k4_scmbsort) )).

fof(dt_k1_scmisort,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(B)
        & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & ~ v1_sf_mastr(C)
        & m1_scmfsa_2(C) )
     => ( v1_funct_1(k1_scmisort(A,B,C))
        & v1_funct_2(k1_scmisort(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & m2_relset_1(k1_scmisort(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) )).

fof(dt_k2_scmisort,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k4_numbers)
        & m1_relset_1(B,A,k4_numbers)
        & m1_subset_1(C,A) )
     => v1_int_1(k2_scmisort(A,B,C)) ) )).

fof(redefinition_k2_scmisort,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k4_numbers)
        & m1_relset_1(B,A,k4_numbers)
        & m1_subset_1(C,A) )
     => k2_scmisort(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k3_scmisort,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ( v1_ami_3(k3_scmisort(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k3_scmisort(A))
        & m1_ami_1(k3_scmisort(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k4_scmisort,axiom,
    ( v1_ami_3(k4_scmisort,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
    & v1_scmfsa_4(k4_scmisort)
    & m1_ami_1(k4_scmisort,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )).
%------------------------------------------------------------------------------