SET007 Axioms: SET007+711.ax


%------------------------------------------------------------------------------
% File     : SET007+711 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On State Machines of Calculating Type
% 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    : fsm_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   1 unit)
%            Number of atoms       :  602 ( 118 equality)
%            Maximal formula depth :   26 (  12 average)
%            Number of connectives :  697 ( 157 ~  ;   3  |; 252  &)
%                                         (   9 <=>; 276 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   0 propositional; 1-5 arity)
%            Number of functors    :   39 (   5 constant; 0-7 arity)
%            Number of variables   :  307 (   0 singleton; 294 !;  13 ?)
%            Maximal term depth    :    9 (   1 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_fsm_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_fsm_1(B,A)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_finseq_1(D,A) )
     => ( ~ v1_xboole_0(k2_fsm_1(A,B,C,D))
        & v1_relat_1(k2_fsm_1(A,B,C,D))
        & v1_funct_1(k2_fsm_1(A,B,C,D))
        & v1_finset_1(k2_fsm_1(A,B,C,D))
        & v1_finseq_1(k2_fsm_1(A,B,C,D)) ) ) )).

fof(rc1_fsm_2,axiom,(
    ! [A] :
    ? [B] :
      ( l1_fsm_2(B,A)
      & v4_fsm_2(B,A) ) )).

fof(rc2_fsm_2,axiom,(
    ! [A] :
    ? [B] :
      ( l1_fsm_2(B,A)
      & ~ v3_struct_0(B) ) )).

fof(rc3_fsm_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l2_fsm_2(C,A,B)
          & v6_fsm_2(C,A,B) ) ) )).

fof(rc4_fsm_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l2_fsm_2(C,A,B)
          & ~ v3_struct_0(C)
          & v6_fsm_2(C,A,B) ) ) )).

fof(fc2_fsm_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_tarski(C,D),B)
        & m1_relset_1(E,k2_tarski(C,D),B) )
     => ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
        & v1_fsm_2(k1_fsm_2(A,B,C,D,E),A)
        & v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) )).

fof(fc3_fsm_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_tarski(C,D),B)
        & m1_relset_1(E,k2_tarski(C,D),B) )
     => ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
        & v1_fsm_2(k1_fsm_2(A,B,C,D,E),A)
        & v5_fsm_2(k1_fsm_2(A,B,C,D,E),A)
        & v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) )).

fof(rc5_fsm_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] :
          ( l2_fsm_2(C,A,B)
          & ~ v3_struct_0(C)
          & v1_fsm_2(C,A)
          & v5_fsm_2(C,A) ) ) )).

fof(rc6_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( l1_fsm_2(B,A)
          & ~ v3_struct_0(B)
          & v1_fsm_2(B,A)
          & v5_fsm_2(B,A) ) ) )).

fof(t1_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_fsm_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k2_fsm_1(A,C,D,k12_finseq_1(A,B)) = k2_finseq_4(u1_struct_0(C),D,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k1_domain_1(u1_struct_0(C),A,D,B))) ) ) ) ) )).

fof(t2_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_fsm_1(D,A) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => k2_fsm_1(A,D,E,k2_finseq_4(A,B,C)) = k3_finseq_4(u1_struct_0(D),E,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),u1_struct_0(D),u1_fsm_1(A,D),k1_domain_1(u1_struct_0(D),A,E,B)),k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),u1_struct_0(D),u1_fsm_1(A,D),k1_domain_1(u1_struct_0(D),A,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),u1_struct_0(D),u1_fsm_1(A,D),k1_domain_1(u1_struct_0(D),A,E,B)),C))) ) ) ) ) ) )).

fof(t3_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l1_fsm_1(E,A) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => k2_fsm_1(A,E,F,k3_finseq_4(A,B,C,D)) = k3_scmpds_1(u1_struct_0(E),F,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,F,B)),k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,F,B)),C)),k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,F,B)),C)),D))) ) ) ) ) ) ) )).

fof(d1_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( v1_fsm_2(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & m2_subset_1(C,k1_numbers,k5_numbers) )
               => ! [D] :
                    ( m2_finseq_1(D,A)
                   => ! [E] :
                        ( m2_finseq_1(E,A)
                       => ( ( k1_funct_1(D,np__1) = k1_funct_1(E,np__1)
                            & r1_xreal_0(C,k1_nat_1(k3_finseq_1(D),np__1))
                            & r1_xreal_0(C,k1_nat_1(k3_finseq_1(E),np__1)) )
                         => k1_funct_1(k2_fsm_1(A,B,u2_fsm_1(A,B),D),C) = k1_funct_1(k2_fsm_1(A,B,u2_fsm_1(A,B),E),C) ) ) ) ) ) ) ) )).

fof(t4_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( v1_fsm_2(B,A)
           => ! [C] :
                ( m2_finseq_1(C,A)
               => ! [D] :
                    ( m2_finseq_1(D,A)
                   => ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
                     => r3_xboole_0(k2_fsm_1(A,B,u2_fsm_1(A,B),C),k2_fsm_1(A,B,u2_fsm_1(A,B),D)) ) ) ) ) ) ) )).

fof(t5_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ! [C] :
                ( m2_finseq_1(C,A)
               => ! [D] :
                    ( m2_finseq_1(D,A)
                   => ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
                     => r3_xboole_0(k2_fsm_1(A,B,u2_fsm_1(A,B),C),k2_fsm_1(A,B,u2_fsm_1(A,B),D)) ) ) )
           => v1_fsm_2(B,A) ) ) ) )).

fof(t6_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( v1_fsm_2(B,A)
           => ! [C] :
                ( m2_finseq_1(C,A)
               => ! [D] :
                    ( m2_finseq_1(D,A)
                   => ( ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
                        & k3_finseq_1(C) = k3_finseq_1(D) )
                     => k2_fsm_1(A,B,u2_fsm_1(A,B),C) = k2_fsm_1(A,B,u2_fsm_1(A,B),D) ) ) ) ) ) ) )).

fof(t7_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ! [C] :
                ( m2_finseq_1(C,A)
               => ! [D] :
                    ( m2_finseq_1(D,A)
                   => ( ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
                        & k3_finseq_1(C) = k3_finseq_1(D) )
                     => k2_fsm_1(A,B,u2_fsm_1(A,B),C) = k2_fsm_1(A,B,u2_fsm_1(A,B),D) ) ) )
           => v1_fsm_2(B,A) ) ) ) )).

fof(d2_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r1_fsm_2(A,B,C,D)
                  <=> ? [E] :
                        ( m2_finseq_1(E,A)
                        & r1_fsm_1(A,B,k8_finseq_1(A,k12_finseq_1(A,D),E),u2_fsm_1(A,B),C) ) ) ) ) ) ) )).

fof(d3_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( v2_fsm_2(C,A,B)
              <=> ? [D] :
                    ( m2_finseq_1(D,A)
                    & r1_fsm_1(A,B,D,u2_fsm_1(A,B),C) ) ) ) ) ) )).

fof(t8_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_fsm_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( r1_fsm_2(A,C,D,B)
                   => v2_fsm_2(D,A,C) ) ) ) ) ) )).

fof(t9_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ~ ( v2_fsm_2(C,A,B)
                  & C != u2_fsm_1(A,B)
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ~ r1_fsm_2(A,B,C,D) ) ) ) ) ) )).

fof(t10_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => v2_fsm_2(u2_fsm_1(A,B),A,B) ) ) )).

fof(t11_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_fsm_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ~ ( v1_fsm_2(C,A)
                      & r1_fsm_2(A,C,D,B)
                      & ! [E] :
                          ( ( ~ v1_xboole_0(E)
                            & m2_subset_1(E,k1_numbers,k5_numbers) )
                         => ? [F] :
                              ( m2_finseq_1(F,A)
                              & r1_xreal_0(E,k1_nat_1(k3_finseq_1(F),np__1))
                              & k1_funct_1(F,np__1) = B
                              & ~ ( D = k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),F),E)
                                  & ! [G] :
                                      ( ( ~ v1_xboole_0(G)
                                        & m2_subset_1(G,k1_numbers,k5_numbers) )
                                     => ~ ( ~ r1_xreal_0(E,G)
                                          & k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),F),G) = D ) ) ) ) ) ) ) ) ) ) )).

fof(d4_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( v3_fsm_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => v2_fsm_2(C,A,B) ) ) ) ) )).

fof(t12_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,C)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,D)) ) ) )
           => v1_fsm_2(B,A) ) ) ) )).

fof(t13_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ( E != u2_fsm_1(A,B)
                           => k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,C)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,D)) ) ) ) )
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,D,C)) != u2_fsm_1(A,B) ) ) )
           => v1_fsm_2(B,A) ) ) ) )).

fof(t14_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ( v3_fsm_2(B,A)
              & v1_fsm_2(B,A) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( E != u2_fsm_1(A,B)
                         => k1_funct_1(k2_fsm_1(A,B,E,k12_finseq_1(A,C)),np__2) = k1_funct_1(k2_fsm_1(A,B,E,k12_finseq_1(A,D)),np__2) ) ) ) ) ) ) ) )).

fof(t15_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ( v3_fsm_2(B,A)
              & v1_fsm_2(B,A) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( E != u2_fsm_1(A,B)
                         => k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,C)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,E,D)) ) ) ) ) ) ) ) )).

fof(t16_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ( ( v3_fsm_2(B,A)
              & v1_fsm_2(B,A) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ~ ( k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,u2_fsm_1(A,B),D)) != k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,u2_fsm_1(A,B),E))
                                & k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,F,C)) = u2_fsm_1(A,B) ) ) ) ) ) ) ) ) )).

fof(d5_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_fsm_2(C,A) )
             => ( r2_fsm_2(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                    & r1_fsm_2(A,C,D,B)
                    & r2_hidden(D,u1_fsm_2(A,C)) ) ) ) ) ) )).

fof(d6_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_2(B,A) )
         => ( v5_fsm_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => r2_fsm_2(A,C,B) ) ) ) ) )).

fof(d7_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,D,E] :
              ( ( v1_funct_1(E)
                & v1_funct_2(E,k2_tarski(C,D),B)
                & m2_relset_1(E,k2_tarski(C,D),B) )
             => ! [F] :
                  ( ( ~ v3_struct_0(F)
                    & v6_fsm_2(F,A,B)
                    & l2_fsm_2(F,A,B) )
                 => ( F = k1_fsm_2(A,B,C,D,E)
                  <=> ( u1_struct_0(F) = k2_tarski(C,D)
                      & u1_fsm_1(A,F) = k2_funcop_1(k2_zfmisc_1(k2_tarski(C,D),A),D)
                      & u4_fsm_1(A,B,F) = E
                      & u2_fsm_1(A,F) = C
                      & u1_fsm_2(A,F) = k1_tarski(D) ) ) ) ) ) ) )).

fof(t17_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D,E,F] :
                  ( ( v1_funct_1(F)
                    & v1_funct_2(F,k2_tarski(D,E),A)
                    & m2_relset_1(F,k2_tarski(D,E),A) )
                 => ! [G] :
                      ( ( ~ v1_xboole_0(G)
                        & m2_subset_1(G,k1_numbers,k5_numbers) )
                     => ( r1_xreal_0(G,k1_nat_1(k3_finseq_1(C),np__1))
                       => ( r1_xreal_0(G,np__1)
                          | k1_funct_1(k2_fsm_1(B,k1_fsm_2(B,A,D,E,F),u2_fsm_1(B,k1_fsm_2(B,A,D,E,F)),C),G) = E ) ) ) ) ) ) ) )).

fof(t18_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_2(D,B,A) )
                 => ~ ( v1_fsm_2(D,B)
                      & r2_fsm_2(B,C,D)
                      & ~ r2_hidden(u2_fsm_1(B,D),u1_fsm_2(B,D))
                      & ! [E] :
                          ( ( ~ v1_xboole_0(E)
                            & m2_subset_1(E,k1_numbers,k5_numbers) )
                         => ~ ( ! [F] :
                                  ( m2_finseq_1(F,B)
                                 => ( ( r1_xreal_0(E,k1_nat_1(k3_finseq_1(F),np__1))
                                      & k1_funct_1(F,np__1) = C )
                                   => r2_hidden(k1_funct_1(k2_fsm_1(B,D,u2_fsm_1(B,D),F),E),u1_fsm_2(B,D)) ) )
                              & ! [F] :
                                  ( m2_finseq_1(F,B)
                                 => ! [G] :
                                      ( ( ~ v1_xboole_0(G)
                                        & m2_subset_1(G,k1_numbers,k5_numbers) )
                                     => ~ ( r1_xreal_0(G,k1_nat_1(k3_finseq_1(F),np__1))
                                          & k1_funct_1(F,np__1) = C
                                          & ~ r1_xreal_0(E,G)
                                          & r2_hidden(k1_funct_1(k2_fsm_1(B,D,u2_fsm_1(B,D),F),G),u1_fsm_2(B,D)) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_2(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( r3_fsm_2(A,B,C,D,E)
                    <=> ? [F] :
                          ( ~ v1_xboole_0(F)
                          & m2_subset_1(F,k1_numbers,k5_numbers)
                          & ! [G] :
                              ( m2_finseq_1(G,A)
                             => ( k1_funct_1(G,np__1) = D
                               => ( ( r1_xreal_0(F,k1_nat_1(k3_finseq_1(G),np__1))
                                   => ( E = k1_funct_1(u4_fsm_1(A,B,C),k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),F))
                                      & r2_hidden(k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),F),u1_fsm_2(A,C)) ) )
                                  & ! [H] :
                                      ( ( ~ v1_xboole_0(H)
                                        & m2_subset_1(H,k1_numbers,k5_numbers) )
                                     => ~ ( ~ r1_xreal_0(F,H)
                                          & r1_xreal_0(H,k1_nat_1(k3_finseq_1(G),np__1))
                                          & r2_hidden(k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),H),u1_fsm_2(A,C)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_2(D,A,B) )
                 => ( r2_hidden(u2_fsm_1(A,D),u1_fsm_2(A,D))
                   => r3_fsm_2(A,B,D,C,k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),u2_fsm_1(A,D))) ) ) ) ) ) )).

fof(t20_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_2(D,A,B) )
                 => ~ ( v1_fsm_2(D,A)
                      & r2_fsm_2(A,C,D)
                      & ~ r2_hidden(u2_fsm_1(A,D),u1_fsm_2(A,D))
                      & ! [E] :
                          ( m1_subset_1(E,B)
                         => ~ r3_fsm_2(A,B,D,C,E) ) ) ) ) ) ) )).

fof(t21_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_2(D,A,B) )
                 => ( ( v1_fsm_2(D,A)
                      & r2_fsm_2(A,C,D) )
                   => ! [E] :
                        ( m1_subset_1(E,B)
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ( ( r3_fsm_2(A,B,D,C,E)
                                & r3_fsm_2(A,B,D,C,F) )
                             => E = F ) ) ) ) ) ) ) ) )).

fof(t22_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_2(C,k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A))) )
             => ( ( v1_fsm_2(C,k2_zfmisc_1(A,A))
                  & u1_struct_0(C) = k2_xboole_0(A,k1_tarski(A))
                  & u1_fsm_2(k2_zfmisc_1(A,A),C) = A
                  & u2_fsm_1(k2_zfmisc_1(A,A),C) = A
                  & u4_fsm_1(k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A)),C) = k6_partfun1(u1_struct_0(C))
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => k8_funct_2(k2_zfmisc_1(u1_struct_0(C),k2_zfmisc_1(A,A)),u1_struct_0(C),u1_fsm_1(k2_zfmisc_1(A,A),C),k1_domain_1(u1_struct_0(C),k2_zfmisc_1(A,A),u2_fsm_1(k2_zfmisc_1(A,A),C),k1_domain_1(A,A,D,E))) = k2_binop_1(A,A,A,B,D,E) ) ) )
               => ( v5_fsm_2(C,k2_zfmisc_1(A,A))
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => r3_fsm_2(k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A)),C,k1_domain_1(A,A,D,E),k2_binop_1(A,A,A,B,D,E)) ) ) ) ) ) ) ) )).

fof(t23_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
          & u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k4_square_1(B,C)) ) ) ) ) )).

fof(t24_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
          & u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k3_square_1(B,C)) ) ) ) ) )).

fof(t25_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
          & u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = k3_real_1(B,C) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k3_real_1(B,C)) ) ) ) ) )).

fof(t26_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
          & u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ ( r1_xreal_0(B,np__0)
                        & r1_xreal_0(C,np__0) )
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__1 ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ( r1_xreal_0(B,np__0)
                      & r1_xreal_0(C,np__0) )
                   => ( ( B != np__0
                        & C != np__0 )
                      | k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__0 ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(np__0,B)
                      & ~ r1_xreal_0(np__0,C)
                      & k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) != k1_real_1(np__1) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k4_square_1(k2_absvalue(B),k2_absvalue(C))) ) ) ) ) )).

fof(d9_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_fsm_2(C,A)
                & v5_fsm_2(C,A)
                & l2_fsm_2(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( E = k2_fsm_2(A,B,C,D)
                      <=> r3_fsm_2(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t27_fsm_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k7_domain_1(k1_numbers,np__0,np__1),A)
                    & m2_relset_1(D,k7_domain_1(k1_numbers,np__0,np__1),A) )
                 => k2_fsm_2(B,A,k1_fsm_2(B,A,np__0,np__1,D),C) = k1_funct_1(D,np__1) ) ) ) ) )).

fof(t28_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k4_square_1(B,C) ) ) ) ) )).

fof(t29_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r1_xreal_0(C,B)
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k3_square_1(B,C) ) ) ) ) )).

fof(t30_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = k3_real_1(B,C) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k3_real_1(B,C) ) ) ) ) )).

fof(t31_fsm_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
        & l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
     => ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
          & u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
          & u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ ( r1_xreal_0(B,np__0)
                        & r1_xreal_0(C,np__0) )
                   => k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__1 ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ( r1_xreal_0(B,np__0)
                      & r1_xreal_0(C,np__0) )
                   => ( ( B != np__0
                        & C != np__0 )
                      | k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__0 ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(np__0,B)
                      & ~ r1_xreal_0(np__0,C)
                      & k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) != k1_real_1(np__1) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k4_square_1(k2_absvalue(B),k2_absvalue(C)) ) ) ) ) )).

fof(dt_l1_fsm_2,axiom,(
    ! [A,B] :
      ( l1_fsm_2(B,A)
     => l1_fsm_1(B,A) ) )).

fof(existence_l1_fsm_2,axiom,(
    ! [A] :
    ? [B] : l1_fsm_2(B,A) )).

fof(dt_l2_fsm_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( l2_fsm_2(C,A,B)
         => ( l1_fsm_2(C,A)
            & l3_fsm_1(C,A,B) ) ) ) )).

fof(existence_l2_fsm_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] : l2_fsm_2(C,A,B) ) )).

fof(abstractness_v4_fsm_2,axiom,(
    ! [A,B] :
      ( l1_fsm_2(B,A)
     => ( v4_fsm_2(B,A)
       => B = g1_fsm_2(A,u1_struct_0(B),u1_fsm_1(A,B),u2_fsm_1(A,B),u1_fsm_2(A,B)) ) ) )).

fof(abstractness_v6_fsm_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & l2_fsm_2(C,A,B) )
     => ( v6_fsm_2(C,A,B)
       => C = g2_fsm_2(A,B,u1_struct_0(C),u1_fsm_1(B,C),u4_fsm_1(A,B,C),u2_fsm_1(B,C),u1_fsm_2(B,C)) ) ) )).

fof(dt_k1_fsm_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_tarski(C,D),B)
        & m1_relset_1(E,k2_tarski(C,D),B) )
     => ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
        & v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B)
        & l2_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) )).

fof(dt_k2_fsm_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v1_fsm_2(C,A)
        & v5_fsm_2(C,A)
        & l2_fsm_2(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k2_fsm_2(A,B,C,D),B) ) )).

fof(dt_u1_fsm_2,axiom,(
    ! [A,B] :
      ( l1_fsm_2(B,A)
     => m1_subset_1(u1_fsm_2(A,B),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_g1_fsm_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,A),B)
        & m1_relset_1(C,k2_zfmisc_1(B,A),B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k1_zfmisc_1(B)) )
     => ( v4_fsm_2(g1_fsm_2(A,B,C,D,E),A)
        & l1_fsm_2(g1_fsm_2(A,B,C,D,E),A) ) ) )).

fof(free_g1_fsm_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,A),B)
        & m1_relset_1(C,k2_zfmisc_1(B,A),B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k1_zfmisc_1(B)) )
     => ! [F,G,H,I,J] :
          ( g1_fsm_2(A,B,C,D,E) = g1_fsm_2(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(dt_g2_fsm_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,A),C)
        & m1_relset_1(D,k2_zfmisc_1(C,A),C)
        & v1_funct_1(E)
        & v1_funct_2(E,C,B)
        & m1_relset_1(E,C,B)
        & m1_subset_1(F,C)
        & m1_subset_1(G,k1_zfmisc_1(C)) )
     => ( v6_fsm_2(g2_fsm_2(A,B,C,D,E,F,G),A,B)
        & l2_fsm_2(g2_fsm_2(A,B,C,D,E,F,G),A,B) ) ) )).

fof(free_g2_fsm_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(C,A),C)
        & m1_relset_1(D,k2_zfmisc_1(C,A),C)
        & v1_funct_1(E)
        & v1_funct_2(E,C,B)
        & m1_relset_1(E,C,B)
        & m1_subset_1(F,C)
        & m1_subset_1(G,k1_zfmisc_1(C)) )
     => ! [H,I,J,K,L,M,N] :
          ( g2_fsm_2(A,B,C,D,E,F,G) = g2_fsm_2(H,I,J,K,L,M,N)
         => ( A = H
            & B = I
            & C = J
            & D = K
            & E = L
            & F = M
            & G = N ) ) ) )).
%------------------------------------------------------------------------------