SET007 Axioms: SET007+413.ax


%------------------------------------------------------------------------------
% File     : SET007+413 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Minimization of Finite State Machines
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  167 (   9 unit)
%            Number of atoms       : 1452 ( 147 equality)
%            Maximal formula depth :   29 (  12 average)
%            Number of connectives : 1741 ( 456 ~  ;   1  |; 604  &)
%                                         (  32 <=>; 648 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-6 arity)
%            Number of functors    :   50 (   4 constant; 0-6 arity)
%            Number of variables   :  773 (   0 singleton; 742 !;  31 ?)
%            Maximal term depth    :    6 (   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(cc1_fsm_1,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ( v1_finset_1(B)
            & v1_setfam_1(B) ) ) ) )).

fof(rc1_fsm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ? [B] :
          ( m1_eqrel_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_setfam_1(B) ) ) )).

fof(rc2_fsm_1,axiom,(
    ! [A] :
    ? [B] :
      ( l1_fsm_1(B,A)
      & v1_fsm_1(B,A) ) )).

fof(rc3_fsm_1,axiom,(
    ! [A] :
    ? [B] :
      ( l1_fsm_1(B,A)
      & ~ v3_struct_0(B)
      & v6_group_1(B) ) )).

fof(rc4_fsm_1,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A) ) )).

fof(fc1_fsm_1,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => v1_finset_1(u1_struct_0(A)) ) )).

fof(rc5_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l2_fsm_1(C,A,B)
          & v2_fsm_1(C,A,B) ) ) )).

fof(rc6_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l3_fsm_1(C,A,B)
          & v3_fsm_1(C,A,B) ) ) )).

fof(fc2_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & 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) )
     => ( ~ v3_struct_0(g1_fsm_1(A,B,C,D))
        & v6_group_1(g1_fsm_1(A,B,C,D))
        & v1_fsm_1(g1_fsm_1(A,B,C,D),A) ) ) )).

fof(fc3_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_finset_1(C)
        & 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,k2_zfmisc_1(C,A),B)
        & m1_relset_1(E,k2_zfmisc_1(C,A),B)
        & m1_subset_1(F,C) )
     => ( ~ v3_struct_0(g2_fsm_1(A,B,C,D,E,F))
        & v6_group_1(g2_fsm_1(A,B,C,D,E,F))
        & v2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B) ) ) )).

fof(fc4_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_finset_1(C)
        & 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) )
     => ( ~ v3_struct_0(g3_fsm_1(A,B,C,D,E,F))
        & v6_group_1(g3_fsm_1(A,B,C,D,E,F))
        & v3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B) ) ) )).

fof(rc7_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l2_fsm_1(C,A,B)
          & ~ v3_struct_0(C)
          & v6_group_1(C) ) ) )).

fof(rc8_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( l3_fsm_1(C,A,B)
          & ~ v3_struct_0(C)
          & v6_group_1(C) ) ) )).

fof(fc5_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B) )
     => ( ~ v3_struct_0(k11_fsm_1(A,B,C))
        & v6_group_1(k11_fsm_1(A,B,C))
        & v2_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) )).

fof(rc9_fsm_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] :
          ( l2_fsm_1(C,A,B)
          & ~ v3_struct_0(C)
          & v6_group_1(C)
          & v5_fsm_1(C,A,B) ) ) )).

fof(rc10_fsm_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] :
          ( l2_fsm_1(C,A,B)
          & ~ v3_struct_0(C)
          & v6_group_1(C)
          & v7_fsm_1(C,A,B) ) ) )).

fof(rc11_fsm_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] :
          ( l2_fsm_1(C,A,B)
          & ~ v3_struct_0(C)
          & v6_group_1(C)
          & v5_fsm_1(C,A,B)
          & v7_fsm_1(C,A,B) ) ) )).

fof(fc6_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B) )
     => ( ~ v1_xboole_0(k12_fsm_1(A,B,C))
        & v1_finset_1(k12_fsm_1(A,B,C)) ) ) )).

fof(fc7_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & v6_group_1(D)
        & l2_fsm_1(D,A,B) )
     => ( ~ v3_struct_0(k13_fsm_1(A,B,C,D))
        & v6_group_1(k13_fsm_1(A,B,C,D))
        & v2_fsm_1(k13_fsm_1(A,B,C,D),A,B) ) ) )).

fof(t1_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(B,A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( B = k1_nat_1(A,C)
                      & r1_xreal_0(np__1,C) ) ) ) ) ) )).

fof(t2_fsm_1,axiom,(
    $true )).

fof(t3_fsm_1,axiom,(
    $true )).

fof(t4_fsm_1,axiom,(
    $true )).

fof(t5_fsm_1,axiom,(
    $true )).

fof(t6_fsm_1,axiom,(
    $true )).

fof(t7_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( ( v3_funct_2(D,A,B)
                      & v3_funct_2(E,B,C) )
                   => v3_funct_2(k7_funct_2(A,B,C,D,E),A,C) ) ) ) ) ) )).

fof(t8_fsm_1,axiom,(
    ! [A,B] :
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( k8_eqrel_1(A,B) = k8_eqrel_1(A,C)
           => B = C ) ) ) )).

fof(t9_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(t10_fsm_1,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => v1_finset_1(B) ) ) )).

fof(t11_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ~ ( r2_hidden(C,B)
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ~ r2_hidden(D,C) ) ) ) ) )).

fof(t12_fsm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => r1_xreal_0(k4_card_1(B),k4_card_1(A)) ) ) )).

fof(t13_fsm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r1_setfam_1(B,C)
               => r1_xreal_0(k4_card_1(C),k4_card_1(B)) ) ) ) ) )).

fof(t14_fsm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( r1_setfam_1(B,C)
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(A),C)
                   => ? [E] :
                        ( m2_subset_1(E,k1_zfmisc_1(A),B)
                        & r1_tarski(E,D) ) ) ) ) ) ) )).

fof(t15_fsm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ( ( r1_setfam_1(B,C)
                  & k4_card_1(B) = k4_card_1(C) )
               => B = C ) ) ) ) )).

fof(d1_fsm_1,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,u1_struct_0(B))
                 => k1_fsm_1(A,B,C,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,D,C)) ) ) ) ) )).

fof(d2_fsm_1,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] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( m2_finseq_1(E,u1_struct_0(B))
                     => ( E = k2_fsm_1(A,B,C,D)
                      <=> ( k1_funct_1(E,np__1) = C
                          & k3_finseq_1(E) = k1_nat_1(k3_finseq_1(D),np__1)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(np__1,F)
                                  & r1_xreal_0(F,k3_finseq_1(D))
                                  & ! [G] :
                                      ( m1_subset_1(G,A)
                                     => ! [H] :
                                          ( m1_subset_1(H,u1_struct_0(B))
                                         => ! [I] :
                                              ( m1_subset_1(I,u1_struct_0(B))
                                             => ~ ( G = k1_funct_1(D,F)
                                                  & H = k1_funct_1(E,F)
                                                  & I = k1_funct_1(E,k1_nat_1(F,np__1))
                                                  & k1_fsm_1(A,B,G,H) = I ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_fsm_1,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))
             => k2_fsm_1(A,B,C,k6_finseq_1(A)) = k4_matrix_2(u1_struct_0(B),C) ) ) ) )).

fof(d3_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r1_fsm_1(A,B,C,D,E)
                      <=> k1_funct_1(k2_fsm_1(A,B,D,C),k1_nat_1(k3_finseq_1(C),np__1)) = E ) ) ) ) ) ) )).

fof(t17_fsm_1,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))
             => r1_fsm_1(A,B,k6_finseq_1(A),C,C) ) ) ) )).

fof(d4_fsm_1,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,u1_struct_0(B))
                 => ( r2_fsm_1(A,B,C,D)
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                        & E = k1_funct_1(D,np__1)
                        & k2_fsm_1(A,B,E,C) = D ) ) ) ) ) ) )).

fof(t18_fsm_1,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))
             => r2_fsm_1(A,B,k6_finseq_1(A),k4_matrix_2(u1_struct_0(B),C)) ) ) ) )).

fof(d5_fsm_1,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] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( E = k3_fsm_1(A,B,C,D)
                      <=> r1_fsm_1(A,B,D,C,E) ) ) ) ) ) ) )).

fof(t19_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_fsm_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( k1_funct_1(k2_fsm_1(A,B,D,C),k3_finseq_1(k2_fsm_1(A,B,D,C))) = E
                      <=> r1_fsm_1(A,B,C,D,E) ) ) ) ) ) ) )).

fof(t20_fsm_1,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)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(np__1,F)
                              & r1_xreal_0(F,k3_finseq_1(C)) )
                           => k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),F) = k1_funct_1(k2_fsm_1(A,B,E,C),F) ) ) ) ) ) ) ) )).

fof(t21_fsm_1,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)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r1_fsm_1(A,B,C,E,F)
                           => k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),np__1)) = F ) ) ) ) ) ) ) )).

fof(t22_fsm_1,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)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r1_fsm_1(A,B,C,E,F)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( ( r1_xreal_0(np__1,G)
                                    & r1_xreal_0(G,k1_nat_1(k3_finseq_1(D),np__1)) )
                                 => k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),G)) = k1_funct_1(k2_fsm_1(A,B,F,D),G) ) ) ) ) ) ) ) ) ) )).

fof(t23_fsm_1,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)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r1_fsm_1(A,B,C,E,F)
                           => k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)) = k7_finseq_1(k2_finseq_3(k1_nat_1(k3_finseq_1(C),np__1),k2_fsm_1(A,B,E,C)),k2_fsm_1(A,B,F,D)) ) ) ) ) ) ) ) )).

fof(d6_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_1(E,A)
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => ( F = k4_fsm_1(A,B,C,D,E)
                          <=> ( k3_finseq_1(F) = k3_finseq_1(E)
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( r2_hidden(G,k4_finseq_1(E))
                                   => k1_funct_1(F,G) = k1_funct_1(u3_fsm_1(A,B,C),k4_tarski(k1_funct_1(k2_fsm_1(A,C,D,E),G),k1_funct_1(E,G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k4_fsm_1(A,B,C,D,k6_finseq_1(A)) = k6_finseq_1(B) ) ) ) ) )).

fof(d7_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l3_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_1(E,A)
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => ( F = k5_fsm_1(A,B,C,D,E)
                          <=> ( k3_finseq_1(F) = k1_nat_1(k3_finseq_1(E),np__1)
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( r2_hidden(G,k2_finseq_1(k1_nat_1(k3_finseq_1(E),np__1)))
                                   => k1_funct_1(F,G) = k1_funct_1(u4_fsm_1(A,B,C),k1_funct_1(k2_fsm_1(A,C,D,E),G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l3_fsm_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => k1_funct_1(k5_fsm_1(A,B,D,E,C),np__1) = k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),E) ) ) ) ) ) )).

fof(t26_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(E))
                             => ( r1_fsm_1(A,E,C,F,G)
                               => k4_fsm_1(A,B,E,F,k8_finseq_1(A,C,D)) = k8_finseq_1(B,k4_fsm_1(A,B,E,F,C),k4_fsm_1(A,B,E,G,D)) ) ) ) ) ) ) ) ) )).

fof(t27_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & l2_fsm_1(F,A,B) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(E))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(E))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(F))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(F))
                                         => ~ ( r1_fsm_1(A,E,C,G,H)
                                              & r1_fsm_1(A,F,C,I,J)
                                              & k4_fsm_1(A,B,E,H,D) != k4_fsm_1(A,B,F,J,D)
                                              & k4_fsm_1(A,B,E,G,k8_finseq_1(A,C,D)) = k4_fsm_1(A,B,F,I,k8_finseq_1(A,C,D)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l3_fsm_1(D,A,B) )
                 => ( r3_fsm_1(A,B,C,D)
                  <=> ! [E] :
                        ( m2_finseq_1(E,A)
                       => k8_finseq_1(B,k4_matrix_2(B,k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),u2_fsm_1(A,D))),k4_fsm_1(A,B,C,u2_fsm_1(A,C),E)) = k5_fsm_1(A,B,D,u2_fsm_1(A,D),E) ) ) ) ) ) ) )).

fof(t28_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l3_fsm_1(C,A,B) )
             => ? [D] :
                  ( ~ v3_struct_0(D)
                  & v6_group_1(D)
                  & l2_fsm_1(D,A,B)
                  & r3_fsm_1(A,B,D,C) ) ) ) ) )).

fof(t29_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ? [D] :
                  ( ~ v3_struct_0(D)
                  & v6_group_1(D)
                  & l3_fsm_1(D,A,B)
                  & r3_fsm_1(A,B,C,D) ) ) ) ) )).

fof(d9_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ( r4_fsm_1(A,B,C,D)
                  <=> ! [E] :
                        ( m2_finseq_1(E,A)
                       => k4_fsm_1(A,B,C,u2_fsm_1(A,C),E) = k4_fsm_1(A,B,D,u2_fsm_1(A,D),E) ) ) ) ) ) ) )).

fof(t30_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ( ( r4_fsm_1(A,B,C,D)
                          & r4_fsm_1(A,B,D,E) )
                       => r4_fsm_1(A,B,C,E) ) ) ) ) ) ) )).

fof(d10_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r5_fsm_1(A,B,C,D,E)
                      <=> ! [F] :
                            ( m2_finseq_1(F,A)
                           => k4_fsm_1(A,B,C,D,F) = k4_fsm_1(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(t31_fsm_1,axiom,(
    $true )).

fof(t32_fsm_1,axiom,(
    $true )).

fof(t33_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ( ( r5_fsm_1(A,B,C,D,E)
                              & r5_fsm_1(A,B,C,E,F) )
                           => r5_fsm_1(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t34_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,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,G,C))
                               => ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(D),np__1)))
                                     => k1_funct_1(k2_fsm_1(A,E,G,k8_finseq_1(A,k4_matrix_2(A,C),D)),k1_nat_1(H,np__1)) = k1_funct_1(k2_fsm_1(A,E,F,D),H) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,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,G,C))
                               => k4_fsm_1(A,B,E,G,k8_finseq_1(A,k4_matrix_2(A,C),D)) = k8_finseq_1(B,k4_matrix_2(B,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),B,u3_fsm_1(A,B,E),k1_domain_1(u1_struct_0(E),A,G,C))),k4_fsm_1(A,B,E,F,D)) ) ) ) ) ) ) ) ) )).

fof(t36_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,B,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r5_fsm_1(B,A,C,D,E)
                      <=> ! [F] :
                            ( m1_subset_1(F,B)
                           => ( k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,D,F)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,E,F))
                              & r5_fsm_1(B,A,C,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,E,F))) ) ) ) ) ) ) ) ) )).

fof(t37_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,B,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r5_fsm_1(B,A,C,D,E)
                       => ! [F] :
                            ( m2_finseq_1(F,B)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(G,k4_finseq_1(F))
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(C))
                                       => ! [I] :
                                            ( m1_subset_1(I,u1_struct_0(C))
                                           => ~ ( H = k1_funct_1(k2_fsm_1(B,C,D,F),G)
                                                & I = k1_funct_1(k2_fsm_1(B,C,E,F),G)
                                                & r5_fsm_1(B,A,C,H,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d11_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r6_fsm_1(A,B,C,D,E,F)
                          <=> ! [G] :
                                ( m2_finseq_1(G,A)
                               => ( r1_xreal_0(k3_finseq_1(G),F)
                                 => k4_fsm_1(A,B,C,D,G) = k4_fsm_1(A,B,C,E,G) ) ) ) ) ) ) ) ) ) )).

fof(t38_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => r6_fsm_1(B,C,D,E,E,A) ) ) ) ) ) )).

fof(t39_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( r6_fsm_1(B,C,D,E,F,A)
                           => r6_fsm_1(B,C,D,F,E,A) ) ) ) ) ) ) ) )).

fof(t40_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(D))
                             => ( ( r6_fsm_1(B,C,D,E,F,A)
                                  & r6_fsm_1(B,C,D,F,G,A) )
                               => r6_fsm_1(B,C,D,E,G,A) ) ) ) ) ) ) ) ) )).

fof(t41_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( r5_fsm_1(B,C,D,E,F)
                           => r6_fsm_1(B,C,D,E,F,A) ) ) ) ) ) ) ) )).

fof(t42_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => r6_fsm_1(A,B,C,D,E,np__0) ) ) ) ) ) )).

fof(t43_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,C,D) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(E))
                             => ( r6_fsm_1(C,D,E,F,G,k1_nat_1(A,B))
                               => r6_fsm_1(C,D,E,F,G,A) ) ) ) ) ) ) ) ) )).

fof(t44_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,C,B) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( r1_xreal_0(np__1,A)
                           => ( r6_fsm_1(C,B,D,E,F,A)
                            <=> ( r6_fsm_1(C,B,D,E,F,np__1)
                                & ! [G] :
                                    ( m1_subset_1(G,C)
                                   => ! [H] :
                                        ( m2_subset_1(H,k1_numbers,k5_numbers)
                                       => ( H = k6_xcmplx_0(A,np__1)
                                         => r6_fsm_1(C,B,D,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),C),u1_struct_0(D),u1_fsm_1(C,D),k1_domain_1(u1_struct_0(D),C,E,G)),k8_funct_2(k2_zfmisc_1(u1_struct_0(D),C),u1_struct_0(D),u1_fsm_1(C,D),k1_domain_1(u1_struct_0(D),C,F,G)),H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v3_relat_2(E)
                        & v8_relat_2(E)
                        & v1_partfun1(E,u1_struct_0(C),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(C)) )
                     => ( E = k6_fsm_1(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(C))
                               => ( r2_hidden(k1_domain_1(u1_struct_0(C),u1_struct_0(C),F,G),E)
                                <=> r6_fsm_1(A,B,C,F,G,D) ) ) ) ) ) ) ) ) ) )).

fof(d13_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k7_fsm_1(A,B,C,D) = k8_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,D)) ) ) ) ) )).

fof(t45_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => r1_setfam_1(k7_fsm_1(B,C,D,k1_nat_1(A,np__1)),k7_fsm_1(B,C,D,A)) ) ) ) ) )).

fof(t46_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,A)) = k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,k1_nat_1(A,np__1)))
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,k1_nat_1(A,E))) = k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,A)) ) ) ) ) ) ) )).

fof(t47_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_fsm_1(B,C,D,k1_nat_1(A,E)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) ) )).

fof(t48_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k7_fsm_1(B,C,D,k1_nat_1(A,np__1)) != k7_fsm_1(B,C,D,A)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(E,A)
                            & k7_fsm_1(B,C,D,k1_nat_1(E,np__1)) = k7_fsm_1(B,C,D,E) ) ) ) ) ) ) ) )).

fof(t49_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,B,C) )
                 => ~ ( k7_fsm_1(B,C,D,A) != k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
                      & r1_xreal_0(k4_card_1(k7_fsm_1(B,C,D,k1_nat_1(A,np__1))),k4_card_1(k7_fsm_1(B,C,D,A))) ) ) ) ) ) )).

fof(t50_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k6_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,np__0),D) = u1_struct_0(C) ) ) ) ) )).

fof(t51_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => k7_fsm_1(A,B,C,np__0) = k1_tarski(u1_struct_0(C)) ) ) ) )).

fof(t52_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
                   => k7_fsm_1(B,C,D,k1_nat_1(A,np__1)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) )).

fof(d14_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_eqrel_1(D,u1_struct_0(C))
                 => ( v4_fsm_1(D,A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(C))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ( r5_fsm_1(A,B,C,E,F)
                            <=> ? [G] :
                                  ( m2_subset_1(G,k1_zfmisc_1(u1_struct_0(C)),D)
                                  & r2_hidden(E,G)
                                  & r2_hidden(F,G) ) ) ) ) ) ) ) ) ) )).

fof(t53_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ( v4_fsm_1(k7_fsm_1(B,C,D,A),B,C,D)
                   => k6_fsm_1(B,C,D,k1_nat_1(A,np__1)) = k6_fsm_1(B,C,D,A) ) ) ) ) ) )).

fof(t54_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
                  <=> v4_fsm_1(k7_fsm_1(B,C,D,A),B,C,D) ) ) ) ) ) )).

fof(t55_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,B,C) )
                 => ~ ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(E,A)
                              & v4_fsm_1(k7_fsm_1(B,C,D,E),B,C,D) ) ) ) ) ) ) ) )).

fof(d15_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_eqrel_1(D,u1_struct_0(C))
                 => ( D = k8_fsm_1(A,B,C)
                  <=> v4_fsm_1(D,A,B,C) ) ) ) ) ) )).

fof(t56_fsm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,B,C) )
                 => ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
                   => k8_fsm_1(B,C,D) = k7_fsm_1(B,C,D,A) ) ) ) ) ) )).

fof(d16_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
                         => ( F = k9_fsm_1(A,B,C,D,E)
                          <=> ? [G] :
                                ( m1_subset_1(G,u1_struct_0(C))
                                & ? [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                    & r2_hidden(G,D)
                                    & k1_nat_1(H,np__1) = k4_card_1(u1_struct_0(C))
                                    & F = k6_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,H),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,G,E))) ) ) ) ) ) ) ) ) ) )).

fof(d17_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( F = k10_fsm_1(A,B,C,D,E)
                          <=> ? [G] :
                                ( m1_subset_1(G,u1_struct_0(C))
                                & r2_hidden(G,D)
                                & F = k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,G,E)) ) ) ) ) ) ) ) ) )).

fof(d18_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( v2_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ( D = k11_fsm_1(A,B,C)
                  <=> ( u1_struct_0(D) = k8_fsm_1(A,B,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(D))
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(C))
                                 => ( r2_hidden(G,E)
                                   => ( r2_hidden(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,G,F)),k1_funct_1(u1_fsm_1(A,D),k4_tarski(E,F)))
                                      & k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,G,F)) = k1_funct_1(u3_fsm_1(A,B,D),k4_tarski(E,F)) ) ) ) ) )
                      & r2_hidden(u2_fsm_1(A,C),u2_fsm_1(A,D)) ) ) ) ) ) ) )).

fof(t57_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v6_group_1(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(D))
                             => ( ( D = k11_fsm_1(A,B,E)
                                  & r2_hidden(F,G) )
                               => ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(C),np__1)))
                                     => r2_hidden(k1_funct_1(k2_fsm_1(A,E,F,C),H),k1_funct_1(k2_fsm_1(A,D,G,C),H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t58_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => r4_fsm_1(A,B,C,k11_fsm_1(A,B,C)) ) ) ) )).

fof(d19_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ( r7_fsm_1(A,B,C,D)
                  <=> ? [E] :
                        ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
                        & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D))
                        & v3_funct_2(E,u1_struct_0(C),u1_struct_0(D))
                        & k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,u2_fsm_1(A,C)) = u2_fsm_1(A,D)
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,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,F,G))) = 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(u1_struct_0(C),u1_struct_0(D),E,F),G))
                                  & k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,F,G)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),B,u3_fsm_1(A,B,D),k1_domain_1(u1_struct_0(D),A,k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,F),G)) ) ) ) ) ) ) ) ) ) )).

fof(t59_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ( ( r7_fsm_1(A,B,C,D)
                          & r7_fsm_1(A,B,D,E) )
                       => r7_fsm_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t60_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,A) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,B,A) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
                                & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
                             => ( ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(D))
                                   => ! [I] :
                                        ( m1_subset_1(I,B)
                                       => k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),u1_struct_0(D),u1_fsm_1(B,D),k1_domain_1(u1_struct_0(D),B,H,I))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(E),B),u1_struct_0(E),u1_fsm_1(B,E),k1_domain_1(u1_struct_0(E),B,k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,H),I)) ) )
                               => ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( ( r1_xreal_0(np__1,H)
                                        & r1_xreal_0(H,k1_nat_1(k3_finseq_1(C),np__1)) )
                                     => k1_funct_1(G,k1_funct_1(k2_fsm_1(B,D,F,C),H)) = k1_funct_1(k2_fsm_1(B,E,k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,F),C),H) ) ) ) ) ) ) ) ) ) ) )).

fof(t61_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,B,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,B,A) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(C),u1_struct_0(D))
                                & m2_relset_1(G,u1_struct_0(C),u1_struct_0(D)) )
                             => ( ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,u2_fsm_1(B,C)) = u2_fsm_1(B,D)
                                  & ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(C))
                                     => ! [I] :
                                          ( m1_subset_1(I,B)
                                         => ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,H,I))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),u1_struct_0(D),u1_fsm_1(B,D),k1_domain_1(u1_struct_0(D),B,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,H),I))
                                            & k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,H,I)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),A,u3_fsm_1(B,A,D),k1_domain_1(u1_struct_0(D),B,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,H),I)) ) ) ) )
                               => ( r5_fsm_1(B,A,C,E,F)
                                <=> r5_fsm_1(B,A,D,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,E),k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,F)) ) ) ) ) ) ) ) ) ) )).

fof(t62_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ~ ( C = k11_fsm_1(A,B,D)
                              & E != F
                              & r5_fsm_1(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(d20_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ( v5_fsm_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(C))
                       => ~ ( D != E
                            & r5_fsm_1(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(t63_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => v5_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ) )).

fof(t64_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & v5_fsm_1(C,A,B)
                & l2_fsm_1(C,A,B) )
             => r7_fsm_1(A,B,C,k11_fsm_1(A,B,C)) ) ) ) )).

fof(t65_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ( v5_fsm_1(C,A,B)
              <=> ? [D] :
                    ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,A,B)
                    & r7_fsm_1(A,B,C,k11_fsm_1(A,B,D)) ) ) ) ) ) )).

fof(d21_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( v6_fsm_1(D,A,B,C)
                  <=> ? [E] :
                        ( m2_finseq_1(E,A)
                        & r1_fsm_1(A,C,E,u2_fsm_1(A,C),D) ) ) ) ) ) ) )).

fof(d22_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ( v7_fsm_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => v6_fsm_1(D,A,B,C) ) ) ) ) ) )).

fof(t66_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & v7_fsm_1(C,A,B)
                & l2_fsm_1(C,A,B) )
             => v7_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ) )).

fof(t67_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,B,A) )
             => ( r1_tarski(k12_fsm_1(B,A,C),u1_struct_0(C))
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ( r2_hidden(D,k12_fsm_1(B,A,C))
                    <=> v6_fsm_1(D,B,A,C) ) ) ) ) ) ) )).

fof(t68_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,B,A) )
             => ( v1_funct_1(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)))
                & v1_funct_2(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)),k2_zfmisc_1(k12_fsm_1(B,A,C),B),k12_fsm_1(B,A,C))
                & m2_relset_1(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)),k2_zfmisc_1(k12_fsm_1(B,A,C),B),k12_fsm_1(B,A,C)) ) ) ) ) )).

fof(t69_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(k12_fsm_1(A,B,C),A),k12_fsm_1(A,B,C))
                    & m2_relset_1(D,k2_zfmisc_1(k12_fsm_1(A,B,C),A),k12_fsm_1(A,B,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(k12_fsm_1(A,B,C),A),B)
                        & m2_relset_1(E,k2_zfmisc_1(k12_fsm_1(A,B,C),A),B) )
                     => ! [F] :
                          ( m1_subset_1(F,k12_fsm_1(A,B,C))
                         => ( ( D = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k2_zfmisc_1(k12_fsm_1(A,B,C),A))
                              & E = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k2_zfmisc_1(k12_fsm_1(A,B,C),A))
                              & F = u2_fsm_1(A,C) )
                           => r4_fsm_1(A,B,C,g2_fsm_1(A,B,k12_fsm_1(A,B,C),D,E,F)) ) ) ) ) ) ) ) )).

fof(t70_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,B,A) )
             => ? [D] :
                  ( ~ v3_struct_0(D)
                  & v6_group_1(D)
                  & v7_fsm_1(D,B,A)
                  & l2_fsm_1(D,B,A)
                  & u1_fsm_1(B,D) = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B))
                  & u3_fsm_1(B,A,D) = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B))
                  & u2_fsm_1(B,D) = u2_fsm_1(B,C)
                  & r4_fsm_1(B,A,C,D) ) ) ) ) )).

fof(d24_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & l2_fsm_1(C,A,B) )
         => ! [D] :
              ( ( ~ v3_struct_0(D)
                & l2_fsm_1(D,A,B) )
             => ! [E] :
                  ( ( v2_fsm_1(E,A,B)
                    & l2_fsm_1(E,A,B) )
                 => ( E = k13_fsm_1(A,B,C,D)
                  <=> ( u1_struct_0(E) = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
                      & u1_fsm_1(A,E) = k1_funct_4(u1_fsm_1(A,C),u1_fsm_1(A,D))
                      & u3_fsm_1(A,B,E) = k1_funct_4(u3_fsm_1(A,B,C),u3_fsm_1(A,B,D))
                      & u2_fsm_1(A,E) = u2_fsm_1(A,C) ) ) ) ) ) ) )).

fof(t71_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v6_group_1(G)
                                & l2_fsm_1(G,A,B) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(G))
                                 => ( ( G = k13_fsm_1(A,B,D,E)
                                      & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                                      & F = H )
                                   => k2_fsm_1(A,D,F,C) = k2_fsm_1(A,G,H,C) ) ) ) ) ) ) ) ) ) )).

fof(t72_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v6_group_1(G)
                                & l2_fsm_1(G,A,B) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(G))
                                 => ( ( G = k13_fsm_1(A,B,D,E)
                                      & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                                      & F = H )
                                   => k4_fsm_1(A,B,D,F,C) = k4_fsm_1(A,B,G,H,C) ) ) ) ) ) ) ) ) ) )).

fof(t73_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v6_group_1(G)
                                & l2_fsm_1(G,A,B) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(G))
                                 => ( ( G = k13_fsm_1(A,B,D,E)
                                      & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                                      & F = H )
                                   => k2_fsm_1(A,E,F,C) = k2_fsm_1(A,G,H,C) ) ) ) ) ) ) ) ) ) )).

fof(t74_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(E))
                         => ! [G] :
                              ( ( ~ v3_struct_0(G)
                                & v6_group_1(G)
                                & l2_fsm_1(G,A,B) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(G))
                                 => ( ( G = k13_fsm_1(A,B,D,E)
                                      & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                                      & F = H )
                                   => k4_fsm_1(A,B,E,F,C) = k4_fsm_1(A,B,G,H,C) ) ) ) ) ) ) ) ) ) )).

fof(t75_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v5_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v5_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ~ ( C = k13_fsm_1(A,B,D,E)
                          & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                          & r4_fsm_1(A,B,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
                             => ~ ( r2_hidden(u2_fsm_1(A,D),F)
                                  & r2_hidden(u2_fsm_1(A,E),F)
                                  & F = u2_fsm_1(A,k11_fsm_1(A,B,C)) ) ) ) ) ) ) ) ) )).

fof(t76_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v5_fsm_1(E,A,B)
                        & v7_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(C))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(D))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(D))
                                     => ~ ( H = F
                                          & I = G
                                          & r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                                          & r4_fsm_1(A,B,D,E)
                                          & C = k13_fsm_1(A,B,D,E)
                                          & ~ r5_fsm_1(A,B,D,H,I)
                                          & r5_fsm_1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t77_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v5_fsm_1(E,A,B)
                        & v7_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(C))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(D))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(D))
                                     => ~ ( H = F
                                          & I = G
                                          & r1_subset_1(u1_struct_0(E),u1_struct_0(D))
                                          & r4_fsm_1(A,B,E,D)
                                          & C = k13_fsm_1(A,B,E,D)
                                          & ~ r5_fsm_1(A,B,D,H,I)
                                          & r5_fsm_1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t78_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v6_group_1(E)
                        & v5_fsm_1(E,A,B)
                        & v7_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                          & r4_fsm_1(A,B,D,E)
                          & C = k13_fsm_1(A,B,D,E) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
                           => ! [G] :
                                ( m1_subset_1(G,F)
                               => ! [H] :
                                    ( m1_subset_1(H,F)
                                   => ~ ( r2_hidden(G,u1_struct_0(D))
                                        & r2_hidden(H,u1_struct_0(D))
                                        & G != H ) ) ) ) ) ) ) ) ) ) )).

fof(t79_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v6_group_1(E)
                        & v5_fsm_1(E,A,B)
                        & v7_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                          & r4_fsm_1(A,B,D,E)
                          & C = k13_fsm_1(A,B,D,E) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
                           => ! [G] :
                                ( m1_subset_1(G,F)
                               => ! [H] :
                                    ( m1_subset_1(H,F)
                                   => ~ ( r2_hidden(G,u1_struct_0(E))
                                        & r2_hidden(H,u1_struct_0(E))
                                        & G != H ) ) ) ) ) ) ) ) ) ) )).

fof(t80_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v6_group_1(E)
                        & v5_fsm_1(E,A,B)
                        & v7_fsm_1(E,A,B)
                        & l2_fsm_1(E,A,B) )
                     => ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
                          & r4_fsm_1(A,B,D,E)
                          & C = k13_fsm_1(A,B,D,E) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
                           => ? [G] :
                                ( m1_subset_1(G,F)
                                & ? [H] :
                                    ( m1_subset_1(H,F)
                                    & r2_hidden(G,u1_struct_0(D))
                                    & r2_hidden(H,u1_struct_0(E))
                                    & ! [I] :
                                        ( m1_subset_1(I,F)
                                       => ( I = G
                                          | I = H ) ) ) ) ) ) ) ) ) ) ) )).

fof(t81_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & l2_fsm_1(D,A,B) )
                 => ? [E] :
                      ( ~ v3_struct_0(E)
                      & v6_group_1(E)
                      & l2_fsm_1(E,A,B)
                      & ? [F] :
                          ( ~ v3_struct_0(F)
                          & v6_group_1(F)
                          & l2_fsm_1(F,A,B)
                          & r1_subset_1(u1_struct_0(E),u1_struct_0(F))
                          & r7_fsm_1(A,B,E,C)
                          & r7_fsm_1(A,B,F,D) ) ) ) ) ) ) )).

fof(t82_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l2_fsm_1(D,A,B) )
                 => ( r7_fsm_1(A,B,C,D)
                   => r4_fsm_1(A,B,C,D) ) ) ) ) ) )).

fof(t83_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & v5_fsm_1(C,A,B)
                & v7_fsm_1(C,A,B)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ( ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
                      & r4_fsm_1(A,B,C,D) )
                   => r7_fsm_1(A,B,C,D) ) ) ) ) ) )).

fof(t84_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & v7_fsm_1(C,A,B)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ( r4_fsm_1(A,B,C,D)
                   => r7_fsm_1(A,B,k11_fsm_1(A,B,C),k11_fsm_1(A,B,D)) ) ) ) ) ) )).

fof(t85_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_group_1(C)
                & v5_fsm_1(C,A,B)
                & v7_fsm_1(C,A,B)
                & l2_fsm_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_group_1(D)
                    & v5_fsm_1(D,A,B)
                    & v7_fsm_1(D,A,B)
                    & l2_fsm_1(D,A,B) )
                 => ( r7_fsm_1(A,B,C,D)
                  <=> r4_fsm_1(A,B,C,D) ) ) ) ) ) )).

fof(dt_l1_fsm_1,axiom,(
    ! [A,B] :
      ( l1_fsm_1(B,A)
     => l1_struct_0(B) ) )).

fof(existence_l1_fsm_1,axiom,(
    ! [A] :
    ? [B] : l1_fsm_1(B,A) )).

fof(dt_l2_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( l2_fsm_1(C,A,B)
         => l1_fsm_1(C,A) ) ) )).

fof(existence_l2_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] : l2_fsm_1(C,A,B) ) )).

fof(dt_l3_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( l3_fsm_1(C,A,B)
         => l1_fsm_1(C,A) ) ) )).

fof(existence_l3_fsm_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] : l3_fsm_1(C,A,B) ) )).

fof(abstractness_v1_fsm_1,axiom,(
    ! [A,B] :
      ( l1_fsm_1(B,A)
     => ( v1_fsm_1(B,A)
       => B = g1_fsm_1(A,u1_struct_0(B),u1_fsm_1(A,B),u2_fsm_1(A,B)) ) ) )).

fof(abstractness_v2_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & l2_fsm_1(C,A,B) )
     => ( v2_fsm_1(C,A,B)
       => C = g2_fsm_1(A,B,u1_struct_0(C),u1_fsm_1(B,C),u3_fsm_1(A,B,C),u2_fsm_1(B,C)) ) ) )).

fof(abstractness_v3_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & l3_fsm_1(C,A,B) )
     => ( v3_fsm_1(C,A,B)
       => C = g3_fsm_1(A,B,u1_struct_0(C),u1_fsm_1(B,C),u4_fsm_1(A,B,C),u2_fsm_1(B,C)) ) ) )).

fof(symmetry_r4_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,A,B) )
     => ( r4_fsm_1(A,B,C,D)
       => r4_fsm_1(A,B,D,C) ) ) )).

fof(reflexivity_r4_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,A,B) )
     => r4_fsm_1(A,B,C,C) ) )).

fof(symmetry_r5_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,u1_struct_0(C)) )
     => ( r5_fsm_1(A,B,C,D,E)
       => r5_fsm_1(A,B,C,E,D) ) ) )).

fof(reflexivity_r5_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,u1_struct_0(C)) )
     => r5_fsm_1(A,B,C,D,D) ) )).

fof(symmetry_r7_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,A,B) )
     => ( r7_fsm_1(A,B,C,D)
       => r7_fsm_1(A,B,D,C) ) ) )).

fof(reflexivity_r7_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,A,B) )
     => r7_fsm_1(A,B,C,C) ) )).

fof(dt_k1_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_fsm_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k1_fsm_1(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k2_fsm_1,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) )
     => m2_finseq_1(k2_fsm_1(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k3_fsm_1,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) )
     => m1_subset_1(k3_fsm_1(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k4_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_finseq_1(E,A) )
     => m2_finseq_1(k4_fsm_1(A,B,C,D,E),B) ) )).

fof(dt_k5_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l3_fsm_1(C,A,B)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_finseq_1(E,A) )
     => m2_finseq_1(k5_fsm_1(A,B,C,D,E),B) ) )).

fof(dt_k6_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => ( v3_relat_2(k6_fsm_1(A,B,C,D))
        & v8_relat_2(k6_fsm_1(A,B,C,D))
        & v1_partfun1(k6_fsm_1(A,B,C,D),u1_struct_0(C),u1_struct_0(C))
        & m2_relset_1(k6_fsm_1(A,B,C,D),u1_struct_0(C),u1_struct_0(C)) ) ) )).

fof(dt_k7_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,k5_numbers) )
     => ( ~ v1_xboole_0(k7_fsm_1(A,B,C,D))
        & m1_eqrel_1(k7_fsm_1(A,B,C,D),u1_struct_0(C)) ) ) )).

fof(dt_k8_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B) )
     => m1_eqrel_1(k8_fsm_1(A,B,C),u1_struct_0(C)) ) )).

fof(dt_k9_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,k8_fsm_1(A,B,C))
        & m1_subset_1(E,A) )
     => m2_subset_1(k9_fsm_1(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C)) ) )).

fof(dt_k10_fsm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B)
        & m1_subset_1(D,k8_fsm_1(A,B,C))
        & m1_subset_1(E,A) )
     => m1_subset_1(k10_fsm_1(A,B,C,D,E),B) ) )).

fof(dt_k11_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v6_group_1(C)
        & l2_fsm_1(C,A,B) )
     => ( v2_fsm_1(k11_fsm_1(A,B,C),A,B)
        & l2_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) )).

fof(dt_k12_fsm_1,axiom,(
    $true )).

fof(dt_k13_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & l2_fsm_1(C,A,B)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,A,B) )
     => ( v2_fsm_1(k13_fsm_1(A,B,C,D),A,B)
        & l2_fsm_1(k13_fsm_1(A,B,C,D),A,B) ) ) )).

fof(dt_u1_fsm_1,axiom,(
    ! [A,B] :
      ( l1_fsm_1(B,A)
     => ( v1_funct_1(u1_fsm_1(A,B))
        & v1_funct_2(u1_fsm_1(A,B),k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B))
        & m2_relset_1(u1_fsm_1(A,B),k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B)) ) ) )).

fof(dt_u2_fsm_1,axiom,(
    ! [A,B] :
      ( l1_fsm_1(B,A)
     => m1_subset_1(u2_fsm_1(A,B),u1_struct_0(B)) ) )).

fof(dt_u3_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & l2_fsm_1(C,A,B) )
     => ( v1_funct_1(u3_fsm_1(A,B,C))
        & v1_funct_2(u3_fsm_1(A,B,C),k2_zfmisc_1(u1_struct_0(C),A),B)
        & m2_relset_1(u3_fsm_1(A,B,C),k2_zfmisc_1(u1_struct_0(C),A),B) ) ) )).

fof(dt_u4_fsm_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & l3_fsm_1(C,A,B) )
     => ( v1_funct_1(u4_fsm_1(A,B,C))
        & v1_funct_2(u4_fsm_1(A,B,C),u1_struct_0(C),B)
        & m2_relset_1(u4_fsm_1(A,B,C),u1_struct_0(C),B) ) ) )).

fof(dt_g1_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( 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) )
     => ( v1_fsm_1(g1_fsm_1(A,B,C,D),A)
        & l1_fsm_1(g1_fsm_1(A,B,C,D),A) ) ) )).

fof(free_g1_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( 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) )
     => ! [E,F,G,H] :
          ( g1_fsm_1(A,B,C,D) = g1_fsm_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).

fof(dt_g2_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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,k2_zfmisc_1(C,A),B)
        & m1_relset_1(E,k2_zfmisc_1(C,A),B)
        & m1_subset_1(F,C) )
     => ( v2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B)
        & l2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B) ) ) )).

fof(free_g2_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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,k2_zfmisc_1(C,A),B)
        & m1_relset_1(E,k2_zfmisc_1(C,A),B)
        & m1_subset_1(F,C) )
     => ! [G,H,I,J,K,L] :
          ( g2_fsm_1(A,B,C,D,E,F) = g2_fsm_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) )).

fof(dt_g3_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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) )
     => ( v3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B)
        & l3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B) ) ) )).

fof(free_g3_fsm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ 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) )
     => ! [G,H,I,J,K,L] :
          ( g3_fsm_1(A,B,C,D,E,F) = g3_fsm_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) )).

fof(d23_fsm_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l2_fsm_1(C,A,B) )
             => k12_fsm_1(A,B,C) = a_3_0_fsm_1(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_fsm_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v3_struct_0(D)
        & l2_fsm_1(D,B,C) )
     => ( r2_hidden(A,a_3_0_fsm_1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(D))
            & A = E
            & v6_fsm_1(E,B,C,D) ) ) ) )).
%------------------------------------------------------------------------------