SET007 Axioms: SET007+292.ax


%------------------------------------------------------------------------------
% File     : SET007+292 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Preliminaries to the Lambek Calculus
% 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    : prelamb [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   88 (   3 unit)
%            Number of atoms       :  810 ( 143 equality)
%            Maximal formula depth :   30 (  10 average)
%            Number of connectives :  849 ( 127 ~  ;   1  |; 399  &)
%                                         (  30 <=>; 292 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   1 propositional; 0-3 arity)
%            Number of functors    :   50 (  11 constant; 0-6 arity)
%            Number of variables   :  379 (   0 singleton; 322 !;  57 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_prelamb,axiom,(
    ? [A] :
      ( l1_prelamb(A)
      & v1_prelamb(A) ) )).

fof(rc2_prelamb,axiom,(
    ? [A] :
      ( l1_prelamb(A)
      & ~ v3_struct_0(A)
      & v1_prelamb(A) ) )).

fof(rc3_prelamb,axiom,(
    ? [A] :
      ( l2_prelamb(A)
      & v9_prelamb(A) ) )).

fof(rc4_prelamb,axiom,(
    ? [A] :
      ( l2_prelamb(A)
      & ~ v3_struct_0(A)
      & v9_prelamb(A) ) )).

fof(rc5_prelamb,axiom,(
    ? [A] :
      ( l2_prelamb(A)
      & ~ v3_struct_0(A)
      & v10_prelamb(A) ) )).

fof(d1_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_prelamb(A),B,C) ) ) ) )).

fof(d2_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_prelamb(A),B,C) ) ) ) )).

fof(d3_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u3_prelamb(A),B,C) ) ) ) )).

fof(d4_prelamb,axiom,(
    $true )).

fof(d5_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ( ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__0
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__0
                      & ? [D] :
                          ( m1_subset_1(D,u1_struct_0(A))
                          & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k12_finseq_1(u1_struct_0(A),D),D) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__1
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__1
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                  & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(D,k2_prelamb(A,E,F))
                                  & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),D,k12_finseq_1(u1_struct_0(A),F)),E) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__2
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__1
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                  & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(D,k1_prelamb(A,F,E))
                                  & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),F),D),E) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__3
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__2
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m2_finseq_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m2_finseq_1(F,u1_struct_0(A))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(A))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(A))
                                          & ? [I] :
                                              ( m1_subset_1(I,u1_struct_0(A))
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,G,H))),D),F),I)
                                              & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,H)
                                              & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),I) ) ) ) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__4
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__2
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m2_finseq_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m2_finseq_1(F,u1_struct_0(A))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(A))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(A))
                                          & ? [I] :
                                              ( m1_subset_1(I,u1_struct_0(A))
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,H,G))),F),I)
                                              & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,H)
                                              & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),I) ) ) ) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__5
                 => ( v2_prelamb(C,A,B)
                  <=> ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ( k10_trees_2(k1_relat_1(B),C) = np__1
                          & ? [E] :
                              ( m2_finseq_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(A))
                                      & ? [H] :
                                          ( m2_finseq_1(H,u1_struct_0(A))
                                          & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,F,G))),H),D)
                                          & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),F)),k12_finseq_1(u1_struct_0(A),G)),H),D) ) ) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__6
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__2
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m2_finseq_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(A))
                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),D,E),k3_prelamb(A,F,G))
                                      & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,F)
                                      & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(E,G) ) ) ) ) ) ) )
                & ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__7
                 => ( v2_prelamb(C,A,B)
                  <=> ( k10_trees_2(k1_relat_1(B),C) = np__2
                      & ? [D] :
                          ( m2_finseq_1(D,u1_struct_0(A))
                          & ? [E] :
                              ( m2_finseq_1(E,u1_struct_0(A))
                              & ? [F] :
                                  ( m2_finseq_1(F,u1_struct_0(A))
                                  & ? [G] :
                                      ( m1_subset_1(G,u1_struct_0(A))
                                      & ? [H] :
                                          ( m1_subset_1(H,u1_struct_0(A))
                                          & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),H)
                                          & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,G)
                                          & k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),H) ) ) ) ) ) ) ) )
                & ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__0
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__1
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__2
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__3
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__4
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__5
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__6
                    & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7
                    & ~ ( v2_prelamb(C,A,B)
                      <=> ~ $true ) ) ) ) ) ) )).

fof(d6_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_prelamb(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & B = k1_prelamb(A,C,D) ) ) ) ) ) )).

fof(d7_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v4_prelamb(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & B = k2_prelamb(A,C,D) ) ) ) ) ) )).

fof(d8_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_prelamb(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & B = k3_prelamb(A,C,D) ) ) ) ) ) )).

fof(d9_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v6_prelamb(B,A)
          <=> ( ~ v3_prelamb(B,A)
              & ~ v4_prelamb(B,A)
              & ~ v5_prelamb(B,A) ) ) ) ) )).

fof(d10_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_prelamb(A,B,C)
              <=> ( v1_finset_1(k1_relat_1(B))
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ( ( k10_trees_2(k1_relat_1(B),D) = np__0
                          | k10_trees_2(k1_relat_1(B),D) = np__2 )
                        & ( k10_trees_2(k1_relat_1(B),D) = np__0
                         => v6_prelamb(k4_prelamb(A,B,D),A) )
                        & ~ ( k10_trees_2(k1_relat_1(B),D) = np__2
                            & ! [E] :
                                ( m1_subset_1(E,u1_struct_0(A))
                               => ! [F] :
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ~ ( ~ ( k4_prelamb(A,B,D) != k2_prelamb(A,E,F)
                                            & k4_prelamb(A,B,D) != k1_prelamb(A,E,F)
                                            & k4_prelamb(A,B,D) != k3_prelamb(A,E,F) )
                                        & k1_funct_1(B,k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__0))) = E
                                        & k1_funct_1(B,k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__1))) = F ) ) ) ) ) ) ) ) ) ) ) )).

fof(d11_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ( v7_prelamb(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( ~ ( v3_prelamb(B,A)
                    & v4_prelamb(B,A) )
                & ~ ( v3_prelamb(B,A)
                    & v5_prelamb(B,A) )
                & ~ ( v4_prelamb(B,A)
                    & v5_prelamb(B,A) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( v1_funct_1(C)
                  & v1_finset_1(C)
                  & v3_trees_2(C)
                  & m3_trees_2(C,u1_struct_0(A))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_finset_1(D)
                        & v3_trees_2(D)
                        & m3_trees_2(D,u1_struct_0(A)) )
                     => ( r1_prelamb(A,D,B)
                      <=> C = D ) ) ) ) ) ) ) )).

fof(d12_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v7_prelamb(A)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_finset_1(C)
                  & v3_trees_2(C)
                  & m3_trees_2(C,u1_struct_0(A)) )
               => ( C = k5_prelamb(A,B)
                <=> ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_finset_1(D)
                        & v3_trees_2(D)
                        & m3_trees_2(D,u1_struct_0(A)) )
                     => ( r1_prelamb(A,D,B)
                      <=> C = D ) ) ) ) ) ) ) )).

fof(d13_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
         => ( m1_prelamb(B,A)
          <=> ( v1_finset_1(k1_relat_1(B))
              & ! [C] :
                  ( m1_trees_1(C,k1_relat_1(B))
                 => v2_prelamb(C,A,B) ) ) ) ) ) )).

fof(t1_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ( k10_trees_2(k1_relat_1(B),C) = np__1
               => r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)),k1_relat_1(B)) ) ) ) ) )).

fof(t2_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ( k10_trees_2(k1_relat_1(B),C) = np__2
               => ( r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)),k1_relat_1(B))
                  & r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)),k1_relat_1(B)) ) ) ) ) ) )).

fof(t3_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__0
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != k6_prelamb(A,k12_finseq_1(u1_struct_0(A),D),D) ) ) ) ) ) )).

fof(t4_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__1
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m2_finseq_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,E,k2_prelamb(A,F,G))
                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F) ) ) ) ) ) ) ) ) ) )).

fof(t5_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__2
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m2_finseq_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,E,k1_prelamb(A,G,F))
                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),G),E),F) ) ) ) ) ) ) ) ) ) )).

fof(t6_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__3
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m1_trees_1(E,k1_relat_1(B))
                         => ! [F] :
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m2_finseq_1(G,u1_struct_0(A))
                                 => ! [H] :
                                      ( m2_finseq_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ! [K] :
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                                      & E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,I,J))),F),H),K)
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,J)
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__4
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m1_trees_1(E,k1_relat_1(B))
                         => ! [F] :
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m2_finseq_1(G,u1_struct_0(A))
                                 => ! [H] :
                                      ( m2_finseq_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ! [K] :
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                                      & E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,F),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,J,I))),H),K)
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,J)
                                                      & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_prelamb(C,A)
             => ! [D] :
                  ( m1_trees_1(D,k1_relat_1(C))
                 => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,D)) = np__5
                      & ! [E] :
                          ( m1_trees_1(E,k1_relat_1(C))
                         => ! [F] :
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m2_finseq_1(I,u1_struct_0(A))
                                         => ~ ( E = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__0))
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,G,H))),I),B)
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),G)),k12_finseq_1(u1_struct_0(A),H)),I),B) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t9_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__6
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m1_trees_1(E,k1_relat_1(B))
                         => ! [F] :
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m2_finseq_1(G,u1_struct_0(A))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                              & E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),F,G),k3_prelamb(A,H,I))
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,H)
                                              & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,G,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t10_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__7
                  & ! [D] :
                      ( m1_trees_1(D,k1_relat_1(B))
                     => ! [E] :
                          ( m1_trees_1(E,k1_relat_1(B))
                         => ! [F] :
                              ( m2_finseq_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m2_finseq_1(G,u1_struct_0(A))
                                 => ! [H] :
                                      ( m2_finseq_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ! [J] :
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
                                                  & E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
                                                  & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,F),H),J)
                                                  & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,I)
                                                  & k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t11_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m1_trees_1(C,k1_relat_1(B))
             => ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__0
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__1
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__2
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__3
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__4
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__5
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__6
                  & k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7 ) ) ) ) )).

fof(d14_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
         => ( v8_prelamb(B,A)
          <=> ! [C] :
                ( m1_trees_1(C,k1_relat_1(B))
               => k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7 ) ) ) ) )).

fof(d15_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k5_numbers)
            & m2_relset_1(B,u1_struct_0(A),k5_numbers) )
         => ( B = k7_prelamb(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),k5_numbers,B,C) = k4_card_1(k1_relat_1(k5_prelamb(A,C))) ) ) ) ) )).

fof(d16_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( k2_mcart_1(k1_funct_1(B,k1_xboole_0)) = np__7
                 => ( C = k9_prelamb(A,B)
                  <=> ? [D] :
                        ( m2_finseq_1(D,u1_struct_0(A))
                        & ? [E] :
                            ( m2_finseq_1(E,u1_struct_0(A))
                            & ? [F] :
                                ( m2_finseq_1(F,u1_struct_0(A))
                                & ? [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                    & ? [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                        & k1_mcart_1(k1_funct_1(B,k1_xboole_0)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),H)
                                        & k1_mcart_1(k1_funct_1(B,k12_finseq_1(k5_numbers,np__0))) = k6_prelamb(A,D,G)
                                        & k1_mcart_1(k1_funct_1(B,k12_finseq_1(k5_numbers,np__1))) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),H)
                                        & C = k3_real_1(k1_nat_1(k8_funct_2(u1_struct_0(A),k5_numbers,k7_prelamb(A),G),k8_funct_2(u1_struct_0(A),k5_numbers,k7_prelamb(A),H)),k15_rvsum_1(k8_prelamb(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),k7_prelamb(A)))) ) ) ) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(B,k1_xboole_0)) != np__7
                 => ( C = k9_prelamb(A,B)
                  <=> C = np__0 ) ) ) ) ) ) )).

fof(d18_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,B,C)
              <=> r2_hidden(k6_prelamb(A,B,C),u4_prelamb(A)) ) ) ) ) )).

fof(d19_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_prelamb(A) )
     => ( v10_prelamb(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),B) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),D)),C)
                       => r2_prelamb(A,B,k2_prelamb(A,C,D)) ) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),D),B),C)
                       => r2_prelamb(A,B,k1_prelamb(A,D,C)) ) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m2_finseq_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_prelamb(A,B,F)
                                      & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),E)),D),G) )
                                   => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,E,F))),B),D),G) ) ) ) ) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m2_finseq_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_prelamb(A,B,F)
                                      & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),E)),D),G) )
                                   => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,B),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,F,E))),D),G) ) ) ) ) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),D)),k12_finseq_1(u1_struct_0(A),E)),C),F)
                               => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,D,E))),C),F) ) ) ) ) ) )
          & ! [B] :
              ( m2_finseq_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m2_finseq_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r2_prelamb(A,B,D)
                              & r2_prelamb(A,C,E) )
                           => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),B,C),k3_prelamb(A,D,E)) ) ) ) ) ) ) ) ) )).

fof(t12_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,C)),k12_finseq_1(u1_struct_0(A),C)),B)
                & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,C,B))),B) ) ) ) ) )).

fof(t13_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k2_prelamb(A,C,k1_prelamb(A,B,C)))
                & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k1_prelamb(A,k2_prelamb(A,C,B),C)) ) ) ) ) )).

fof(t14_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,C)),k2_prelamb(A,k2_prelamb(A,B,D),k2_prelamb(A,C,D))) ) ) ) ) )).

fof(t15_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,B,C)),k1_prelamb(A,k1_prelamb(A,D,B),k1_prelamb(A,D,C))) ) ) ) ) )).

fof(t16_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
                   => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,D)),k2_prelamb(A,C,D))
                      & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,D,B)),k1_prelamb(A,D,C)) ) ) ) ) ) ) )).

fof(t17_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
                   => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,D,C)),k2_prelamb(A,D,B))
                      & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,C,D)),k1_prelamb(A,B,D)) ) ) ) ) ) ) )).

fof(t18_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,k1_prelamb(A,k2_prelamb(A,B,C),B))),k2_prelamb(A,B,C)) ) ) ) )).

fof(t19_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
               => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,C,B))
                  & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,B,C)) ) ) ) ) ) )).

fof(t20_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,B,B))
            & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,B,B)) ) ) ) )).

fof(t21_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,k2_prelamb(A,B,k1_prelamb(A,C,B)),C))
                & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,C,k1_prelamb(A,k2_prelamb(A,B,C),B))) ) ) ) ) )).

fof(t22_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,k2_prelamb(A,k2_prelamb(A,B,C),k2_prelamb(A,D,C)),k2_prelamb(A,B,D)))
                    & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,k1_prelamb(A,D,B),k1_prelamb(A,k1_prelamb(A,C,D),k1_prelamb(A,C,B)))) ) ) ) ) ) )).

fof(t23_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),B)
               => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,C,k2_prelamb(A,C,B)))
                  & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,k1_prelamb(A,B,C),C)) ) ) ) ) ) )).

fof(t24_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,k2_prelamb(A,C,C))),B) ) ) ) )).

fof(d20_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_prelamb(A,B,C)
              <=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
                  & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),C),B) ) ) ) ) ) )).

fof(t25_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_prelamb(A,B,B) ) ) )).

fof(t26_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r3_prelamb(A,k2_prelamb(A,B,C),k2_prelamb(A,B,k1_prelamb(A,k2_prelamb(A,B,C),B))) ) ) ) )).

fof(t27_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r3_prelamb(A,k2_prelamb(A,B,k3_prelamb(A,C,D)),k2_prelamb(A,k2_prelamb(A,B,D),C)) ) ) ) ) )).

fof(t28_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,B,k2_prelamb(A,C,D))),k2_prelamb(A,k3_prelamb(A,B,C),D)) ) ) ) ) )).

fof(t29_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k2_prelamb(A,k3_prelamb(A,B,C),C))
                & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k1_prelamb(A,C,k3_prelamb(A,C,B))) ) ) ) ) )).

fof(t30_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_prelamb(A)
        & l2_prelamb(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r3_prelamb(A,k3_prelamb(A,k3_prelamb(A,B,C),D),k3_prelamb(A,B,k3_prelamb(A,C,D))) ) ) ) ) )).

fof(dt_m1_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( m1_prelamb(B,A)
         => ( v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) ) ) ) )).

fof(existence_m1_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ? [B] : m1_prelamb(B,A) ) )).

fof(dt_m2_prelamb,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & ~ v1_xboole_0(B) )
     => ! [C] :
          ( m2_prelamb(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)))
            & m2_relset_1(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B))) ) ) ) )).

fof(existence_m2_prelamb,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : m2_prelamb(C,A,B) ) )).

fof(dt_l1_prelamb,axiom,(
    ! [A] :
      ( l1_prelamb(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_prelamb,axiom,(
    ? [A] : l1_prelamb(A) )).

fof(dt_l2_prelamb,axiom,(
    ! [A] :
      ( l2_prelamb(A)
     => l1_prelamb(A) ) )).

fof(existence_l2_prelamb,axiom,(
    ? [A] : l2_prelamb(A) )).

fof(abstractness_v1_prelamb,axiom,(
    ! [A] :
      ( l1_prelamb(A)
     => ( v1_prelamb(A)
       => A = g1_prelamb(u1_struct_0(A),u1_prelamb(A),u2_prelamb(A),u3_prelamb(A)) ) ) )).

fof(abstractness_v9_prelamb,axiom,(
    ! [A] :
      ( l2_prelamb(A)
     => ( v9_prelamb(A)
       => A = g2_prelamb(u1_struct_0(A),u1_prelamb(A),u2_prelamb(A),u3_prelamb(A),u4_prelamb(A)) ) ) )).

fof(dt_k1_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_prelamb(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_prelamb(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_prelamb(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k4_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & v1_funct_1(B)
        & v1_finset_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,u1_struct_0(A))
        & m1_subset_1(C,k1_relat_1(B)) )
     => m1_subset_1(k4_prelamb(A,B,C),u1_struct_0(A)) ) )).

fof(redefinition_k4_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & v1_funct_1(B)
        & v1_finset_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,u1_struct_0(A))
        & m1_subset_1(C,k1_relat_1(B)) )
     => k4_prelamb(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k5_prelamb,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k5_prelamb(A,B))
        & v1_finset_1(k5_prelamb(A,B))
        & v3_trees_2(k5_prelamb(A,B))
        & m3_trees_2(k5_prelamb(A,B),u1_struct_0(A)) ) ) )).

fof(dt_k6_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_prelamb(A,B,C),k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A))) ) )).

fof(redefinition_k6_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k6_prelamb(A,B,C) = k4_tarski(B,C) ) )).

fof(dt_k7_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ( v1_funct_1(k7_prelamb(A))
        & v1_funct_2(k7_prelamb(A),u1_struct_0(A),k5_numbers)
        & m2_relset_1(k7_prelamb(A),u1_struct_0(A),k5_numbers) ) ) )).

fof(dt_k8_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k5_numbers)
        & m1_relset_1(C,A,k5_numbers) )
     => m2_finseq_1(k8_prelamb(A,B,C),k1_numbers) ) )).

fof(redefinition_k8_prelamb,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k5_numbers)
        & m1_relset_1(C,A,k5_numbers) )
     => k8_prelamb(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k9_prelamb,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A)
        & m1_prelamb(B,A) )
     => m2_subset_1(k9_prelamb(A,B),k1_numbers,k5_numbers) ) )).

fof(dt_u1_prelamb,axiom,(
    ! [A] :
      ( l1_prelamb(A)
     => ( v1_funct_1(u1_prelamb(A))
        & v1_funct_2(u1_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_u2_prelamb,axiom,(
    ! [A] :
      ( l1_prelamb(A)
     => ( v1_funct_1(u2_prelamb(A))
        & v1_funct_2(u2_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_u3_prelamb,axiom,(
    ! [A] :
      ( l1_prelamb(A)
     => ( v1_funct_1(u3_prelamb(A))
        & v1_funct_2(u3_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u3_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_u4_prelamb,axiom,(
    ! [A] :
      ( l2_prelamb(A)
     => m2_relset_1(u4_prelamb(A),k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) ) )).

fof(dt_g1_prelamb,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A) )
     => ( v1_prelamb(g1_prelamb(A,B,C,D))
        & l1_prelamb(g1_prelamb(A,B,C,D)) ) ) )).

fof(free_g1_prelamb,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A) )
     => ! [E,F,G,H] :
          ( g1_prelamb(A,B,C,D) = g1_prelamb(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).

fof(dt_g2_prelamb,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(E,k3_finseq_2(A),A) )
     => ( v9_prelamb(g2_prelamb(A,B,C,D,E))
        & l2_prelamb(g2_prelamb(A,B,C,D,E)) ) ) )).

fof(free_g2_prelamb,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A)
        & m1_relset_1(E,k3_finseq_2(A),A) )
     => ! [F,G,H,I,J] :
          ( g2_prelamb(A,B,C,D,E) = g2_prelamb(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(d17_prelamb,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_prelamb(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)))
                & m2_relset_1(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B))) )
             => ( m2_prelamb(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k3_prelamb(A,D,E)) = a_5_0_prelamb(A,B,C,D,E)
                          & k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k2_prelamb(A,D,E)) = a_5_1_prelamb(A,B,C,D,E)
                          & k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k1_prelamb(A,E,D)) = a_5_2_prelamb(A,B,C,D,E) ) ) ) ) ) ) ) )).

fof(fraenkel_a_5_0_prelamb,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(B)
        & l1_prelamb(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B)) )
     => ( r2_hidden(A,a_5_0_prelamb(B,C,D,E,F))
      <=> ? [G,H] :
            ( m2_finseq_2(G,C,k3_finseq_2(C))
            & m2_finseq_2(H,C,k3_finseq_2(C))
            & A = k8_finseq_1(C,G,H)
            & r2_hidden(G,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E))
            & r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F)) ) ) ) )).

fof(fraenkel_a_5_1_prelamb,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(B)
        & l1_prelamb(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B)) )
     => ( r2_hidden(A,a_5_1_prelamb(B,C,D,E,F))
      <=> ? [G] :
            ( m2_finseq_2(G,C,k3_finseq_2(C))
            & A = G
            & ! [H] :
                ( m2_finseq_2(H,C,k3_finseq_2(C))
               => ( r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F))
                 => r2_hidden(k8_finseq_1(C,G,H),k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E)) ) ) ) ) ) )).

fof(fraenkel_a_5_2_prelamb,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(B)
        & l1_prelamb(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(B)) )
     => ( r2_hidden(A,a_5_2_prelamb(B,C,D,E,F))
      <=> ? [G] :
            ( m2_finseq_2(G,C,k3_finseq_2(C))
            & A = G
            & ! [H] :
                ( m2_finseq_2(H,C,k3_finseq_2(C))
               => ( r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F))
                 => r2_hidden(k8_finseq_1(C,H,G),k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E)) ) ) ) ) ) )).
%------------------------------------------------------------------------------