SET007 Axioms: SET007+419.ax


%------------------------------------------------------------------------------
% File     : SET007+419 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Terms Over Many Sorted Universal Algebra
% 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    : msaterm [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   80 (   0 unit)
%            Number of atoms       :  853 (  79 equality)
%            Maximal formula depth :   34 (  13 average)
%            Number of connectives :  957 ( 184 ~  ;   4  |; 382  &)
%                                         (   9 <=>; 378 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   0 propositional; 1-6 arity)
%            Number of functors    :   56 (  11 constant; 0-5 arity)
%            Number of variables   :  401 (   0 singleton; 393 !;   8 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) )).

fof(fc2_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_msaterm(A,B))
        & v3_trees_3(k1_msaterm(A,B)) ) ) )).

fof(cc1_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_msaterm(A,B))
         => v1_finset_1(C) ) ) )).

fof(d1_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => k1_msaterm(A,B) = k4_dtconstr(k5_msafree(A,B)) ) ) )).

fof(d2_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_struct_0(C,k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B)))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                 => ( m1_msaterm(D,A,B,C)
                  <=> m2_dtconstr(D,k5_msafree(A,B),C) ) ) ) ) ) )).

fof(t1_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ( ( r2_hidden(k4_trees_4(k4_tarski(C,u1_struct_0(A)),D),k1_msaterm(A,B))
                      & v6_trees_3(D) )
                  <=> m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) )).

fof(t2_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ~ ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,k1_funct_1(B,D))
                         => k1_funct_1(C,k1_xboole_0) != k4_tarski(E,D) ) )
                  & ~ r2_hidden(k1_funct_1(C,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) )).

fof(t3_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
                 => ~ ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ~ ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
                                & k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) ) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,k1_funct_1(B,E))
                             => k1_funct_1(D,k1_xboole_0) != k4_tarski(F,E) ) )
                      & ~ r2_hidden(k1_funct_1(D,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) ) )).

fof(t4_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_funct_1(B,C))
                 => m1_dtconstr(k1_trees_4(k4_tarski(D,C)),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) )).

fof(t5_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(B,D))
                     => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(E,D)
                       => C = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) ) )).

fof(t6_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( r2_hidden(E,k1_funct_1(u4_msualg_1(A,C),D))
                     => m1_dtconstr(k1_trees_4(k4_tarski(E,D)),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))) ) ) ) ) ) )).

fof(t7_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
                            & k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) )
                         => D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) )).

fof(t8_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(B,D))
                     => m1_dtconstr(k1_trees_4(k4_tarski(E,D)),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))) ) ) ) ) ) )).

fof(t9_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(B,E))
                         => ( k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E)
                           => D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ) )).

fof(t10_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ~ ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A))
                      & ! [E] :
                          ( m1_msaterm(E,A,B,k2_msaterm(A,B,D))
                         => C != k4_trees_4(k4_tarski(D,u1_struct_0(A)),E) ) ) ) ) ) ) )).

fof(d3_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => k4_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) )).

fof(d4_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(C,D))
                     => k5_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) )).

fof(t11_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) )).

fof(t12_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_tarski(k7_msafree(A,B,C),k1_msaterm(A,B)) ) ) ) )).

fof(t13_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k1_msaterm(A,B) = k3_card_3(k8_msafree(A,B)) ) ) )).

fof(d5_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k7_msaterm(A,B,C)
                  <=> r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) ) )).

fof(t14_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(B,D))
                     => ( C = k1_trees_4(k4_tarski(E,D))
                       => k7_msaterm(A,B,C) = D ) ) ) ) ) ) )).

fof(t15_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
                            & D = k1_trees_4(k4_tarski(F,E)) )
                         => k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),D) = E ) ) ) ) ) ) )).

fof(t16_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(B,E))
                         => ( D = k1_trees_4(k4_tarski(F,E))
                           => k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),D) = E ) ) ) ) ) ) ) )).

fof(t17_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A))
                   => k7_msaterm(A,B,C) = k2_msualg_1(A,D) ) ) ) ) ) )).

fof(t18_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,C),D))
                     => k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),k4_msaterm(A,C,B,D,E)) = D ) ) ) ) ) )).

fof(t19_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( l3_msualg_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(B,D))
                     => k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),k5_msaterm(A,C,B,D,E)) = D ) ) ) ) ) )).

fof(t20_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                 => k7_msaterm(A,B,k6_msaterm(A,B,k2_msaterm(A,B,C),D)) = k2_msualg_1(A,C) ) ) ) ) )).

fof(t21_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                 => ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                  <=> r1_lang1(k5_msafree(A,B),k2_msaterm(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),D)) ) ) ) ) ) )).

fof(t22_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                 => ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                    & k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C))
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k4_finseq_1(D))
                         => m1_dtconstr(k1_funct_1(D,E),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ) ) )).

fof(t23_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r2_hidden(E,k4_finseq_1(D))
                       => ! [F] :
                            ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                           => ( F = k1_funct_1(D,E)
                             => ( F = k4_finseq_4(k5_numbers,k1_msaterm(A,B),D,E)
                                & k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E)
                                & k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) ) ) ) ) ) )).

fof(t24_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ~ ( ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                        | k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) )
                      & ( ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ~ ( r2_hidden(E,k4_finseq_1(D))
                                & ! [F] :
                                    ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                                   => ~ ( F = k1_funct_1(D,E)
                                        & k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) )
                        | ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ~ ( r2_hidden(E,k4_finseq_1(D))
                                & ! [F] :
                                    ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                                   => ~ ( F = k1_funct_1(D,E)
                                        & k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) )
                      & ~ m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) )).

fof(t25_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                 => ~ ( ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                        | k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) )
                      & ( ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k4_finseq_1(D))
                             => ! [F] :
                                  ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                                 => ( F = k1_funct_1(D,E)
                                   => k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) )
                        | ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k4_finseq_1(D))
                             => ! [F] :
                                  ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                                 => ( F = k1_funct_1(D,E)
                                   => k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) )
                      & ~ m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) )).

fof(t26_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( r2_pboole(u1_struct_0(A),B,C)
               => ! [D] :
                    ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
                   => m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) ) ) ) ) ) )).

fof(t27_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C))
                 => m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ) ) ) )).

fof(d6_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ( m2_msaterm(C,A,B)
              <=> r2_hidden(k1_funct_1(C,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) )).

fof(d7_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) )
             => ( m3_msaterm(C,A,B)
              <=> ? [D] :
                    ( m2_msaterm(D,A,B)
                    & r2_hidden(D,C) ) ) ) ) ) )).

fof(t28_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ( ~ v1_trees_9(C)
               => m2_msaterm(C,A,B) ) ) ) ) )).

fof(t29_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
             => ! [D] :
                  ( m1_trees_1(D,k1_relat_1(C))
                 => m1_dtconstr(k7_trees_2(u1_struct_0(k5_msafree(A,B)),C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) )).

fof(d8_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( m4_msaterm(C,A,B)
              <=> r5_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) ) ) ) ) )).

fof(t30_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( r2_hidden(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(C,D))
                         => E != F ) ) ) ) ) ) )).

fof(d9_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ( r1_msaterm(A,B,C,D,E,F)
                          <=> ( k1_relat_1(F) = k1_relat_1(D)
                              & ! [G] :
                                  ( m1_trees_1(G,k1_relat_1(F))
                                 => ( ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                       => ! [I] :
                                            ( m1_subset_1(I,k1_funct_1(C,H))
                                           => ( k1_funct_1(D,G) = k4_tarski(I,H)
                                             => k1_funct_1(F,G) = k8_funct_2(k1_funct_1(C,H),k1_funct_1(u4_msualg_1(A,B),H),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),E,H),I) ) ) )
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                       => ! [I] :
                                            ( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),H))
                                           => ( k1_funct_1(D,G) = k4_tarski(I,H)
                                             => k1_funct_1(F,G) = I ) ) )
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_msualg_1(A))
                                       => ( k1_funct_1(D,G) = k4_tarski(H,u1_struct_0(A))
                                         => k1_funct_1(F,G) = k1_funct_1(k5_msualg_1(A,H,B),k2_trees_9(F,G)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),F))
                             => ( D = k1_trees_4(k4_tarski(G,F))
                               => r1_msaterm(A,B,C,D,E,k2_trees_4(k1_funct_1(u4_msualg_1(A,B),F),G)) ) ) ) ) ) ) ) ) )).

fof(t32_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,k1_funct_1(C,F))
                             => ( D = k1_trees_4(k4_tarski(G,F))
                               => r1_msaterm(A,B,C,D,E,k2_trees_4(k1_funct_1(u4_msualg_1(A,B),F),k8_funct_2(k1_funct_1(C,F),k1_funct_1(u4_msualg_1(A,B),F),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),E,F),G))) ) ) ) ) ) ) ) ) )).

fof(t33_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(A))
                     => ! [F] :
                          ( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G)
                                & v6_trees_3(G) )
                             => ~ ( k3_finseq_1(G) = k3_finseq_1(F)
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ! [I] :
                                          ( m1_dtconstr(I,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                                         => ~ ( r2_hidden(H,k4_finseq_1(F))
                                              & I = k1_funct_1(F,H)
                                              & ! [J] :
                                                  ( ( v1_relat_1(J)
                                                    & v1_funct_1(J)
                                                    & v1_finset_1(J)
                                                    & v3_trees_2(J) )
                                                 => ~ ( J = k1_funct_1(G,H)
                                                      & r1_msaterm(A,B,C,I,D,J) ) ) ) ) )
                                  & ! [H] :
                                      ( ( v1_relat_1(H)
                                        & v1_funct_1(H)
                                        & v1_finset_1(H)
                                        & v3_trees_2(H) )
                                     => ~ ( H = k4_trees_4(k1_funct_1(k5_msualg_1(A,E,B),k16_trees_3(G)),G)
                                          & r1_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t34_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ( r1_msaterm(A,B,C,E,D,F)
                           => ! [G] :
                                ( m1_trees_1(G,k1_relat_1(E))
                               => ! [H] :
                                    ( m1_trees_1(H,k1_relat_1(F))
                                   => ( H = G
                                     => r1_msaterm(A,B,C,k8_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E,G),D,k5_trees_2(F,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(A))
                     => ! [F] :
                          ( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finset_1(G)
                                & v3_trees_2(G) )
                             => ~ ( r1_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D,G)
                                  & ! [H] :
                                      ( ( v1_relat_1(H)
                                        & v1_funct_1(H)
                                        & v1_finseq_1(H)
                                        & v6_trees_3(H) )
                                     => ~ ( k3_finseq_1(H) = k3_finseq_1(F)
                                          & G = k4_trees_4(k1_funct_1(k5_msualg_1(A,E,B),k16_trees_3(H)),H)
                                          & ! [I] :
                                              ( m2_subset_1(I,k1_numbers,k5_numbers)
                                             => ! [J] :
                                                  ( m1_dtconstr(J,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                                                 => ~ ( r2_hidden(I,k4_finseq_1(F))
                                                      & J = k1_funct_1(F,I)
                                                      & ! [K] :
                                                          ( ( v1_relat_1(K)
                                                            & v1_funct_1(K)
                                                            & v1_finset_1(K)
                                                            & v3_trees_2(K) )
                                                         => ~ ( K = k1_funct_1(H,I)
                                                              & r1_msaterm(A,B,C,J,D,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ? [F] :
                          ( v1_relat_1(F)
                          & v1_funct_1(F)
                          & v1_finset_1(F)
                          & v3_trees_2(F)
                          & r1_msaterm(A,B,C,D,E,F) ) ) ) ) ) ) )).

fof(t37_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finset_1(G)
                                & v3_trees_2(G) )
                             => ( ( r1_msaterm(A,B,C,D,E,F)
                                  & r1_msaterm(A,B,C,D,E,G) )
                               => F = G ) ) ) ) ) ) ) ) )).

fof(t38_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ( r1_msaterm(A,B,C,D,E,F)
                           => r2_hidden(k1_funct_1(F,k1_xboole_0),k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D))) ) ) ) ) ) ) ) )).

fof(d10_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D)))
                         => ( F = k9_msaterm(A,B,C,D,E)
                          <=> ? [G] :
                                ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finset_1(G)
                                & v3_trees_2(G)
                                & r1_msaterm(A,B,C,D,E,G)
                                & F = k1_funct_1(G,k1_xboole_0) ) ) ) ) ) ) ) ) )).

fof(t39_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ( r1_msaterm(A,B,C,E,D,F)
                           => k9_msaterm(A,B,C,E,D) = k1_funct_1(F,k1_xboole_0) ) ) ) ) ) ) ) )).

fof(t40_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finset_1(F)
                            & v3_trees_2(F) )
                         => ( r1_msaterm(A,B,C,E,D,F)
                           => ! [G] :
                                ( m1_trees_1(G,k1_relat_1(E))
                               => k1_funct_1(F,G) = k9_msaterm(A,B,C,k8_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E,G),D) ) ) ) ) ) ) ) ) )).

fof(t41_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),E))
                         => k9_msaterm(A,B,C,k4_msaterm(A,B,C,E,F),D) = F ) ) ) ) ) ) )).

fof(t42_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(C,E))
                         => k9_msaterm(A,B,C,k5_msaterm(A,B,C,E,F),D) = k8_funct_2(k1_funct_1(C,E),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),D,E),F) ) ) ) ) ) ) )).

fof(t43_msaterm,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_msaterm(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_msualg_1(A))
                     => ! [F] :
                          ( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ( ( k3_finseq_1(G) = k3_finseq_1(F)
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( r2_hidden(H,k4_finseq_1(F))
                                       => ! [I] :
                                            ( m1_dtconstr(I,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
                                           => ( I = k1_funct_1(F,H)
                                             => k1_funct_1(G,H) = k9_msaterm(A,B,C,I,D) ) ) ) ) )
                               => k9_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D) = k1_funct_1(k5_msualg_1(A,E,B),G) ) ) ) ) ) ) ) ) )).

fof(s1_msaterm,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s1_msaterm))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(f2_s1_msaterm,A))
             => p1_s1_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_msualg_1(f1_s1_msaterm))
         => ! [B] :
              ( m1_msaterm(B,f1_s1_msaterm,f2_s1_msaterm,k2_msaterm(f1_s1_msaterm,f2_s1_msaterm,A))
             => ( ! [C] :
                    ( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm)),k5_trees_3(u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm))),k1_msaterm(f1_s1_msaterm,f2_s1_msaterm))
                   => ( r2_hidden(C,k2_relat_1(B))
                     => p1_s1_msaterm(C) ) )
               => p1_s1_msaterm(k4_trees_4(k4_tarski(A,u1_struct_0(f1_s1_msaterm)),B)) ) ) ) )
   => ! [A] :
        ( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm)),k5_trees_3(u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm))),k1_msaterm(f1_s1_msaterm,f2_s1_msaterm))
       => p1_s1_msaterm(A) ) )).

fof(s2_msaterm,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_msaterm))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),A))
             => p1_s2_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_msaterm))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(f3_s2_msaterm,A))
             => p1_s2_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_msualg_1(f1_s2_msaterm))
         => ! [B] :
              ( m1_msaterm(B,f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),k2_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),A))
             => ( ! [C] :
                    ( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))),k1_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))
                   => ( r2_hidden(C,k2_relat_1(B))
                     => p1_s2_msaterm(C) ) )
               => p1_s2_msaterm(k12_trees_4(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k2_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),A),B)) ) ) ) )
   => ! [A] :
        ( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))),k1_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))
       => p1_s2_msaterm(A) ) )).

fof(s3_msaterm,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_msaterm))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),A))
             => p1_s3_msaterm(k4_msaterm(f1_s3_msaterm,f2_s3_msaterm,f3_s3_msaterm,A,B)) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s3_msaterm))
         => ! [B] :
              ( m1_subset_1(B,k1_funct_1(f3_s3_msaterm,A))
             => p1_s3_msaterm(k5_msaterm(f1_s3_msaterm,f2_s3_msaterm,f3_s3_msaterm,A,B)) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_msualg_1(f1_s3_msaterm))
         => ! [B] :
              ( m1_msaterm(B,f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),k2_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),A))
             => ( ! [C] :
                    ( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))),k1_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))
                   => ( r2_hidden(C,k2_relat_1(B))
                     => p1_s3_msaterm(C) ) )
               => p1_s3_msaterm(k6_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),k2_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),A),B)) ) ) ) )
   => ! [A] :
        ( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))),k1_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))
       => p1_s3_msaterm(A) ) )).

fof(dt_m1_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
     => ! [D] :
          ( m1_msaterm(D,A,B,C)
         => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) )).

fof(existence_m1_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
     => ? [D] : m1_msaterm(D,A,B,C) ) )).

fof(dt_m2_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] :
          ( m2_msaterm(C,A,B)
         => m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) )).

fof(existence_m2_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ? [C] : m2_msaterm(C,A,B) ) )).

fof(dt_m3_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] :
          ( m3_msaterm(C,A,B)
         => ( ~ v1_xboole_0(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) ) ) )).

fof(existence_m3_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ? [C] : m3_msaterm(C,A,B) ) )).

fof(dt_m4_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m4_msaterm(C,A,B)
         => ( v2_relat_1(C)
            & m1_pboole(C,u1_struct_0(A)) ) ) ) )).

fof(existence_m4_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] : m4_msaterm(C,A,B) ) )).

fof(dt_k1_msaterm,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) )).

fof(dt_k2_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_struct_0(k2_msaterm(A,B,C),k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B))) ) )).

fof(redefinition_k2_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => k2_msaterm(A,B,C) = k6_msafree(A,B,C) ) )).

fof(dt_k3_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_msaterm(A,B))
        & m1_subset_1(D,k1_relat_1(C)) )
     => m1_subset_1(k3_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B))) ) )).

fof(redefinition_k3_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_msaterm(A,B))
        & m1_subset_1(D,k1_relat_1(C)) )
     => k3_msaterm(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k4_msaterm,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) )
     => m1_dtconstr(k4_msaterm(A,B,C,D,E),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) )).

fof(dt_k5_msaterm,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_funct_1(C,D)) )
     => m1_dtconstr(k5_msaterm(A,B,C,D,E),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) )).

fof(dt_k6_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B)))
        & m1_msaterm(D,A,B,C) )
     => m1_dtconstr(k6_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) )).

fof(redefinition_k6_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B)))
        & m1_msaterm(D,A,B,C) )
     => k6_msaterm(A,B,C,D) = k4_trees_4(C,D) ) )).

fof(dt_k7_msaterm,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_msaterm(A,B)) )
     => m1_subset_1(k7_msaterm(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k8_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_msaterm(A,B))
        & m1_subset_1(D,k1_relat_1(C)) )
     => m1_dtconstr(k8_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) )).

fof(redefinition_k8_msaterm,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k1_msaterm(A,B))
        & m1_subset_1(D,k1_relat_1(C)) )
     => k8_msaterm(A,B,C,D) = k5_trees_2(C,D) ) )).

fof(dt_k9_msaterm,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m4_msaterm(C,A,B)
        & m1_subset_1(D,k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
        & m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B)) )
     => m1_subset_1(k9_msaterm(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D))) ) )).
%------------------------------------------------------------------------------