SET007 Axioms: SET007+400.ax


%------------------------------------------------------------------------------
% File     : SET007+400 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Many Sorted Quotient 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    : msualg_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (   1 unit)
%            Number of atoms       :  594 (  36 equality)
%            Maximal formula depth :   19 (  12 average)
%            Number of connectives :  634 (  99 ~  ;   0  |; 339  &)
%                                         (  20 <=>; 176 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-4 arity)
%            Number of functors    :   49 (   2 constant; 0-6 arity)
%            Number of variables   :  257 (   0 singleton; 253 !;   4 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_msualg_4,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_msualg_4(B) ) )).

fof(cc1_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m1_msualg_4(D,A,B,C)
         => v1_msualg_4(D) ) ) )).

fof(rc2_msualg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B) ) ) )).

fof(rc3_msualg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B)
          & v4_msualg_4(C,A,B) ) ) )).

fof(fc1_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v4_msualg_1(k14_msualg_4(A,B,C),A)
        & v5_msualg_1(k14_msualg_4(A,B,C),A) ) ) )).

fof(d1_msualg_4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_msualg_4(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => v1_relat_1(k1_funct_1(A,B)) ) ) ) )).

fof(d2_msualg_4,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m1_pboole(D,A)
             => ( m1_msualg_4(D,A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).

fof(d3_msualg_4,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_msualg_4(C,A,B,B)
         => ( v2_msualg_4(C,A,B)
          <=> ! [D,E] :
                ( m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D))
               => ( ( r2_hidden(D,A)
                    & k1_funct_1(C,D) = E )
                 => ( v3_relat_2(E)
                    & v8_relat_2(E)
                    & v1_partfun1(E,k1_funct_1(B,D),k1_funct_1(B,D))
                    & m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(d4_msualg_4,axiom,(
    $true )).

fof(d5_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( v3_msualg_4(C,A,B)
              <=> v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ) )).

fof(t1_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v3_msualg_4(D,A,B)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                 => ( v3_relat_2(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C))
                    & v8_relat_2(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C))
                    & v1_partfun1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),C))
                    & m2_relset_1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),C)) ) ) ) ) ) )).

fof(d6_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ( v4_msualg_4(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,k3_msualg_1(A,D,B))
                       => ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,D,B))
                           => ( ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( r2_hidden(G,k1_relat_1(E))
                                   => r2_hidden(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),G))) ) )
                             => r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),E),k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),F)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) ) ) ) ) ) ) ) ) )).

fof(d7_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => k3_msualg_4(A,B,C,D,E) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),D),k2_msualg_4(A,B,C,D),E) ) ) ) ) ) )).

fof(d8_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( ( v2_relat_1(D)
                    & m1_pboole(D,u1_struct_0(A)) )
                 => ( D = k4_msualg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k8_eqrel_1(k1_funct_1(u4_msualg_1(A,B),E),k2_msualg_4(A,B,C,E)) ) ) ) ) ) ) )).

fof(d9_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
                 => ! [E] :
                      ( m1_subset_1(E,k3_msualg_1(A,B,C))
                     => ! [F] :
                          ( m1_subset_1(F,k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k4_msualg_4(A,C,D))))
                         => ( F = k7_msualg_4(A,B,C,D,E)
                          <=> ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B)))
                                 => k1_funct_1(F,G) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)),k2_msualg_4(A,C,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)),k1_funct_1(E,G)) ) ) ) ) ) ) ) ) ) )).

fof(d10_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
                        & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) )
                     => ( E = k8_msualg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k2_msualg_1(A,B)))
                           => k1_funct_1(E,F) = k3_msualg_4(A,C,D,k2_msualg_1(A,B),F) ) ) ) ) ) ) ) )).

fof(d11_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
                        & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B)) )
                     => ( E = k9_msualg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => k1_funct_1(E,F) = k7_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(d12_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)))
                 => ( D = k10_msualg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)),D,E) = k8_msualg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(d13_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))))
                 => ( D = k11_msualg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),D,E) = k9_msualg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(t2_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
                 => ! [E] :
                      ~ ( r2_hidden(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
                        & ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => E != k7_msualg_4(A,B,C,D,F) ) ) ) ) ) ) )).

fof(d14_msualg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
                        & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) )
                     => ( E = k12_msualg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => ( r2_hidden(k7_msualg_4(A,B,C,D,F),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
                             => k1_funct_1(E,k7_msualg_4(A,B,C,D,F)) = k1_funct_1(k1_partfun1(k3_msualg_1(A,B,C),k4_msualg_1(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B),k5_msualg_1(A,B,C),k8_msualg_4(A,B,C,D)),F) ) ) ) ) ) ) ) ) )).

fof(d15_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)))
                 => ( D = k13_msualg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)),D,E) = k12_msualg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(d16_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => k14_msualg_4(A,B,C) = g3_msualg_1(A,k4_msualg_4(A,B,C),k13_msualg_4(A,B,C)) ) ) ) )).

fof(d17_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D))
                        & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D)) )
                     => ( E = k15_msualg_4(A,B,C,D)
                      <=> ! [F] :
                            ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,B),D))
                           => k1_funct_1(E,F) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),D),k2_msualg_4(A,B,C,D),F) ) ) ) ) ) ) ) )).

fof(d18_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)))
                 => ( D = k16_msualg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),D,E) = k15_msualg_4(A,B,C,E) ) ) ) ) ) ) )).

fof(t3_msualg_4,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] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
             => r2_msualg_3(A,B,k14_msualg_4(A,B,C),k16_msualg_4(A,B,C)) ) ) ) )).

fof(d19_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( v3_relat_2(F)
                            & v8_relat_2(F)
                            & v1_partfun1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E))
                            & m2_relset_1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) )
                         => ( F = k17_msualg_4(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
                               => ! [H] :
                                    ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),E))
                                   => ( r2_hidden(k4_tarski(G,H),F)
                                    <=> k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) ) ) ) ) ) ) ) ) ) ) )).

fof(d20_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => ! [E] :
                        ( ( v3_msualg_4(E,A,B)
                          & v4_msualg_4(E,A,B)
                          & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                       => ( E = k18_msualg_4(A,B,C,D)
                        <=> ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => k2_msualg_4(A,B,E,F) = k17_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) ) )).

fof(d21_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_msualg_3(A,B,C,D)
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
                              & m2_relset_1(F,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) )
                           => ( F = k19_msualg_4(A,B,C,D,E)
                            <=> ! [G] :
                                  ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
                                 => k1_funct_1(F,k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),E),k17_msualg_4(A,B,C,D,E),G)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) ) ) ) ) ) ) ) ) ) )).

fof(d22_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C))
                     => ( E = k20_msualg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C),E,F) = k19_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t4_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => r3_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C,k20_msualg_4(A,B,C,D)) ) ) ) ) ) )).

fof(t5_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r2_msualg_3(A,B,C,D)
                   => r4_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C,k20_msualg_4(A,B,C,D)) ) ) ) ) ) )).

fof(t6_msualg_4,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] :
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r2_msualg_3(A,B,C,D)
                   => r6_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C) ) ) ) ) ) )).

fof(dt_m1_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m1_msualg_4(D,A,B,C)
         => m1_pboole(D,A) ) ) )).

fof(existence_m1_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m1_msualg_4(D,A,B,C) ) )).

fof(dt_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) )).

fof(redefinition_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k2_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ( v3_relat_2(k2_msualg_4(A,B,C,D))
        & v8_relat_2(k2_msualg_4(A,B,C,D))
        & v1_partfun1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D))
        & m2_relset_1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) ) ) )).

fof(redefinition_k2_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => k2_msualg_4(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k3_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) )
     => m1_subset_1(k3_msualg_4(A,B,C,D,E),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),D))) ) )).

fof(dt_k4_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => ( v2_relat_1(k4_msualg_4(A,B,C))
        & m1_pboole(k4_msualg_4(A,B,C),u1_struct_0(A)) ) ) )).

fof(dt_k5_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_msualg_1(A))
        & m1_pboole(C,u1_msualg_1(A))
        & m3_pboole(D,u1_msualg_1(A),B,C)
        & m1_subset_1(E,u1_msualg_1(A)) )
     => ( v1_funct_1(k5_msualg_4(A,B,C,D,E))
        & v1_funct_2(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
        & m2_relset_1(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) )).

fof(redefinition_k5_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_msualg_1(A))
        & m1_pboole(C,u1_msualg_1(A))
        & m3_pboole(D,u1_msualg_1(A),B,C)
        & m1_subset_1(E,u1_msualg_1(A)) )
     => k5_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k6_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ( v2_relat_1(k6_msualg_4(A,B,C))
        & m1_pboole(k6_msualg_4(A,B,C),k4_finseq_1(B)) ) ) )).

fof(redefinition_k6_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => k6_msualg_4(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k7_msualg_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C))
        & m1_subset_1(E,k3_msualg_1(A,B,C)) )
     => m1_subset_1(k7_msualg_4(A,B,C,D,E),k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k4_msualg_4(A,C,D)))) ) )).

fof(dt_k8_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
     => ( v1_funct_1(k8_msualg_4(A,B,C,D))
        & v1_funct_2(k8_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
        & m2_relset_1(k8_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) ) ) )).

fof(dt_k9_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
     => ( v1_funct_1(k9_msualg_4(A,B,C,D))
        & v1_funct_2(k9_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
        & m2_relset_1(k9_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B)) ) ) )).

fof(dt_k10_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => m3_pboole(k10_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C))) ) )).

fof(dt_k11_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => m3_pboole(k11_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C)))) ) )).

fof(dt_k12_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
     => ( v1_funct_1(k12_msualg_4(A,B,C,D))
        & v1_funct_2(k12_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
        & m2_relset_1(k12_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) ) ) )).

fof(dt_k13_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => m3_pboole(k13_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C))) ) )).

fof(dt_k14_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => l3_msualg_1(k14_msualg_4(A,B,C),A) ) )).

fof(dt_k15_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ( v1_funct_1(k15_msualg_4(A,B,C,D))
        & v1_funct_2(k15_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D))
        & m2_relset_1(k15_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D)) ) ) )).

fof(dt_k16_msualg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
     => m3_pboole(k16_msualg_4(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C))) ) )).

fof(dt_k17_msualg_4,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)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( v3_relat_2(k17_msualg_4(A,B,C,D,E))
        & v8_relat_2(k17_msualg_4(A,B,C,D,E))
        & v1_partfun1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E))
        & m2_relset_1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) ) ) )).

fof(dt_k18_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
     => ( v3_msualg_4(k18_msualg_4(A,B,C,D),A,B)
        & v4_msualg_4(k18_msualg_4(A,B,C,D),A,B)
        & m1_msualg_4(k18_msualg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k19_msualg_4,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)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( v1_funct_1(k19_msualg_4(A,B,C,D,E))
        & v1_funct_2(k19_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
        & m2_relset_1(k19_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) ) )).

fof(dt_k20_msualg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
     => m3_pboole(k20_msualg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C)) ) )).
%------------------------------------------------------------------------------